Abstract

Coupling an oscillator to a single two-level system is one of the most fundamental interactions in quantum physics. We report on a dynamical effect during which a thermal state of an oscillator is unconditionally transformed to a highly nonclassical state with negative Wigner function values by mere absorbtion by a single uncontrolled two-level system. This complements the traditional test of Rabi oscillations and it serves as a simply measurable witness that the process in question is highly nonclassical. The process is experimentally feasible with possible experimental implementation in a number of experimental platforms with intrinsic Jaynes-Cummings interaction and it has the potential of enabling deterministic generation of nonclassical quantum states.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  37. C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
    [Crossref] [PubMed]
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    [Crossref]

2015 (1)

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
[Crossref]

2014 (1)

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).
[Crossref]

2013 (6)

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
[Crossref]

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (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, 623–653 (2013).
[Crossref]

R. Kumar, E. Barrios, C. Kupchak, and A. I. Lvovsky, “Experimental characterization of Bosonic creation and annihilation operators,” Phys. Rev. Lett. 110, 130403 (2013)
[Crossref] [PubMed]

2012 (4)

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
[Crossref] [PubMed]

A. Mari and J. Eisert, “Positive Wigner functions render classical simulation of quantum computation efficient,” Phys. Rev. Lett. 109, 230503 (2012).
[Crossref]

C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

2011 (3)

T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011).
[Crossref]

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
[Crossref] [PubMed]

2010 (2)

L. Hu, X. Xu, Z. Wang, and X. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[Crossref]

M. Bellini and A. Zavatta, “Manipulating light states by single-photon addition and subtraction,” Prog. Opt. 55, 41–83 (2010).
[Crossref]

2009 (2)

P. Marek and J. Fiurášek, “Resources for universal quantum-state manipulation and engineering,” Phys. Rev. A 79, 062321 (2009).
[Crossref]

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

2008 (2)

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[Crossref] [PubMed]

S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

2007 (1)

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

2005 (1)

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[Crossref]

2003 (1)

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[Crossref]

2002 (1)

T. Richter and W. Vogel, “Nonclassicality of quantum states: a hierarchy of observable conditions,” Phys. Rev. Lett. 89, 283601 (2002).
[Crossref]

2001 (1)

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[Crossref]

1996 (2)

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[Crossref] [PubMed]

D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
[Crossref] [PubMed]

1995 (1)

C. T. Lee, “Theorem on nonclassical states,” Phys. Rev. A 52, 3374–3376 (1995).
[Crossref] [PubMed]

1993 (2)

B. W. Shore, “Sir Peter Knight and the JaynesCummings model,” J. Mod. Opt. 54, 2009–2016 (1993).
[Crossref]

H. Moya-Cessa, V. Bužek, M. S. Kim, and P. L. Knight, ”Intrinsic decoherence in the atom-field interaction,” Phys. Rev. A 48, 3900–3905 (1993).
[Crossref] [PubMed]

1992 (1)

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[Crossref] [PubMed]

1991 (1)

G. J. Milburn, “Intrinsic decoherence in quantum mechanics,” Phys. Rev. A 44, 5401–5406 (1991).
[Crossref] [PubMed]

1987 (1)

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[Crossref] [PubMed]

1982 (1)

P. L. Knight and P. M. Radmore, “Quantum revivals of a two-level system driven by chaotic radiation,” Phys. Lett. A 90, 342–346 (1982).
[Crossref]

1980 (1)

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[Crossref]

1963 (3)

E.T. Jaynes and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[Crossref]

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[Crossref]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[Crossref]

1932 (1)

E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[Crossref]

Agarwal, G. S.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[Crossref] [PubMed]

Amini, H.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

Ansmann, M.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

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, 623–653 (2013).
[Crossref]

Barreiro, J. T.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Barrios, E.

R. Kumar, E. Barrios, C. Kupchak, and A. I. Lvovsky, “Experimental characterization of Bosonic creation and annihilation operators,” Phys. Rev. Lett. 110, 130403 (2013)
[Crossref] [PubMed]

Baur, M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[Crossref] [PubMed]

Bellini, M.

T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011).
[Crossref]

M. Bellini and A. Zavatta, “Manipulating light states by single-photon addition and subtraction,” Prog. Opt. 55, 41–83 (2010).
[Crossref]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

Bernu, J.

S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Bialczak, R. C.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Bianchetti, R.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[Crossref] [PubMed]

Blais, A.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[Crossref] [PubMed]

Blatt, R.

C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
[Crossref]

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[Crossref]

Bozyigit, D.

C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
[Crossref] [PubMed]

Brandl, M.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Braun, D.

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).
[Crossref]

Brune, M.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[Crossref]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[Crossref] [PubMed]

Bužek, V.

