Abstract

By exchange of virtual microwave photon induced by a transmission line resonator, the nonlinear interaction between a nitrogen-vacancy-center ensemble (NVE) and a superconducting charge qubit is achieved in circuit quantum electrodynamics, where the nonlinear coupling results from the second order of the coupling between the magnetic field of the transmission line resonator and the charge qubit. In our case, the nonlinear coupling can be much enhanced by a factor of the total spin number in the NVE. As an application, we present a potentially practical scheme to realize the squeezing of the NVE using the nonlinear coupling, which is within reach of the currently available technology.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Witnessing quantum entanglement in ensembles of nitrogen–vacancy centers coupled to a superconducting resonator

Yusef Maleki and Aleksei M. Zheltikov
Opt. Express 26(14) 17849-17858 (2018)

Macroscopically distinct superposition in a spin ensemble coupled to superconducting flux-qubits

Leilei Yan, Shilei Su, Qizhe Hou, Wanli Yang, and Mang Feng
Opt. Express 27(2) 377-390 (2019)

Quantum memory and non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble

Rui-Xia Wang, Kang Cai, Zhang-Qi Yin, and Gui-Lu Long
Opt. Express 25(24) 30149-30161 (2017)

References

  • View by:
  • |
  • |
  • |

  1. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University).
  2. B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13 (1986).
    [Crossref] [PubMed]
  3. F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
    [Crossref] [PubMed]
  4. K. Moon and S. M. Girvin, “Theory of microwave parametric down-conversion and squeezing using circuit QED,” Phys. Rev. Lett. 95, 140504 (2005).
    [Crossref] [PubMed]
  5. X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
    [Crossref]
  6. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
    [Crossref]
  7. A. Imamöglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467 (1997).
    [Crossref]
  8. K. Jacobs, “Engineering quantum states of a nanoresonator via a simple auxiliary system,” Phys. Rev. Lett. 99, 117203 (2007).
    [Crossref] [PubMed]
  9. K. Jacobs and A. J. Landahl, “Engineering giant nonlinearities in quantum nanosystems,” Phys. Rev. Lett. 103, 067201 (2009).
    [Crossref] [PubMed]
  10. G. Chen, Y. P. Zhang, L. T. Xiao, J. Q. Liang, and S. T. Jia, “Strong nonlinear coupling between an ultracold atomic ensemble and a nanomechanical oscillator,” Opt. Express 18, 23016–23023 (2010).
    [Crossref] [PubMed]
  11. G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
    [Crossref]
  12. S. Rebić, J. Twamley, and G. J. Milburn, “Giant Kerr nonlinearities in circuit quantum electrodynamics,” Phys. Rev. Lett. 103, 150503 (2009).
    [Crossref]
  13. C. P. Sun, L. F. Wei, Y. X. Liu, and F. Nori, “Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits,” Phys. Rev. A 73, 022318 (2006).
    [Crossref]
  14. M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78, 062303 (2008).
    [Crossref]
  15. S. Kumar and D. P. DiVincenzo, “Exploiting Kerr cross nonlinearity in circuit quantum electrodynamics for nondemolition measurements,” Phys. Rev. B 82, 014512 (2010).
    [Crossref]
  16. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
    [Crossref] [PubMed]
  17. I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
    [Crossref] [PubMed]
  18. A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
    [Crossref] [PubMed]
  19. A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
    [Crossref]
  20. Mika A. Sillanpää, J. I. Park, and R. W. Simmonds, “Coherent quantum state storage and transfer between two phase qubits via a resonant cavity,” Nature 449, 438–442 (2007).
    [Crossref] [PubMed]
  21. W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
    [Crossref]
  22. Y. Cao, W. Y. Huo, Q. Ai, and G. L. Long, “Theory of degenerate three-wave mixing using circuit QED in solid-state circuits,” Phys. Rev. A 84, 053846 (2011).
    [Crossref]
  23. N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
    [Crossref]
  24. A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
    [Crossref] [PubMed]
  25. T. Ojanen and J. Salo, “Possible scheme for on-chip element for squeezed microwave generation,” Phys. Rev. B 75, 184508 (2007).
    [Crossref]
  26. Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
    [Crossref]
  27. Y. M. Liu, “Virtual-photon-induced entanglement with two nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” SCIENCE CHINA Physics, Mechanics Astronomy 56(11), 2138 (2013)
    [Crossref]
  28. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
    [Crossref] [PubMed]
  29. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
    [Crossref] [PubMed]
  30. F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
    [Crossref] [PubMed]
  31. Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
    [Crossref]
  32. D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
    [Crossref]
  33. X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
    [Crossref] [PubMed]
  34. W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
    [Crossref]
  35. W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
    [Crossref]
  36. Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
    [Crossref]
  37. Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
    [Crossref]
  38. Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
    [Crossref] [PubMed]
  39. N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
    [Crossref]
  40. Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-state engineering with Josephson-junction devices,” Rev. Mod. Phys. 73, 357 (2001).
    [Crossref]
  41. H Fröhlich, “Theory of the superconducting state. I. The ground state at the absolute zero of temperature,” Phys. Rev. 79, 845 (1950)
    [Crossref]
  42. K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: Prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A 82, 033810 (2010)
    [Crossref]
  43. T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098 (1940)
    [Crossref]
  44. K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 272003 (1983)
    [Crossref]
  45. P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
    [Crossref]
  46. T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
    [Crossref]
  47. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
    [Crossref] [PubMed]

