Abstract

Integrated nonlinear waveguide structures enable generation of quantum entangled photons. We describe theoretically the effects of spatially inhomogeneous loss on the creation of photon pairs through spontaneous parametric down-conversion in quadratically nonlinear directional couplers, where photons experience effective parity-time (PT) symmetric potential due to the presence of optical loss in one of the waveguides. We show that for losses below the PT-breaking threshold, the quantum photon states can be flexibly tuned similarly to conservative couplers, whereas for stronger losses, the correlations between two waveguide modes are suppressed. We also formulate a quantum-classical correspondence with sum-frequency generation for fast evaluation of device performance. These results can be applied for the design of quantum plasmonic circuits.

© 2018 Chinese Laser Press

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References

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  1. A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
    [Crossref]
  2. I. A. Walmsley, “Quantum optics: science and technology in a new light,” Science 348, 525–530 (2015).
    [Crossref]
  3. C. L. Xiong, B. Bell, and B. J. Eggleton, “CMOS-compatible photonic devices for single-photon generation,” Nanophotonics 5, 427–439 (2016).
    [Crossref]
  4. A. S. Solntsev and A. A. Sukhorukov, “Path-entangled photon sources on nonlinear chips,” Rev. Phys. 2, 19–31 (2017).
    [Crossref]
  5. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
    [Crossref]
  6. C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
    [Crossref]
  7. V. V. Konotop, J. K. Yang, and D. A. Zezyulin, “Nonlinear waves in PT-symmetric systems,” Rev. Mod. Phys. 88, 035002 (2016).
    [Crossref]
  8. S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
    [Crossref]
  9. B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
    [Crossref]
  10. G. S. Agarwal and K. N. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  23. F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

2017 (3)

A. S. Solntsev and A. A. Sukhorukov, “Path-entangled photon sources on nonlinear chips,” Rev. Phys. 2, 19–31 (2017).
[Crossref]

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

S. Vashahri-Ghamsari, B. He, and M. Xiao, “Continuous-variable entanglement generation using a hybrid PT-symmetric system,” Phys. Rev. A 96, 033806 (2017).
[Crossref]

2016 (6)

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

B. He, L. Yang, and M. Xiao, “Dynamical phonon laser in coupled active-passive microresonators,” Phys. Rev. A 94, 031802 (2016).
[Crossref]

A. N. Poddubny, I. V. Iorsh, and A. A. Sukhorukov, “Generation of photon-plasmon quantum states in nonlinear hyperbolic metamaterials,” Phys. Rev. Lett. 117, 123901 (2016).
[Crossref]

C. L. Xiong, B. Bell, and B. J. Eggleton, “CMOS-compatible photonic devices for single-photon generation,” Nanophotonics 5, 427–439 (2016).
[Crossref]

V. V. Konotop, J. K. Yang, and D. A. Zezyulin, “Nonlinear waves in PT-symmetric systems,” Rev. Mod. Phys. 88, 035002 (2016).
[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

2015 (3)

I. A. Walmsley, “Quantum optics: science and technology in a new light,” Science 348, 525–530 (2015).
[Crossref]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

L. G. Helt and M. J. Steel, “Effect of scattering loss on connections between classical and quantum processes in second-order nonlinear waveguides,” Opt. Lett. 40, 1460–1463 (2015).
[Crossref]

2014 (2)

M. Ornigotti and A. Szameit, “Quasi PT-symmetry in passive photonic lattices,” J. Opt. 16, 065501 (2014).
[Crossref]

D. A. Antonosyan, A. S. Solntsev, and A. A. Sukhorukov, “Effect of loss on photon-pair generation in nonlinear waveguide arrays,” Phys. Rev. A 90, 043845 (2014).
[Crossref]

2013 (1)

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref]

2012 (1)

G. S. Agarwal and K. N. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
[Crossref]

2010 (1)

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

2009 (1)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

2008 (1)

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

1987 (1)

Agarwal, G. S.

G. S. Agarwal and K. N. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
[Crossref]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Antonosyan, D. A.