H. Moya-Cessa, V. Bužek, M. S. Kim, and P. L. Knight, ”Intrinsic decoherence in the atom-field interaction,” Phys. Rev. A 48, 3900–3905 (1993).
[Crossref] [PubMed]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

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M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
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E.T. Jaynes and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
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D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
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C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
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M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
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J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
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C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
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A. Mari and J. Eisert, “Positive Wigner functions render classical simulation of quantum computation efficient,” Phys. Rev. Lett. 109, 230503 (2012).
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C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
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J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
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P. Marek and J. Fiurášek, “Resources for universal quantum-state manipulation and engineering,” Phys. Rev. A 79, 062321 (2009).
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B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
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G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
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Garca-Patrn, R.

C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
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C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
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G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
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G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
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B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
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C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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Göppl, M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
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Gronbech-Jensen, N.

E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
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M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
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Haroche, S.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
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J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
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M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
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C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
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P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
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M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Home, J. P.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
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L. Hu, X. Xu, Z. Wang, and X. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
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D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
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E.T. Jaynes and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
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M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
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D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).
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C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
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Keitch, B.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
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Kienzler, D.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
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T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011).
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M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
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H. Moya-Cessa, V. Bužek, M. S. Kim, and P. L. Knight, ”Intrinsic decoherence in the atom-field interaction,” Phys. Rev. A 48, 3900–3905 (1993).
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D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
[Crossref] [PubMed]

Kirchmair, G.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
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M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
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H. Moya-Cessa, V. Bužek, M. S. Kim, and P. L. Knight, ”Intrinsic decoherence in the atom-field interaction,” Phys. Rev. A 48, 3900–3905 (1993).
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P. L. Knight and P. M. Radmore, “Quantum revivals of a two-level system driven by chaotic radiation,” Phys. Lett. A 90, 342–346 (1982).
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E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
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R. Kumar, E. Barrios, C. Kupchak, and A. I. Lvovsky, “Experimental characterization of Bosonic creation and annihilation operators,” Phys. Rev. Lett. 110, 130403 (2013)
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Kupchak, C.

R. Kumar, E. Barrios, C. Kupchak, and A. I. Lvovsky, “Experimental characterization of Bosonic creation and annihilation operators,” Phys. Rev. Lett. 110, 130403 (2013)
[Crossref] [PubMed]

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C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
[Crossref] [PubMed]

Lanyon, B. P.

C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
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C. T. Lee, “Theorem on nonclassical states,” Phys. Rev. A 52, 3374–3376 (1995).
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J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[Crossref] [PubMed]

Leghtas, Z.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Leibfried, D.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[Crossref]

D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
[Crossref] [PubMed]

Leupold, F.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
[Crossref]

Lindenfelser, F.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
[Crossref]

Lloyd, S.

C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Lo, H.-Y.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
[Crossref]

Lu, C.-Y.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Lucero, E.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Lvovsky, A. I.

R. Kumar, E. Barrios, C. Kupchak, and A. I. Lvovsky, “Experimental characterization of Bosonic creation and annihilation operators,” Phys. Rev. Lett. 110, 130403 (2013)
[Crossref] [PubMed]

Maali, A.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[Crossref] [PubMed]

Marek, P.

P. Marek and J. Fiurášek, “Resources for universal quantum-state manipulation and engineering,” Phys. Rev. A 79, 062321 (2009).
[Crossref]

Mari, A.

A. Mari and J. Eisert, “Positive Wigner functions render classical simulation of quantum computation efficient,” Phys. Rev. Lett. 109, 230503 (2012).
[Crossref]

Marinelli, M.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
[Crossref]

Martinez, E.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Martinis, J. M.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Meekhof, D. M.

D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
[Crossref] [PubMed]

Milburn, G. J.

G. J. Milburn, “Intrinsic decoherence in quantum mechanics,” Phys. Rev. A 44, 5401–5406 (1991).
[Crossref] [PubMed]

Mirrahimi, M.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

Monroe, C.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[Crossref]

D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
[Crossref] [PubMed]

Monz, T.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Moya-Cessa, H.

H. Moya-Cessa, V. Bužek, M. S. Kim, and P. L. Knight, ”Intrinsic decoherence in the atom-field interaction,” Phys. Rev. A 48, 3900–3905 (1993).
[Crossref] [PubMed]

Narozhny, N. B.

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[Crossref]

Nebendahl, V.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Neeley, M.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Neergaard-Nielsen, J. S.

E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
[Crossref] [PubMed]

Negnevitsky, V.

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
[Crossref]

Nielsen, B. M.

E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
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Nigg, D.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Nigg, S. E.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
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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, 623–653 (2013).
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M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

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G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Pan, J.-W.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

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A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

Park, E.