2013 (4)

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

Y. M. Liu, “Virtual-photon-induced entanglement with two nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” SCIENCE CHINA Physics, Mechanics Astronomy 56(11), 2138 (2013)
[Crossref]

Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
[Crossref]

2012 (1)

W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
[Crossref]

2011 (5)

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
[Crossref]

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Cao, W. Y. Huo, Q. Ai, and G. L. Long, “Theory of degenerate three-wave mixing using circuit QED in solid-state circuits,” Phys. Rev. A 84, 053846 (2011).
[Crossref]

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

2010 (8)

G. Chen, Y. P. Zhang, L. T. Xiao, J. Q. Liang, and S. T. Jia, “Strong nonlinear coupling between an ultracold atomic ensemble and a nanomechanical oscillator,” Opt. Express 18, 23016–23023 (2010).
[Crossref] [PubMed]

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

S. Kumar and D. P. DiVincenzo, “Exploiting Kerr cross nonlinearity in circuit quantum electrodynamics for nondemolition measurements,” Phys. Rev. B 82, 014512 (2010).
[Crossref]

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: Prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A 82, 033810 (2010)
[Crossref]

2009 (3)

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

K. Jacobs and A. J. Landahl, “Engineering giant nonlinearities in quantum nanosystems,” Phys. Rev. Lett. 103, 067201 (2009).
[Crossref] [PubMed]

S. Rebić, J. Twamley, and G. J. Milburn, “Giant Kerr nonlinearities in circuit quantum electrodynamics,” Phys. Rev. Lett. 103, 150503 (2009).
[Crossref]

2008 (4)

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78, 062303 (2008).
[Crossref]

W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
[Crossref]

A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
[Crossref] [PubMed]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

2007 (4)

T. Ojanen and J. Salo, “Possible scheme for on-chip element for squeezed microwave generation,” Phys. Rev. B 75, 184508 (2007).
[Crossref]

Mika A. Sillanpää, J. I. Park, and R. W. Simmonds, “Coherent quantum state storage and transfer between two phase qubits via a resonant cavity,” Nature 449, 438–442 (2007).
[Crossref] [PubMed]

K. Jacobs, “Engineering quantum states of a nanoresonator via a simple auxiliary system,” Phys. Rev. Lett. 99, 117203 (2007).
[Crossref] [PubMed]

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

2006 (4)

C. P. Sun, L. F. Wei, Y. X. Liu, and F. Nori, “Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits,” Phys. Rev. A 73, 022318 (2006).
[Crossref]

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[Crossref]