D. A. Antonosyan, A. S. Solntsev, and A. A. Sukhorukov, “Effect of loss on photon-pair generation in nonlinear waveguide arrays,” Phys. Rev. A 90, 043845 (2014).
[Crossref]

Baron, A.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Bell, B.

C. L. Xiong, B. Bell, and B. J. Eggleton, “CMOS-compatible photonic devices for single-photon generation,” Nanophotonics 5, 427–439 (2016).
[Crossref]

Boes, A.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Caves, C. M.

Christodoulides, D. N.

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Crouch, D. D.

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Devaux, E.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Dheur, M. C.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Dmitriev, S. V.

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Eggleton, B. J.

C. L. Xiong, B. Bell, and B. J. Eggleton, “CMOS-compatible photonic devices for single-photon generation,” Nanophotonics 5, 427–439 (2016).
[Crossref]

El Ganainy, R.

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Fisher, P.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Greffet, J. J.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Haylock, B.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

He, B.

S. Vashahri-Ghamsari, B. He, and M. Xiao, “Continuous-variable entanglement generation using a hybrid PT-symmetric system,” Phys. Rev. A 96, 033806 (2017).
[Crossref]

B. He, L. Yang, and M. Xiao, “Dynamical phonon laser in coupled active-passive microresonators,” Phys. Rev. A 94, 031802 (2016).
[Crossref]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Helt, L. G.

Huang, J. H.

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

Hugonin, J. P.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Iorsh, I. V.

A. N. Poddubny, I. V. Iorsh, and A. A. Sukhorukov, “Generation of photon-plasmon quantum states in nonlinear hyperbolic metamaterials,” Phys. Rev. Lett. 117, 123901 (2016).
[Crossref]

Kasture, S.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Kip, D.

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Kivshar, Y. S.

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

Klyshko, D.

D. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, 1988).

Konotop, V. V.

V. V. Konotop, J. K. Yang, and D. A. Zezyulin, “Nonlinear waves in PT-symmetric systems,” Rev. Mod. Phys. 88, 035002 (2016).
[Crossref]

Lee, C.

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

Lenzini, F.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Liscidini, M.

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref]

Lobino, M.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Makris, K. G.

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Marquier, F.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Messin, G.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Mitchell, A.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Neshev, D. N.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Ornigotti, M.

M. Ornigotti and A. Szameit, “Quasi PT-symmetry in passive photonic lattices,” J. Opt. 16, 065501 (2014).
[Crossref]

Pertsch, T.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

Poddubny, A. N.

A. N. Poddubny, I. V. Iorsh, and A. A. Sukhorukov, “Generation of photon-plasmon quantum states in nonlinear hyperbolic metamaterials,” Phys. Rev. Lett. 117, 123901 (2016).
[Crossref]

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Qu, K. N.

G. S. Agarwal and K. N. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
[Crossref]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Rousseau, E.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Ruter, C. E.

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Schiek, R.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

Segev, M.

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Setzpfandt, F.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

Sipe, J. E.

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Solntsev, A. S.

A. S. Solntsev and A. A. Sukhorukov, “Path-entangled photon sources on nonlinear chips,” Rev. Phys. 2, 19–31 (2017).
[Crossref]

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

D. A. Antonosyan, A. S. Solntsev, and A. A. Sukhorukov, “Effect of loss on photon-pair generation in nonlinear waveguide arrays,” Phys. Rev. A 90, 043845 (2014).
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F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Steel, M. J.

Suchkov, S. V.

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

Sukhorukov, A. A.

A. S. Solntsev and A. A. Sukhorukov, “Path-entangled photon sources on nonlinear chips,” Rev. Phys. 2, 19–31 (2017).
[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

A. N. Poddubny, I. V. Iorsh, and A. A. Sukhorukov, “Generation of photon-plasmon quantum states in nonlinear hyperbolic metamaterials,” Phys. Rev. Lett. 117, 123901 (2016).
[Crossref]

D. A. Antonosyan, A. S. Solntsev, and A. A. Sukhorukov, “Effect of loss on photon-pair generation in nonlinear waveguide arrays,” Phys. Rev. A 90, 043845 (2014).
[Crossref]

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Szameit, A.

