Abstract

The temporal shape of single photons provides a high-dimensional basis of temporal modes, and can therefore support quantum computing schemes that go beyond the qubit. However, the lack of linear optical components to act as quantum gates has made it challenging to efficiently address specific temporal-mode components from an arbitrary superposition. Recent progress towards realizing such a “quantum pulse gate,” has been proposed using nonlinear optical signal processing to add coherently the effect of multiple stages of quantum frequency conversion. This scheme, called temporal-mode interferometry [D. V. Reddy, Phys. Rev. A 91, 012323 (2015)], has been shown in the case of three-wave mixing to promise near-unity mode-sorting efficiency. Here we demonstrate that it is also possible to achieve high mode-sorting efficiency using four-wave mixing, if one pump pulse is long and the other short — a configuration we call asymmetrically-pumped Bragg scattering.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: a complete framework for quantum information science,” http://arxiv.org/abs/1504.06251 (2015).
  2. J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
    [Crossref]
  3. B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
    [Crossref]
  4. H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
    [Crossref] [PubMed]
  5. A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13770–13778 (2011).
    [Crossref] [PubMed]
  6. D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
    [Crossref] [PubMed]
  7. J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153 (1992).
    [Crossref]
  8. D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
    [Crossref] [PubMed]
  9. D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
    [Crossref]
  10. L. Mejling, S. M. M. Friis, D. V. Reddy, K. Rottwitt, M. G. Raymer, and C. J. McKinstrie, “Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation,” in Advanced Photonics, (Optical Society of America, 2014), paper JTu3A.36.
    [Crossref]
  11. N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
    [Crossref]
  12. G. P. Agrawal, Nonlinear Fiber Optics, , 5th ed. (Academic, 2013).
  13. R. Giacone, C. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
    [Crossref]
  14. H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
    [Crossref] [PubMed]
  15. C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
    [Crossref]
  16. L. Mejling, D. S. Cargill, C. J. McKinstrie, K. Rottwitt, and R. O. Moore, “Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime,” Opt. Express 20, 27454–27475 (2012).
    [Crossref] [PubMed]
  17. L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 8367–8396 (2012).
    [Crossref] [PubMed]
  18. C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
    [Crossref] [PubMed]
  19. W. Wasilewski and M. G. Raymer, “Pairwise entanglement and readout of atomic-ensemble and optical wavepacket modes in traveling-wave Raman interactions,” Phys. Rev. A 73, 063816 (2006).
    [Crossref]
  20. M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
    [Crossref]
  21. S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interferometry with photons,” in Proceedings of CLEO: 2014 Postdeadline Paper Digest, (Optical Society of America, 2014), paper FTh5A.2.

2015 (1)

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

2014 (2)

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (3)

2011 (3)

2010 (2)

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

2008 (1)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

2006 (1)

W. Wasilewski and M. G. Raymer, “Pairwise entanglement and readout of atomic-ensemble and optical wavepacket modes in traveling-wave Raman interactions,” Phys. Rev. A 73, 063816 (2006).
[Crossref]

2000 (1)

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[Crossref] [PubMed]

1995 (1)

R. Giacone, C. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

1992 (1)

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153 (1992).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, , 5th ed. (Academic, 2013).

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Betti, R.

R. Giacone, C. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

Brecht, B.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13770–13778 (2011).
[Crossref] [PubMed]

Cargill, D. S.

Clemmen, S.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interferometry with photons,” in Proceedings of CLEO: 2014 Postdeadline Paper Digest, (Optical Society of America, 2014), paper FTh5A.2.

Eberly, J. H.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[Crossref] [PubMed]

Eckstein, A.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13770–13778 (2011).
[Crossref] [PubMed]

Farsi, A.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interferometry with photons,” in Proceedings of CLEO: 2014 Postdeadline Paper Digest, (Optical Society of America, 2014), paper FTh5A.2.

Friis, S. M. M.

L. Mejling, S. M. M. Friis, D. V. Reddy, K. Rottwitt, M. G. Raymer, and C. J. McKinstrie, “Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation,” in Advanced Photonics, (Optical Society of America, 2014), paper JTu3A.36.
[Crossref]

Gaeta, A. L.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interferometry with photons,” in Proceedings of CLEO: 2014 Postdeadline Paper Digest, (Optical Society of America, 2014), paper FTh5A.2.

Giacone, R.