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
[Crossref]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

2005 (2)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

K. Moon and S. M. Girvin, “Theory of microwave parametric down-conversion and squeezing using circuit QED,” Phys. Rev. Lett. 95, 140504 (2005).
[Crossref] [PubMed]

2004 (5)

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

2001 (1)

Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-state engineering with Josephson-junction devices,” Rev. Mod. Phys. 73, 357 (2001).
[Crossref]

1997 (1)

A. Imamöglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467 (1997).
[Crossref]

1986 (1)

B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13 (1986).
[Crossref] [PubMed]

1983 (1)

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 272003 (1983)
[Crossref]

1950 (1)

H Fröhlich, “Theory of the superconducting state. I. The ground state at the absolute zero of temperature,” Phys. Rev. 79, 845 (1950)
[Crossref]

1940 (1)

T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098 (1940)
[Crossref]

Abe, H.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Achard, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Aguado, R.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

Ai, Q.

Y. Cao, W. Y. Huo, Q. Ai, and G. L. Long, “Theory of degenerate three-wave mixing using circuit QED in solid-state circuits,” Phys. Rev. A 84, 053846 (2011).
[Crossref]

Ashhab, S.

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

Auffeves, A.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Balasubramanian, G.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Barthe, M. F.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Beck, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Bergeal, N.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

Bergonzo, P.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Bertet, P.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

Blais, A.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

Cao, Y.

Y. Cao, W. Y. Huo, Q. Ai, and G. L. Long, “Theory of degenerate three-wave mixing using circuit QED in solid-state circuits,” Phys. Rev. A 84, 053846 (2011).
[Crossref]

Chen, C. Y.

W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
[Crossref]

Chen, G.

G. Chen, Y. P. Zhang, L. T. Xiao, J. Q. Liang, and S. T. Jia, “Strong nonlinear coupling between an ultracold atomic ensemble and a nanomechanical oscillator,” Opt. Express 18, 23016–23023 (2010).
[Crossref] [PubMed]

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

Chen, Q.

W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
[Crossref]

Chiorescu, I.

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

Cho, S. U.

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

Chong, B.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Chow, J. M.

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

Cui, W.

Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
[Crossref]

Deutsch, M.

A. Imamöglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467 (1997).
[Crossref]

Devoret, M. H.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

Dewes, A.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Diniz, I.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

DiVincenzo, D. P.

S. Kumar and D. P. DiVincenzo, “Exploiting Kerr cross nonlinearity in circuit quantum electrodynamics for nondemolition measurements,” Phys. Rev. B 82, 014512 (2010).
[Crossref]

Doherty, A. C.

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78, 062303 (2008).
[Crossref]

Domhan, M.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

Dréau, A.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Du, J.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Du, J. F.

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
[Crossref]

Esteve, D.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Everitt, M. S.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Feng, M.

W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
[Crossref]

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
[Crossref]

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Fröhlich, H

H Fröhlich, “Theory of the superconducting state. I. The ground state at the absolute zero of temperature,” Phys. Rev. 79, 845 (1950)
[Crossref]

Frunzio, L.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Gaebel, T.

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

Gambetta, J. M.

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

Girvin, S. M.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

K. Moon and S. M. Girvin, “Theory of microwave parametric down-conversion and squeezing using circuit QED,” Phys. Rev. Lett. 95, 140504 (2005).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Greentree, A. D.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Grezes, C.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Gruber, A.

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

Hakonen, P. J.

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

Harmans, C. J. P. M.

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

Harneit, W.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Harrison, J. P.

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
[Crossref]

Heikkilä, T. T.

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

Hemmer, P.

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

Hemmer, P. R.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Henschel, K.

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: Prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A 82, 033810 (2010)
[Crossref]

Holstein, T.

T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098 (1940)
[Crossref]

Houck, A. A.

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

Hu, Y.

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
[Crossref]

Huang, R. S.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

Huo, W. Y.

