Abstract

We show how the input–output formalism for cascaded quantum systems combined with the quantum trajectory approach yields a compact and physically intuitive description of single photons propagating through a coupled cavity array. As a new application, we obtain the time-dependent spectrum of such a single photon, which directly reflects the fact that only certain frequency components of single-photon wavepackets are trapped inside the cavities and hence are delayed in time. We include in our description the actual generation of the single photon, by assuming we have a single emitter in one of the resonators.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. J. E. Heebner and R. W. Boyd, “Slow and stopped light ‘slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002).
    [CrossRef]
  4. J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled resonator optical waveguides: toward the slowing and storage of light,” Opt. Photon. News 16(2), 36–40 (2005).
    [CrossRef]
  5. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
    [CrossRef]
  6. T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
    [CrossRef]
  7. J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. 30, 2001–2003 (2005).
    [CrossRef]
  8. J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
    [CrossRef]
  9. J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom,” Phys. Rev. A 79, 023838 (2009).
    [CrossRef]
  10. E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
    [CrossRef]
  11. W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
    [CrossRef]
  12. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [CrossRef]
  13. C. Santori, J. V. David Fattal, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594–597 (2002).
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  14. A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 67901 (2002).
    [CrossRef]
  15. J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
    [CrossRef]
  16. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
    [CrossRef]
  17. J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
    [CrossRef]
  18. H. J. Carmichael, “Quantum trajectory theory for cascaded open systems,” Phys. Rev. Lett. 70, 2273–2276 (1993).
    [CrossRef]
  19. C. W. Gardiner, “Driving a quantum system with the output field from another driven quantum system,” Phys. Rev. Lett. 70, 2269–2272 (1993).
    [CrossRef]
  20. C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, 2004), Vol. 56.
  21. P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
    [CrossRef]
  22. H. Carmichael, An Open Systems Approach to Quantum Optics (Springer, 1993).
  23. R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, “Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs,” Phys. Rev. A 46, 4382–4396 (1992).
    [CrossRef]
  24. K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
    [CrossRef]
  25. M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998).
    [CrossRef]
  26. L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
    [CrossRef]
  27. A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
    [CrossRef]
  28. J. H. Eberly and K. Wodkiewicz, “The time-dependent physical spectrum of light,” J. Opt. Soc. Am. 67, 1252–1261 (1977).
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  29. B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
    [CrossRef]
  30. This is a recent experiment in the single-photon regime using a single atom inside a single cavity, where the nonlinearity introduced by the presence of the atom is exploited to change an incoming laser beam of light (with Poissonian photon-number statistics) into reflected light that is antibunched, characteristic of single photons.
  31. C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
    [CrossRef]
  32. G. Cui and M. G. Raymer, “Emission spectra and quantum efficiency of single-photon sources in the cavity-qed strong-coupling regime,” Phys. Rev. A 73, 053807 (2006).
    [CrossRef]
  33. A. Auffèves, B. Besga, J.-M. Gérard, and J.-P. Poizat, “Spontaneous emission spectrum of a two-level atom in a very-high-q cavity,” Phys. Rev. A 77, 063833 (2008).
    [CrossRef]
  34. L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
    [CrossRef]
  35. M. Havukainen and S. Stenholm, “An open-systems approach to calculating time-dependent spectra,” J. Mod. Opt. 45, 1699–1716 (1998).
    [CrossRef]
  36. H. J. Carmichael, Statistical Methods in Quantum Optics (Springer, 2007), Vol. 2.
  37. H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
    [CrossRef]
  38. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
    [CrossRef]
  39. J. B. Khurgin and R. S. Tucker, Slow Light: Science and Applications (CRC Press, 2008), Vol. 140.
  40. C. R. Otey, M. L. Povinelli, and S. Fan, “Completely capturing light pulses in a few dynamically tuned microcavities,” J. Lightwave Technol. 26, 3784–3793 (2008).
    [CrossRef]

2012 (1)

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

2011 (1)

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

2010 (1)

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

2009 (2)

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom,” Phys. Rev. A 79, 023838 (2009).
[CrossRef]

2008 (5)

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
[CrossRef]