R. Giacone, C. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

Huang, J.

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153 (1992).
[Crossref]

Kumar, P.

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153 (1992).
[Crossref]

Kwiat, P. G.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Langford, N. K.

N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
[Crossref]

Law, C. K.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[Crossref] [PubMed]

McGuinness, H. J.

H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
[Crossref] [PubMed]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

McKinstrie, C.

R. Giacone, C. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

McKinstrie, C. J.

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

L. Mejling, D. S. Cargill, C. J. McKinstrie, K. Rottwitt, and R. O. Moore, “Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime,” Opt. Express 20, 27454–27475 (2012).
[Crossref] [PubMed]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 8367–8396 (2012).
[Crossref] [PubMed]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
[Crossref] [PubMed]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

L. Mejling, S. M. M. Friis, D. V. Reddy, K. Rottwitt, M. G. Raymer, and C. J. McKinstrie, “Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation,” in Advanced Photonics, (Optical Society of America, 2014), paper JTu3A.36.
[Crossref]

Mejling, L.

Milburn, G. J.

N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
[Crossref]

Moore, R. O.

Munro, W. J.

N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
[Crossref]

Prevedel, R.

N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
[Crossref]

Quiring, V.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

Radic, S.

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

Ramelow, S.

N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
[Crossref]

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interferometry with photons,” in Proceedings of CLEO: 2014 Postdeadline Paper Digest, (Optical Society of America, 2014), paper FTh5A.2.

Raymer, M. G.

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 8367–8396 (2012).
[Crossref] [PubMed]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
[Crossref] [PubMed]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

W. Wasilewski and M. G. Raymer, “Pairwise entanglement and readout of atomic-ensemble and optical wavepacket modes in traveling-wave Raman interactions,” Phys. Rev. A 73, 063816 (2006).
[Crossref]

L. Mejling, S. M. M. Friis, D. V. Reddy, K. Rottwitt, M. G. Raymer, and C. J. McKinstrie, “Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation,” in Advanced Photonics, (Optical Society of America, 2014), paper JTu3A.36.
[Crossref]

Reddy, D. V.

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

L. Mejling, S. M. M. Friis, D. V. Reddy, K. Rottwitt, M. G. Raymer, and C. J. McKinstrie, “Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation,” in Advanced Photonics, (Optical Society of America, 2014), paper JTu3A.36.
[Crossref]

Ricken, R.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

Rottwitt, K.

Sansoni, L.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

Silberhorn, C.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13770–13778 (2011).
[Crossref] [PubMed]

Suche, H.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

van Enk, S. J.

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

Walmsley, I. A.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[Crossref] [PubMed]

Wasilewski, W.

W. Wasilewski and M. G. Raymer, “Pairwise entanglement and readout of atomic-ensemble and optical wavepacket modes in traveling-wave Raman interactions,” Phys. Rev. A 73, 063816 (2006).
[Crossref]

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Zeilinger, A.

N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
[Crossref]

Nat. Phys. (1)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Nature (London) (1)

N. K. Langford, S. Ramelow, R. Prevedel, W. J. Munro, G. J. Milburn, and A. Zeilinger, “Efficient quantum computing using coherent photon conversion,” Nature (London) 478(7369), 360–363 (2011).
[Crossref]

Opt. Commun. (1)

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Phys. Plasmas (1)

R. Giacone, C. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

Phys. Rev. A (4)

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

W. Wasilewski and M. G. Raymer, “Pairwise entanglement and readout of atomic-ensemble and optical wavepacket modes in traveling-wave Raman interactions,” Phys. Rev. A 73, 063816 (2006).
[Crossref]

Phys. Rev. Lett. (3)

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[Crossref] [PubMed]

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153 (1992).
[Crossref]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics, , 5th ed. (Academic, 2013).

L. Mejling, S. M. M. Friis, D. V. Reddy, K. Rottwitt, M. G. Raymer, and C. J. McKinstrie, “Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation,” in Advanced Photonics, (Optical Society of America, 2014), paper JTu3A.36.
[Crossref]

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: a complete framework for quantum information science,” http://arxiv.org/abs/1504.06251 (2015).

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interferometry with photons,” in Proceedings of CLEO: 2014 Postdeadline Paper Digest, (Optical Society of America, 2014), paper FTh5A.2.