Y. Cao, W. Y. Huo, Q. Ai, and G. L. Long, “Theory of degenerate three-wave mixing using circuit QED in solid-state circuits,” Phys. Rev. A 84, 053846 (2011).
[Crossref]

W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
[Crossref]

Il’ichev, E.

A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
[Crossref] [PubMed]

Imamöglu, A.

A. Imamöglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467 (1997).
[Crossref]

Isoya, J.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Jacobs, K.

K. Jacobs and A. J. Landahl, “Engineering giant nonlinearities in quantum nanosystems,” Phys. Rev. Lett. 103, 067201 (2009).
[Crossref] [PubMed]

K. Jacobs, “Engineering quantum states of a nanoresonator via a simple auxiliary system,” Phys. Rev. Lett. 99, 117203 (2007).
[Crossref] [PubMed]

Jacques, V.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

Jelezko, F.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

Jia, S. T.

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

G. Chen, Y. P. Zhang, L. T. Xiao, J. Q. Liang, and S. T. Jia, “Strong nonlinear coupling between an ultracold atomic ensemble and a nanomechanical oscillator,” Opt. Express 18, 23016–23023 (2010).
[Crossref] [PubMed]

Johnson, B. R.

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

Kakuyanagi, K.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Karimoto, S.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Kasu, M.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Kemp, A.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Kniepert, J.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Kolesov, R.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Kubo, Y.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Kumar, S.

S. Kumar and D. P. DiVincenzo, “Exploiting Kerr cross nonlinearity in circuit quantum electrodynamics for nondemolition measurements,” Phys. Rev. B 82, 014512 (2010).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Landahl, A. J.

K. Jacobs and A. J. Landahl, “Engineering giant nonlinearities in quantum nanosystems,” Phys. Rev. Lett. 103, 067201 (2009).
[Crossref] [PubMed]

Li, T. F.

Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

Liang, J. Q.

Liu, Y. M.

Y. M. Liu, “Virtual-photon-induced entanglement with two nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” SCIENCE CHINA Physics, Mechanics Astronomy 56(11), 2138 (2013)
[Crossref]

Liu, Y. X.

C. P. Sun, L. F. Wei, Y. X. Liu, and F. Nori, “Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits,” Phys. Rev. A 73, 022318 (2006).
[Crossref]

Long, G. L.

Y. Cao, W. Y. Huo, Q. Ai, and G. L. Long, “Theory of degenerate three-wave mixing using circuit QED in solid-state circuits,” Phys. Rev. A 84, 053846 (2011).
[Crossref]

W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
[Crossref]

Lü, X. Y.

Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

Lü, Xin-You

Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
[Crossref]

Lukin, M. D.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

Majer, J.

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: Prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A 82, 033810 (2010)
[Crossref]

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Makhlin, Y.

Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-state engineering with Josephson-junction devices,” Rev. Mod. Phys. 73, 357 (2001).
[Crossref]

Manson, N. B.

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
[Crossref]

Manucharyan, V. E.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

Marcos, D.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

Markham, M.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Massel, F.

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

McCutcheon, M. W.

A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
[Crossref] [PubMed]

Meijer, J.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Metcalfe, M.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

Milburn, G. J.

S. Rebić, J. Twamley, and G. J. Milburn, “Giant Kerr nonlinearities in circuit quantum electrodynamics,” Phys. Rev. Lett. 103, 150503 (2009).
[Crossref]

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78, 062303 (2008).
[Crossref]

Mizel, A.

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[Crossref]

Mizuochi, N.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

Mooij, J. E.

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

Moon, K.

K. Moon and S. M. Girvin, “Theory of microwave parametric down-conversion and squeezing using circuit QED,” Phys. Rev. Lett. 95, 140504 (2005).
[Crossref] [PubMed]

Morishita, N.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Munro, W. J.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Nakamura, Y.

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

Nakano, H.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Nemoto, K.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Neumann, P.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Neumman, P.

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

Nori, F.

Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
[Crossref]

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
[Crossref] [PubMed]

C. P. Sun, L. F. Wei, Y. X. Liu, and F. Nori, “Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits,” Phys. Rev. A 73, 022318 (2006).
[Crossref]

Ohshima, T.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Ojanen, T.