M. Ornigotti and A. Szameit, “Quasi PT-symmetry in passive photonic lattices,” J. Opt. 16, 065501 (2014).
[Crossref]

Titchener, J.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Vashahri-Ghamsari, S.

S. Vashahri-Ghamsari, B. He, and M. Xiao, “Continuous-variable entanglement generation using a hybrid PT-symmetric system,” Phys. Rev. A 96, 033806 (2017).
[Crossref]

Vest, B.

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Villa, M.

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

Vogel, W.

W. Vogel and D.-G. Welsch, Quantum Optics, 3rd ed. (Wiley, 2006).

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Walmsley, I. A.

I. A. Walmsley, “Quantum optics: science and technology in a new light,” Science 348, 525–530 (2015).
[Crossref]

Wang, J.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Welsch, D.-G.

W. Vogel and D.-G. Welsch, Quantum Optics, 3rd ed. (Wiley, 2006).

Wu, C. W.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

Xiao, M.

S. Vashahri-Ghamsari, B. He, and M. Xiao, “Continuous-variable entanglement generation using a hybrid PT-symmetric system,” Phys. Rev. A 96, 033806 (2017).
[Crossref]

B. He, L. Yang, and M. Xiao, “Dynamical phonon laser in coupled active-passive microresonators,” Phys. Rev. A 94, 031802 (2016).
[Crossref]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Xiong, C. L.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

C. L. Xiong, B. Bell, and B. J. Eggleton, “CMOS-compatible photonic devices for single-photon generation,” Nanophotonics 5, 427–439 (2016).
[Crossref]

Yan, S. B.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Yang, J. K.

V. V. Konotop, J. K. Yang, and D. A. Zezyulin, “Nonlinear waves in PT-symmetric systems,” Rev. Mod. Phys. 88, 035002 (2016).
[Crossref]

Yang, L.

B. He, L. Yang, and M. Xiao, “Dynamical phonon laser in coupled active-passive microresonators,” Phys. Rev. A 94, 031802 (2016).
[Crossref]

Yu, S. Y.

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Zezyulin, D. A.

V. V. Konotop, J. K. Yang, and D. A. Zezyulin, “Nonlinear waves in PT-symmetric systems,” Rev. Mod. Phys. 88, 035002 (2016).
[Crossref]

J. Opt. (1)

M. Ornigotti and A. Szameit, “Quasi PT-symmetry in passive photonic lattices,” J. Opt. 16, 065501 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (2)

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photon. Rev. 10, 131–136 (2016).
[Crossref]

S. V. Suchkov, A. A. Sukhorukov, J. H. Huang, S. V. Dmitriev, C. Lee, and Y. S. Kivshar, “Nonlinear switching and solitons in PT-symmetric photonic systems,” Laser Photon. Rev. 10, 177–213 (2016).
[Crossref]

Nanophotonics (1)

C. L. Xiong, B. Bell, and B. J. Eggleton, “CMOS-compatible photonic devices for single-photon generation,” Nanophotonics 5, 427–439 (2016).
[Crossref]

Nat. Phys. (1)

C. E. Ruter, K. G. Makris, R. El Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (5)

D. A. Antonosyan, A. S. Solntsev, and A. A. Sukhorukov, “Effect of loss on photon-pair generation in nonlinear waveguide arrays,” Phys. Rev. A 90, 043845 (2014).
[Crossref]

G. S. Agarwal and K. N. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
[Crossref]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

B. He, L. Yang, and M. Xiao, “Dynamical phonon laser in coupled active-passive microresonators,” Phys. Rev. A 94, 031802 (2016).
[Crossref]

S. Vashahri-Ghamsari, B. He, and M. Xiao, “Continuous-variable entanglement generation using a hybrid PT-symmetric system,” Phys. Rev. A 96, 033806 (2017).
[Crossref]