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Figures (9)

Fig. 1
Fig. 1 Schematic of the interacting fields in near conversion Bragg scattering. The curved arrows indicate photon transfer illustrated for (i) signal up-conversion, and (ii) signal down-conversion.
Fig. 2
Fig. 2 The two lowest-order (first and second) (a) r-input, (b) s-input, (c) r-output, and (d) s-output Schmidt modes are shown for γ′ = 1.5 and ζ = 20.
Fig. 3
Fig. 3 Single-stage Schmidt coefficients ρ n 2 for (a) varying values of γ′ and ζ = 20, and (b) three different values of ζ for γ′ = 1.5. The legends show the corresponding selectivities, S. Note that the lines labeled with circles are the same in the two figures, and are the Schmidt coefficients belonging to the Schmidt modes in Fig. 2.
Fig. 4
Fig. 4 (a) Single-stage selectivity versus the dimensionless interaction strength γ′ for various values of ζ and (b) the evolution of the three lowest Schmidt coefficients for ζ = 100.
Fig. 5
Fig. 5 Illustration of temporal-mode interferometry using two stages of quantum frequency conversion (QFC) in optical fiber. Original input is a superposition of temporal-modes in the r-channel (green), and the two pumps p (red, continuous-wave/long pulse) and q (orange, pulsed). The shape of the pulsed pump decides the target temporal-mode which is to be converted to a signal in the s-channel (blue). The intermediate stage contains replacement of the pumps and a variable relative phase shift θ (here on the r-channel). Mux and Demux represent wavelength multiplexing and demultiplexing respectively.
Fig. 6
Fig. 6 Schmidt modes of (a,c,e,g) the r-channel and (b,d,f,h) the s-channel for γ′ = 0.825, ζ = 50. All the Schmidt modes have been centered on the normalized time-axis to facilitate comparison. The lack of temporal mode overlap in the DC configuration is apparent when comparing the output Schmidt modes of the first stage in (c,d) with the corresponding input Schmidt modes of the second stage in (e,f). This mismatch is not observed for the RC configuration which is temporally mode matched. The legend in (e) also applies to (f,g,h).
Fig. 7
Fig. 7 Schmidt decomposition of the two-stage combined Green function Gsr for (a–c) RC and (d–f) DC configurations using γ′ = 0.825 and ζ = 200. (a,d) show the values of the six lowest Schmidt coefficients, (b,e) show the r-channel Schmidt modes, and (c,f) show the s-channel Schmidt modes.
Fig. 8
Fig. 8 Dual-stage selectivity versus γ′ for (a) the RC configuration and (b) the DC configuration. The maximum selectivity point is obtained for γ ≈ 0.825 (dotted line), exhibiting stable behavior against variation in ζ.
Fig. 9
Fig. 9 Dual-stage selectivity versus the dimensionless fiber length ζ for γ′ = 0.825.

Equations (32)