T. Ojanen and J. Salo, “Possible scheme for on-chip element for squeezed microwave generation,” Phys. Rev. B 75, 184508 (2007).
[Crossref]

Ong, F. R.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Onoda, S.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Park, J. I.

Mika A. Sillanpää, J. I. Park, and R. W. Simmonds, “Coherent quantum state storage and transfer between two phase qubits via a resonant cavity,” Nature 449, 438–442 (2007).
[Crossref] [PubMed]

Peng, X.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Pirkkalainen, J. M.

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

Popa, I.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

Prawer, S.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Primakoff, H.

T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098 (1940)
[Crossref]

Prober, D. E.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

Rabeau, J. R.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Rebic, S.

S. Rebić, J. Twamley, and G. J. Milburn, “Giant Kerr nonlinearities in circuit quantum electrodynamics,” Phys. Rev. Lett. 103, 150503 (2009).
[Crossref]

Rempp, F.

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

Ritsch, H.

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: Prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A 82, 033810 (2010)
[Crossref]

Roch, J. F.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Roch, J.-F.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Rong, X.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Saito, S.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Salo, J.

T. Ojanen and J. Salo, “Possible scheme for on-chip element for squeezed microwave generation,” Phys. Rev. B 75, 184508 (2007).
[Crossref]

Saloniemi, H.

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

Schackert, F.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

Schmidt, H.

A. Imamöglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467 (1997).
[Crossref]

Schmiedmayer, J.

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: Prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A 82, 033810 (2010)
[Crossref]

Schoelkopf, R. J.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Schoenfeld, R. S.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Schön, G.

Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-state engineering with Josephson-junction devices,” Rev. Mod. Phys. 73, 357 (2001).
[Crossref]

Schreier, J. A.

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

Schuster, D. I.

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Schwab, K. C.

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78, 062303 (2008).
[Crossref]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University).

Sellars, M. J.

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
[Crossref]

Semba, K.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

Shi, F.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Shnirman, A.

Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-state engineering with Josephson-junction devices,” Rev. Mod. Phys. 73, 357 (2001).
[Crossref]

Sillanpää, M. A.

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

Sillanpää, Mika A.

Mika A. Sillanpää, J. I. Park, and R. W. Simmonds, “Coherent quantum state storage and transfer between two phase qubits via a resonant cavity,” Nature 449, 438–442 (2007).
[Crossref] [PubMed]

Simmonds, R. W.

Mika A. Sillanpää, J. I. Park, and R. W. Simmonds, “Coherent quantum state storage and transfer between two phase qubits via a resonant cavity,” Nature 449, 438–442 (2007).
[Crossref] [PubMed]

Sørensen, A. S.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

Stavrias, N.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Stoler, D.

B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13 (1986).
[Crossref] [PubMed]

Sumiya, H.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Sun, C. P.

C. P. Sun, L. F. Wei, Y. X. Liu, and F. Nori, “Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits,” Phys. Rev. A 73, 022318 (2006).
[Crossref]

Taylor, J. M.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

Tissler, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Tokura, Y.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Twamley, J.

S. Rebić, J. Twamley, and G. J. Milburn, “Giant Kerr nonlinearities in circuit quantum electrodynamics,” Phys. Rev. Lett. 103, 150503 (2009).
[Crossref]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Twitchen, D.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Umeda, T.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

van Loock, P.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

Vijay, R.

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

Vion, D.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Wallraff, A.

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

Wang, R.

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

Wang, Y.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Watanabe, H.

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

Wei, L. F.

C. P. Sun, L. F. Wei, Y. X. Liu, and F. Nori, “Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits,” Phys. Rev. A 73, 022318 (2006).
[Crossref]

Wittmann, C.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Wódkiewicz, K.

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 272003 (1983)
[Crossref]

Woods, G.

A. Imamöglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467 (1997).
[Crossref]

Woolley, M. J.