Phys. Rev. Lett. (3)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

M. Liscidini and J. E. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111, 193602 (2013).
[Crossref]

A. N. Poddubny, I. V. Iorsh, and A. A. Sukhorukov, “Generation of photon-plasmon quantum states in nonlinear hyperbolic metamaterials,” Phys. Rev. Lett. 117, 123901 (2016).
[Crossref]

Rev. Mod. Phys. (1)

V. V. Konotop, J. K. Yang, and D. A. Zezyulin, “Nonlinear waves in PT-symmetric systems,” Rev. Mod. Phys. 88, 035002 (2016).
[Crossref]

Rev. Phys. (1)

A. S. Solntsev and A. A. Sukhorukov, “Path-entangled photon sources on nonlinear chips,” Rev. Phys. 2, 19–31 (2017).
[Crossref]

Science (3)

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

I. A. Walmsley, “Quantum optics: science and technology in a new light,” Science 348, 525–530 (2015).
[Crossref]

B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Other (3)

D. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, 1988).

F. Lenzini, A. N. Poddubny, J. Titchener, P. Fisher, A. Boes, S. Kasture, B. Haylock, M. Villa, A. Mitchell, A. S. Solntsev, A. A. Sukhorukov, and M. Lobino, “Direct characterization of a nonlinear photonic circuit’s wave function with laser light,” arXiv: 1703.01007 (2017).

W. Vogel and D.-G. Welsch, Quantum Optics, 3rd ed. (Wiley, 2006).

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Figures (4)

Fig. 1.
Fig. 1. (a) Scheme of generation of photon pairs through the spontaneous parametric down-conversion in a nonlinear PT-symmetric coupler with linear absorption in the second waveguide. (b) Graphical representation of biphoton correlation function |ϕns,ni|2.
Fig. 2.
Fig. 2. Evolution of spatial signal and idler photon correlations between the two waveguide modes along the propagation direction (z) depending on the phase mismatch (Δβ) for different losses in the second waveguide γs=γi=γ. (a)–(c) γ=0.5 below the PT-symmetry breaking threshold. (d)–(f) γ=3 corresponding to PT-broken regime. For all plots, the coupling coefficients are Cs=Ci=1, Cp=0, and pump is coupled to the first waveguide, A1(z=0)=1, A2(z=0)=0, and γp=0.
Fig. 3.
Fig. 3. Normalized photon correlations, |ϕns,ni|2/ns,ni|ϕns,ni|2, versus the phase mismatch and loss in the second waveguide at the fixed propagation distance z=10. The pump is input to the (a)–(c) first [A1(z=0)=1, A2(z=0)=0] or (d)–(f) second waveguide [A1(z=0)=0, A2(z=0)=1]. Dashed lines indicate the linear PT-breaking threshold at γPT=2C. Other parameters correspond to Fig. 2.
Fig. 4.
Fig. 4. (a) Scheme of SFG in passive PT-symmetric nonlinear coupler with linear absorption in one waveguide. (b) Mismatch F between the SPDC and SFG depending on the input power P for |uns(z=0)|2=|vni(z=0)|2=P/2, plotted on a logarithmic scale. The propagation distance is z=10, signal and idler losses are equal γs=γi=0.5, there is no loss in the pump mode γp=0, and the coupling coefficients are Cs=Ci=1, Cp=0.

Equations (6)

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

ϕns,ni(z)z=i(βs+βi)ϕns,ni+δns,niAns(z)iCsϕ3ns,niiCiϕns,3ni(δns,2γs+δni,2γi)ϕns,ni,
Anp(z)z=iβpAniCpA3npδnp,2γpA2,
ϕns,ni(z)=ei(βs+βi)z0zdξnp,np=12Anp(0)G(ξ,np,np;Cp,γp)G(zξ,np,ns;Cs,γs)G(zξ,np,ni;Ci,γi)eiΔβξ,
unsz=iβsunsiCsu3nsδns,2γsu2+wnsvns*,
vniz=iβivniiCiv3niδni,2γiv2+wniuni*,
wnpz=iβpwnpiCpw3npδnp,2γpw2+unpvnp,

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