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[Crossref]

Peaudecerf, B.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

Pinel, O.

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).
[Crossref]

Pirandola, S.

C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Polzik, E. S.

E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
[Crossref] [PubMed]

Quint, S.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
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P. L. Knight and P. M. Radmore, “Quantum revivals of a two-level system driven by chaotic radiation,” Phys. Lett. A 90, 342–346 (1982).
[Crossref]

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J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
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M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
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C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Ralph, T. C.

C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

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G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[Crossref] [PubMed]

Richter, T.

T. Richter and W. Vogel, “Nonclassicality of quantum states: a hierarchy of observable conditions,” Phys. Rev. Lett. 89, 283601 (2002).
[Crossref]

Roos, C. F.

C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
[Crossref]

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Rouchon, P.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

Rybarczyk, T.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

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J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[Crossref]

Sank, D.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Sayrin, C.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Schindler, P.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Schmidt-Kaler, F.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[Crossref] [PubMed]

Schoelkopf, R. J.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

Shannon,

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

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B. W. Shore, “Sir Peter Knight and the JaynesCummings model,” J. Mod. Opt. 54, 2009–2016 (1993).
[Crossref]

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E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
[Crossref] [PubMed]

Steffen, L.

C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
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E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
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G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
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D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).
[Crossref]

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B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrdinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Vogel, W.

T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011).
[Crossref]

T. Richter and W. Vogel, “Nonclassicality of quantum states: a hierarchy of observable conditions,” Phys. Rev. Lett. 89, 283601 (2002).
[Crossref]

Wallraff, A.

C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
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J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[Crossref] [PubMed]

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G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[Crossref] [PubMed]

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M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Wang, S.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
[Crossref]

Wang, Z.

L. Hu, X. Xu, Z. Wang, and X. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[Crossref]

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C. Weedbrook, S. Pirandola, R. Garca-Patrn, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Weinfurter, H.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Wenner, J.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
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E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
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D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
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Wineland, D. J.

D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
[Crossref] [PubMed]

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, 623–653 (2013).
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Xu, X.

L. Hu, X. Xu, Z. Wang, and X. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[Crossref]

L. Hu, X. Xu, Z. Wang, and X. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[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, 623–653 (2013).
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Zavatta, A.

T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011).
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M. Bellini and A. Zavatta, “Manipulating light states by single-photon addition and subtraction,” Prog. Opt. 55, 41–83 (2010).
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A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

Zeilinger, A.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Zhou, X.

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

Zukowski, M.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
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J. Mod. Opt. (1)

B. W. Shore, “Sir Peter Knight and the JaynesCummings model,” J. Mod. Opt. 54, 2009–2016 (1993).
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Nat. Photonics (1)

C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, “Entanglement-enhanced detection of single-photon scattering events,” Nat. Photonics 7, 630–633 (2013).
[Crossref]

Nature (5)

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[Crossref] [PubMed]

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[Crossref] [PubMed]

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
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New J. Phys. (1)

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. Wang, Shannon, S. Quint, M. Brandl, V. Nebendahl, C. F. Roos, M. M. Chwalla, M. Hennrich, and R. Blatt, “A quantum information processor with trapped ions,” New J. Phys. 15, 123012 (2013).
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P. L. Knight and P. M. Radmore, “Quantum revivals of a two-level system driven by chaotic radiation,” Phys. Lett. A 90, 342–346 (1982).
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Phys. Rev. (2)

E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
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A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
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L. Hu, X. Xu, Z. Wang, and X. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
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Phys. Rev. Lett. (10)

C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Phys. Rev. Lett. 106, 220503 (2011).
[Crossref] [PubMed]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
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[Crossref]

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[Crossref] [PubMed]

D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,” Phys. Rev. Lett. 77, 4281–4285 (1996).
[Crossref] [PubMed]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[Crossref]

T. Richter and W. Vogel, “Nonclassicality of quantum states: a hierarchy of observable conditions,” Phys. Rev. Lett. 89, 283601 (2002).
[Crossref]