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78, 062303 (2008).
[Crossref]

Wrachtrup, J.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

Wu, J.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Wubs, M.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

Xiang, Z. L.

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
[Crossref]

Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

Xiao, L. T.

G. Chen, Y. P. Zhang, L. T. Xiao, J. Q. Liang, and S. T. Jia, “Strong nonlinear coupling between an ultracold atomic ensemble and a nanomechanical oscillator,” Opt. Express 18, 23016–23023 (2010).
[Crossref] [PubMed]

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

Xu, N.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Yamasaki, S.

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

Yang, W. L.

W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
[Crossref]

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
[Crossref]

Yang, Y. G.

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

Yin, Z. Q.

W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
[Crossref]

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
[Crossref]

You, J. Q.

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
[Crossref]

Young, J. F.

A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
[Crossref] [PubMed]

Yurke, B.

B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13 (1986).
[Crossref] [PubMed]

Zagoskin, A. M.

A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
[Crossref] [PubMed]

Zhang, H.

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

Zhang, Y. P.

Zheng, D.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Zhou, X.

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[Crossref]

Zhu, X.

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

Zubairy, M. S.

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 272003 (1983)
[Crossref]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University).

Nat. Mater. (1)

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009)
[Crossref] [PubMed]

Nat. Phys. (1)

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006)
[Crossref]

Nature (7)

F. Massel, T. T. Heikkilä, J. M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonator,” Nature 480, 351–354 (2011).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref] [PubMed]

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162 (2004).
[Crossref] [PubMed]

A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating single microwave photons in a circuit,” Nature 449, 328–331 (2007).
[Crossref] [PubMed]

Mika A. Sillanpää, J. I. Park, and R. W. Simmonds, “Coherent quantum state storage and transfer between two phase qubits via a resonant cavity,” Nature 449, 438–442 (2007).
[Crossref] [PubMed]

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[Crossref]

X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
[Crossref] [PubMed]

New J. Phys. (1)

W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
[Crossref]

Opt. Express (1)

Phys. Rev. (2)

T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098 (1940)
[Crossref]

H Fröhlich, “Theory of the superconducting state. I. The ground state at the absolute zero of temperature,” Phys. Rev. 79, 845 (1950)
[Crossref]

Phys. Rev. A (10)

K. Henschel, J. Majer, J. Schmiedmayer, and H. Ritsch, “Cavity QED with an ultracold ensemble on a chip: Prospects for strong magnetic coupling at finite temperatures,” Phys. Rev. A 82, 033810 (2010)
[Crossref]

K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A 272003 (1983)
[Crossref]

G. Chen, H. Zhang, Y. G. Yang, R. Wang, L. T. Xiao, and S. T. Jia, “Qubit-induced high-order nonlinear interaction of the polar molecules in a stripline cavity,” Phys. Rev. A 82, 013601 (2010).
[Crossref]

C. P. Sun, L. F. Wei, Y. X. Liu, and F. Nori, “Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits,” Phys. Rev. A 73, 022318 (2006).
[Crossref]

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78, 062303 (2008).
[Crossref]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

Y. Cao, W. Y. Huo, Q. Ai, and G. L. Long, “Theory of degenerate three-wave mixing using circuit QED in solid-state circuits,” Phys. Rev. A 84, 053846 (2011).
[Crossref]

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A 84, 010301 (2011).
[Crossref]

W. L. Yang, Z. Q. Yin, Q. Chen, C. Y. Chen, and M. Feng, “Two-mode squeezing of distant nitrogen-vacancy-center ensembles by manipulating the reservoir,” Phys. Rev. A 85, 022324 (2012).
[Crossref]

Xin-You Lü, Z. L. Xiang, W. Cui, J. Q. You, and F. Nori, “Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers,” Phys. Rev. A 88, 012329 (2013).
[Crossref]

Phys. Rev. B (4)

T. Ojanen and J. Salo, “Possible scheme for on-chip element for squeezed microwave generation,” Phys. Rev. B 75, 184508 (2007).
[Crossref]