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( z + β p ( 1 ) t ) A p = i γ ( | A p | 2 / 2 + | A q | 2 ) A p ,
( z + β q ( 1 ) t ) A q = i γ ( | A p | 2 + | A q | 2 / 2 ) A q ,
( z + β s ( 1 ) t ) A s = i γ ( | A p | 2 + | A q | 2 ) A s + i γ A p * A q A r ,
( z + β r ( 1 ) t ) A r = i γ ( | A p | 2 + | A q | 2 ) A r + i γ A p A q * A s ,
z A p = i γ | A p | 2 A p / 2 ,
( z + β q ( 1 ) t ) A q = i γ | A p | 2 A q ,
( z + β s ( 1 ) t ) A s = i γ | A p | 2 A s + i γ A p * A q A r ,
( z + β r ( 1 ) t ) A r = i γ | A p | 2 A r + i γ A p A q * A s ,
A p ( z ) = a p ( 0 ) exp ( i γ P p z / 2 ) , A q ( z , t ) = a q ( t β q z ) exp ( i γ P p z ) ,
A j ( l , t ) = k = s , r d t G j k ( t , t ) A k ( 0 , t ) , ( j = s , r ) ,
G r r ( t , t ) = [ H ( t t β s l ) δ ( t t + β r l ) ( a q ( t β r l ) a q ( t ) ) * γ ¯ ( η ( t , t ) ξ ( t , t ) ) 1 / 2 a q * ( t β r l ) J 1 { 2 γ ¯ [ η ( t , t ) ξ ( t , t ) ] 1 / 2 } a q ( t ) × H ( t t + β r l ) H ( t t β s l ) } ] exp [ i Γ p ( t t + β r l 2 β s l ) ] ,
G rs ( t , t ) = i γ ¯ a q * ( t β r l ) J 0 { 2 γ ¯ [ η ( t , t ) ξ ( t , t ) ] 1 / 2 } a p ( t ) × H ( t t + β r l ) H ( t t β s l ) } exp [ i Γ p ( t t + β r l 2 β s l ) ] ,
G s r ( t , t ) = i γ ¯ a p * ( t ) J 0 { 2 γ ¯ [ η ( t , t ) ξ ( t , t ) ] 1 / 2 } a q ( t ) × H ( t t + β r l ) H ( t t + β s l ) exp [ i Γ p ( t t + 2 β r l 3 β s l ) ] ,
G s s ( t , t ) = [ H ( t t + β r l ) δ ( t t β s l ) ( a p ( t ) a p ( t ) ) * γ ¯ ( ξ ( t , t ) η ( t , t ) ) 1 / 2 a p * ( t ) J 1 { 2 γ ¯ [ η ( t , t ) ξ ( t , t ) ] 1 / 2 } a p ( t ) × H ( t t + β r l ) H ( t t + β s l ) ] exp [ i Γ p ( t t + 2 β r l 3 β s l ) ] ,
η ( t , t ) = ( t t β s l ) P p , ξ ( t , t ) = t β r l t d t ¯ | a q ( t ¯ ) | 2 .
G rs ( τ , τ ) = i γ a q * ( τ ζ ) a p ( τ ) 2 ζ J 0 { γ ζ ( τ τ + ζ ) [ erf ( τ + ζ 2 ) erf ( τ ζ 2 ) ] } × H ( τ τ + ζ ) H ( τ τ + ζ ) exp [ i Γ p τ q ( τ τ + 3 ζ ) ] ,
γ = γ P p E q l β rs .
ζ = β rs l 2 τ q ,
G r r ( t , t ) = n = 1 Ψ n ( t ) τ n ψ n * ( t ) ,
G rs ( t , t ) = n = 1 Ψ n ( t ) ρ n ϕ n * ( t ) ,
G s r ( t , t ) = n = 1 Φ n ( t ) ρ n ψ n * ( t ) ,
G s s ( t , t ) = n = 1 Φ n ( t ) τ n ϕ n * ( t ) ,
d t ψ n ( t ) ψ m * ( t ) = δ n m ,
𝒮 = ρ 1 2 n ρ n 2 1 ,
S = ρ 1 2 𝒮 = ρ 1 4 n ρ n 2 1 ,
G r r ( t , t ) = d t [ G r r ( 2 ) ( t , t ) exp ( i θ ) G r r ( 1 ) ( t , t ) + G rs ( 2 ) ( t , t ) G s r ( 1 ) ( t , t ) ] ,
G s r ( t , t ) = d t [ G s r ( 2 ) ( t , t ) exp ( i θ ) G r r ( 1 ) ( t , t ) + G s s ( 2 ) ( t , t ) G s r ( 1 ) ( t , t ) ] ,
G r r ( t , t ) = m , n [ τ m 2 ν m n τ n ( 1 ) exp ( i θ ) ρ m ( 2 ) μ m n ρ n ( 1 ) ] Ψ m ( 2 ) ( t ) ψ n ( 1 ) * ( t ) ,
G s r ( t , t ) = m , n [ ρ m 2 ν m n τ n ( 1 ) exp ( i θ ) + τ m ( 2 ) μ m n ρ n ( 1 ) ] Φ m ( 2 ) ( t ) ψ n ( 1 ) * ( t ) ,
μ m n = d t ϕ m ( 2 ) * ( t ) Φ n ( 1 ) ( t ) , ν m n = d t ψ m ( 2 ) * ( t ) Ψ n ( 1 ) ( t ) ,
A r out ( t ) = a n m [ τ m ( 2 ) ν m n τ n ( 1 ) exp ( i θ ) ρ m ( 2 ) μ m n ρ n ( 1 ) ] Ψ m ( 2 ) ( t ) ,
A s out ( t ) = a n m [ ρ m ( 2 ) ν m n τ n ( 1 ) exp ( i θ ) τ m ( 2 ) μ m n ρ n ( 1 ) ] Φ m ( 2 ) ( t ) .

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