E. Kot, N. Gronbech-Jensen, B. M. Nielsen, J. S. Neergaard-Nielsen, E. S. Polzik, and A. S. Sorensen, “Breakdown of the Classical Description of a Local System,” Phys. Rev. Lett. 108, 233601 (2012).
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[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Absorbtion of a quanta from quantum oscillator by a two-level with thermal populations unconditionally generates negative Wigner function from initially thermal state of the oscillator.
Fig. 2
Fig. 2 Negative values of W(0,0) for initial thermal states with mean energy undergoing absorption of a single photon with accumulated parameter gt. (a): ideal single atom absorption with the two level system in a ground state. (b): ideal single atom absorption with the two-level system being in a thermally excited state with Pe = 0.3. (c): single atom absorption in a detuned regime with g = 1, Δ = 5 and the two level system in a ground state. (d): single atom absorption with the two level system initially in a ground state undergoing loss (spontaneous emission into other modes) with g = 1 and γ = 0.015g.
Fig. 3
Fig. 3 Negative values of W(x, 0) undergoing the ideal single photon absorption with accumulated parameter gt. The two level system initially in a ground state. (a): = 2. (b): = 5. (c): = 10. (d): = 20.
Fig. 4
Fig. 4 Thermal states undergoing the ideal single photon absorption with the two-level system being initially in a ground state. (a) W(x, p) for = 10 and gt = 5.5. (b) W(x, p) for = 10 and gt = 2π. (c) P(n) for = 10 and gt = 5.5. (d) P(n) for = 10 and gt = 2π. The line in figures (c) and (d) follows the coefficients of the initial thermal state.
Fig. 5
Fig. 5 The number distribution P(n) of a thermal state with = 5 undergoing M absorption events with coefficient gt = π.
Fig. 6
Fig. 6 Negative values of W(x, 0) for thermal states undergoing the evolution in the blue-detuned sideband regime. (a): = 2. (b): = 5. (c): = 10. (d): = 20.

Equations (13)

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U J C = exp [ h ¯ g t ( σ + a σ a ) ] = n = 0 ( g t ) n ( σ + a σ a ) n .
U = A g g ( t ) | g g | + A e e ( t ) | e e | + A e g ( t ) | e g | + A g e ( t ) | g e | ,
A g g ( t ) = n = 0 ( g t ) 2 n ( 1 ) n ( a a ) n = cos ( g t n ) , A e e ( t ) = n = 0 ( g t ) 2 n ( 1 ) n ( a a ) n = cos ( g t n + 1 ) , A e g ( t ) = n = 0 ( g t ) 2 n + 1 ( 1 ) n ( a a ) n a = sin ( g t n + 1 ) n + 1 a , A g e ( t ) = n = 0 ( g t ) 2 n + 1 ( 1 ) n ( a a ) n a = sin ( g t n ) n a ,
ρ out = Tr tls [ U ρ in | g g | U ] = A g g ( t ) ρ in A g g ( t ) + A e g ( t ) ρ in A e g ( t ) ,
ρ ( t ) = n = 0 n ¯ n ( 1 + n ¯ ) 1 + n cos 2 ( g t n ) | n n | + n = 1 n ¯ n ( 1 + n ¯ ) 1 + n sin 2 ( g t n ) | n 1 n 1 | .
W ( 0 , 0 ; t ) = 2 π n = 0 n ¯ n ( 1 + n ¯ ) 1 + n cos ( 2 g t n ) .
ρ ( t ) = P e j = e e , g e A j ( t ) ρ in A j ( t ) + ( 1 P e ) j = g g , e g A j ( t ) ρ in A j ( t ) .
d d t ρ ( t ) = i h ¯ [ H ( ρ , t ) ] γ 2 h ¯ 2 [ H , [ H , ρ ( t ) ] ] ,
ρ ( t ) = n = 0 1 4 ( 2 + Δ 2 / 2 ( Δ / 2 ) 2 + g 2 n + ( 2 Δ 2 / 2 ( Δ / 2 ) 2 + g 2 n ) cos ( 2 t ( Δ / 2 ) 2 + g 2 n ) × exp ( 2 γ t ( ( Δ / 2 ) 2 + g 2 n ) ) ) ρ TH ( n ) | n n | + n = 1 g 2 n / 2 ( Δ / 2 ) 2 + g 2 n ( 1 cos ( 2 t ( Δ / 2 ) 2 + g 2 n ) × exp ( 2 γ t ( ( Δ / 2 ) 2 + g 2 n ) ) ) ρ TH ( n ) | n 1 n 1 | .
ρ = m = 0 p m | km 2 km 2 | .
ρ blue = n = 0 n ¯ n ( 1 + n ¯ ) 1 + n [ cos ( g t n + 1 ) ] 2 | n n | + n = 0 n ¯ n ( 1 + n ¯ ) 1 + n [ sin ( g t n + 1 ) ] 2 | n + 1 n + 1 | .
ρ blue = n ¯ + 1 n ¯ n = 0 n ¯ ( n ¯ + 1 ) n + 1 × [ n ¯ n ¯ + 1 cos 2 ( g t n + 1 ) + sin 2 ( g t n ) ] = 2 n ¯ + 1 n ¯ ρ th n ¯ + 1 n ¯ ρ red .
n ¯ ρ blue + ( n ¯ + 1 ) ρ red = ( 2 n ¯ + 1 ) ρ th ,

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