Z. L. Xiang, X. Y. Lü, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

S. Kumar and D. P. DiVincenzo, “Exploiting Kerr cross nonlinearity in circuit quantum electrodynamics for nondemolition measurements,” Phys. Rev. B 82, 014512 (2010).
[Crossref]

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
[Crossref]

Phys. Rev. Lett. (14)

S. Rebić, J. Twamley, and G. J. Milburn, “Giant Kerr nonlinearities in circuit quantum electrodynamics,” Phys. Rev. Lett. 103, 150503 (2009).
[Crossref]

K. Moon and S. M. Girvin, “Theory of microwave parametric down-conversion and squeezing using circuit QED,” Phys. Rev. Lett. 95, 140504 (2005).
[Crossref] [PubMed]

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[Crossref]

B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13 (1986).
[Crossref] [PubMed]

A. Imamöglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467 (1997).
[Crossref]

K. Jacobs, “Engineering quantum states of a nanoresonator via a simple auxiliary system,” Phys. Rev. Lett. 99, 117203 (2007).
[Crossref] [PubMed]

K. Jacobs and A. J. Landahl, “Engineering giant nonlinearities in quantum nanosystems,” Phys. Rev. Lett. 103, 067201 (2009).
[Crossref] [PubMed]

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[Crossref] [PubMed]

A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, “Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit,” Phys. Rev. Lett. 101, 253602 (2008).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[Crossref] [PubMed]

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105210501 (2010).
[Crossref]

Rev. Mod. Phys. (3)

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-state engineering with Josephson-junction devices,” Rev. Mod. Phys. 73, 357 (2001).
[Crossref]

Science (1)

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008)
[Crossref]

SCIENCE CHINA Physics, Mechanics Astronomy (1)

Y. M. Liu, “Virtual-photon-induced entanglement with two nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” SCIENCE CHINA Physics, Mechanics Astronomy 56(11), 2138 (2013)
[Crossref]

Other (1)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1 (a) Schematic of the hybrid system, where the NVE is placed in the antinode of the TLR coupled to the SQ through magnetic field induced by its quantized current. (b) The level structure of the NVE.
Fig. 2
Fig. 2 ((a) ΔX1 versus Ωpt under the different cases, where the soild red, dotted blue, dashed green, and dotdashed pink lines denote Θ/Ωp = 0, Θ/Ωp = 0.001, Θ/Ωp = 0.01, and Θ/Ωp = 0.1, respectively. The inset shows the ΔX2 versus Ωpt. (b) ΔX′1 versus Ωpt under the different cases, where the solid red, dotted blue, dashed green, and dotdashed pink lines denote Θp = 0, Θp = 0.1, Θp = 0.2, and Θp = 0.5, respectively. The inset shows the ΔX′2 versus Ωpt.

Equations (44)

Equations on this page are rendered with MathJax. Learn more.