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

A. Auffèves, B. Besga, J.-M. Gérard, and J.-P. Poizat, “Spontaneous emission spectrum of a two-level atom in a very-high-q cavity,” Phys. Rev. A 77, 063833 (2008).
[CrossRef]

C. R. Otey, M. L. Povinelli, and S. Fan, “Completely capturing light pulses in a few dynamically tuned microcavities,” J. Lightwave Technol. 26, 3784–3793 (2008).
[CrossRef]

2006 (1)

G. Cui and M. G. Raymer, “Emission spectra and quantum efficiency of single-photon sources in the cavity-qed strong-coupling regime,” Phys. Rev. A 73, 053807 (2006).
[CrossRef]

2005 (2)

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled resonator optical waveguides: toward the slowing and storage of light,” Opt. Photon. News 16(2), 36–40 (2005).
[CrossRef]

J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. 30, 2001–2003 (2005).
[CrossRef]

2004 (1)

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

2002 (5)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

C. Santori, J. V. David Fattal, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594–597 (2002).
[CrossRef]

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 67901 (2002).
[CrossRef]

J. E. Heebner and R. W. Boyd, “Slow and stopped light ‘slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q. H. Park, “Scissor solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002).
[CrossRef]

1999 (3)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[CrossRef]

1998 (2)

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998).
[CrossRef]

M. Havukainen and S. Stenholm, “An open-systems approach to calculating time-dependent spectra,” J. Mod. Opt. 45, 1699–1716 (1998).
[CrossRef]

1997 (1)

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

1993 (3)

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
[CrossRef]

H. J. Carmichael, “Quantum trajectory theory for cascaded open systems,” Phys. Rev. Lett. 70, 2273–2276 (1993).
[CrossRef]

C. W. Gardiner, “Driving a quantum system with the output field from another driven quantum system,” Phys. Rev. Lett. 70, 2269–2272 (1993).
[CrossRef]

1992 (2)

R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, “Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs,” Phys. Rev. A 46, 4382–4396 (1992).
[CrossRef]

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef]

1989 (1)

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[CrossRef]

1987 (1)

P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
[CrossRef]

1985 (1)

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

1980 (1)

A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
[CrossRef]

1977 (1)

Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Aspect, A.

A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
[CrossRef]

Auffèves, A.

A. Auffèves, B. Besga, J.-M. Gérard, and J.-P. Poizat, “Spontaneous emission spectrum of a two-level atom in a very-high-q cavity,” Phys. Rev. A 77, 063833 (2008).
[CrossRef]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
[CrossRef]

Baur, A.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Becher, C.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Besga, B.

A. Auffèves, B. Besga, J.-M. Gérard, and J.-P. Poizat, “Spontaneous emission spectrum of a two-level atom in a very-high-q cavity,” Phys. Rev. A 77, 063833 (2008).
[CrossRef]

Boca, A.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

Boozer, A. D.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

Boyd, R. W.

J. E. Heebner, R. W. Boyd, and Q. H. Park, “Scissor solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002).
[CrossRef]

J. E. Heebner and R. W. Boyd, “Slow and stopped light ‘slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002).
[CrossRef]

Brecha, R. J.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[CrossRef]

Briegel, H.-J.

W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[CrossRef]

Buck, J. R.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

Carmichael, H.

H. Carmichael, An Open Systems Approach to Quantum Optics (Springer, 1993).

Carmichael, H. J.

H. J. Carmichael, “Quantum trajectory theory for cascaded open systems,” Phys. Rev. Lett. 70, 2273–2276 (1993).
[CrossRef]

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef]

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[CrossRef]

H. J. Carmichael, Statistical Methods in Quantum Optics (Springer, 2007), Vol. 2.

Castin, Y.

Cirac, J. I.

W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[CrossRef]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

Cohen-Tannoudji, C.

A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
[CrossRef]

Collett, M. J.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

Cui, G.

G. Cui and M. G. Raymer, “Emission spectra and quantum efficiency of single-photon sources in the cavity-qed strong-coupling regime,” Phys. Rev. A 73, 053807 (2006).
[CrossRef]

Dalibard, J.