H tot = H NVE + H FQ + H TLR + H STI + H NTI ,
H NVE = δ S z ,
H SQ = 1 2 E C ( 1 2 n g ) σ z E J cos ( π Φ e Φ 0 ) σ x ,
Φ q = μ 0 S I q 2 π d
Φ q = i k ϕ k ( a k a k ) ,
ϕ k = μ 0 S I 0 ( k ) 2 π d .
Φ q = i ϕ b ( a a ) .
E J ( Φ q ) = E J cos ( π Φ e + Φ q Φ 0 ) .
H 1 = ω a a a 1 2 E C ( 1 2 n g ) σ z E j cos ( π Φ e + Φ q Φ 0 ) σ x .
H 2 = 1 2 Ω σ ˜ z + ω a a a + η ( a 2 σ ˜ + a 2 σ ˜ + ) ,
Ω = E c 2 ( 1 2 n g ) 2 + 4 E J 2 ,
η = ( 1 ) m + 1 E J π 2 ϕ b 2 2 Φ 0 2 cos θ ,
| 0 ˜ = cos ( θ 2 ) | 0 + sin ( θ 2 ) | 1 ,
| 1 ˜ = sin ( θ 2 ) | 0 + cos ( θ 2 ) | 1
H NTI = g ( S + a + S a ) ,
H Tot = 1 2 Ω σ ˜ z + ω a a a + δ S z + η ( a 2 σ ˜ + a 2 σ ˜ + ) + g ( S + a + S a ) .
| 0 P = | g 1 g 2 g N
| 1 P = S ˜ + | g N V = 1 N k = 1 N τ + k | g 1 g 2 g N .
H Tot = 1 2 Ω σ ˜ z + ω a a a + δ S ˜ + S ˜ + η ( a 2 σ ˜ + a 2 σ ˜ + ) + N g ( S ˜ + a + S ˜ a ) .
Δ S = | ω a δ | N g ,
Δ N = | 2 ω a Ω | η ,
F = N g Δ S ( a S ˜ a S ˜ + ) + η Δ N ( a 2 σ ˜ a 2 σ ˜ + ) .
H ˜ Tot 1 2 Ω σ ˜ z + ( ω 0 + χ ) S ˜ + S ˜ + i λ eff ( S ˜ + 2 σ ˜ S ˜ 2 σ ˜ + ) ,
χ = N g 2 Δ S
λ eff = N g 2 η Δ S ( 1 Δ S + 1 Δ N )
S + N c , S N c , S z c c N 2 ,
H ˜ Tot 1 2 Ω σ ˜ z + δ C c c + λ eff ( c 2 σ ˜ + c 2 σ ˜ ) ,
H ˜ R i λ eff ( c 2 σ ˜ + c 2 σ ˜ ) .
S ( κ ) = i κ 2 ( c 2 c 2 ) ,
Δ X 1 = X 1 2 X 1 2 = e κ 2 ,
Δ X 2 = X 2 2 X 2 2 = e κ 2 .
| κ = S ( κ ) | 0 = κ 2 ( c 2 + c 2 ) | 0 .
Ψ ˙ = ( M 0 Θ M 2 ) Ψ ,
Ψ = [ c + c + c c + c 2 ( c + ) 2 ] , M 0 = [ 0 2 κ 2 κ κ 0 0 κ 0 0 ] , M = [ 0 0 0 0 1 0 0 0 1 ] .
c + c + c c + = 2 κ 2 π i d z e z t z ( z + Θ ) 4 κ 2
= e Θ t / 2 ( Θ sinh ( ϰ t / 2 ) ϰ + cosh ( ϰ t / 2 ) )
c 2 = Ω κ e 2 Θ t 2 κ 2 Θ 2 / 8 + ( 4 κ + 5 Θ ) e ( 2 κ 3 2 Θ ) t 16 κ + 4 Θ + ( 4 κ 5 Θ ) e ( 2 κ 3 2 Θ ) t 16 κ 4 Θ ,
Δ X 1 = e Θ t / 2 [ Θ sinh ( ϰ t / 2 ) + 4 ϰ cosh ( ϰ t / 2 ) ] 4 ϰ + ξ
Δ X 2 = e Θ t / 2 [ Θ sinh ( ϰ t / 2 ) + 4 ϰ cosh ( ϰ t / 2 ) ] 4 ϰ ξ ,
ξ = 2 Θ κ e 2 Θ t 8 κ 2 Θ 2 / 2 + ( 4 κ 5 Θ ) e ( 2 κ 3 2 Θ ) t 32 κ 8 Θ ( 4 κ + 5 Θ ) e ( 2 κ 3 2 Θ ) t 32 κ + 8 Θ .
Δ X 1 = ( Θ t 2 ) e 2 Ω p t + e 2 Ω p t 2 ,
Δ X 2 = e Ω p t 1 2 Θ t 2 .
Δ X 1 = exp [ 2 Θ t Ω p t + 2 ( e Θ t 1 ) ] 2 ,
Δ X 2 = exp [ 2 Θ t + Ω p t + 2 ( e Θ t 1 ) ] 2 ,

Metrics