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
[CrossRef]

A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
[CrossRef]

David Fattal, J. V.

C. Santori, J. V. David Fattal, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594–597 (2002).
[CrossRef]

Dayan, B.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Dum, R.

R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, “Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs,” Phys. Rev. A 46, 4382–4396 (1992).
[CrossRef]

Dür, W.

W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[CrossRef]

Eberly, J. H.

Englund, D.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Fan, S.

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom,” Phys. Rev. A 79, 023838 (2009).
[CrossRef]

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

C. R. Otey, M. L. Povinelli, and S. Fan, “Completely capturing light pulses in a few dynamically tuned microcavities,” J. Lightwave Technol. 26, 3784–3793 (2008).
[CrossRef]

J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. 30, 2001–2003 (2005).
[CrossRef]

Fischer, M.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Gardiner, C.

C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, 2004), Vol. 56.

Gardiner, C. W.

C. W. Gardiner, “Driving a quantum system with the output field from another driven quantum system,” Phys. Rev. Lett. 70, 2269–2272 (1993).
[CrossRef]

R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, “Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs,” Phys. Rev. A 46, 4382–4396 (1992).
[CrossRef]

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

Gérard, J.-M.

A. Auffèves, B. Besga, J.-M. Gérard, and J.-P. Poizat, “Spontaneous emission spectrum of a two-level atom in a very-high-q cavity,” Phys. Rev. A 77, 063833 (2008).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Gsell, S.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Hatami, F.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Havukainen, M.

M. Havukainen and S. Stenholm, “An open-systems approach to calculating time-dependent spectra,” J. Mod. Opt. 45, 1699–1716 (1998).
[CrossRef]

Heebner, J. E.

J. E. Heebner and R. W. Boyd, “Slow and stopped light ‘slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q. H. Park, “Scissor solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002).
[CrossRef]

Hennrich, M.

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 67901 (2002).
[CrossRef]

Hepp, C.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Khurgin, J. B.

J. B. Khurgin and R. S. Tucker, Slow Light: Science and Applications (CRC Press, 2008), Vol. 140.

Kimble, H. J.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[CrossRef]

Kipfstuhl, L.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Knight, P. L.

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998).
[CrossRef]

Krauss, T. F.

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

Kuhn, A.

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 67901 (2002).
[CrossRef]

Kuzmich, A.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

Lee, R. K.

Lukin, M. D.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Mabuchi, H.

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

Mandel, L.

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

Marte, M.

P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
[CrossRef]

McKeever, J.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

Miller, R.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

Mølmer, K.

Mücklich, F.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Neu, E.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Ostby, E. P.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Otey, C. R.

Paloczi, G. T.

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled resonator optical waveguides: toward the slowing and storage of light,” Opt. Photon. News 16(2), 36–40 (2005).
[CrossRef]

Park, H.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Park, Q. H.

Parkins, A. S.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, “Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs,” Phys. Rev. A 46, 4382–4396 (1992).
[CrossRef]

Pauly, C.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Plenio, M. B.

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998).
[CrossRef]

Poizat, J.-P.

A. Auffèves, B. Besga, J.-M. Gérard, and J.-P. Poizat, “Spontaneous emission spectrum of a two-level atom in a very-high-q cavity,” Phys. Rev. A 77, 063833 (2008).
[CrossRef]

Poon, J. K. S.

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled resonator optical waveguides: toward the slowing and storage of light,” Opt. Photon. News 16(2), 36–40 (2005).
[CrossRef]

Povinelli, M. L.

Raizen, M. G.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[CrossRef]

Raymer, M. G.

G. Cui and M. G. Raymer, “Emission spectra and quantum efficiency of single-photon sources in the cavity-qed strong-coupling regime,” Phys. Rev. A 73, 053807 (2006).
[CrossRef]

Rempe, G.

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 67901 (2002).
[CrossRef]

Rephaeli, E.

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

Reynaud, S.

A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Rice, P. R.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[CrossRef]

Riedrich-Möller, J.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Rivoire, K.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Roger, G.

A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
[CrossRef]

Santori, C.

C. Santori, J. V. David Fattal, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594–597 (2002).
[CrossRef]

Scherer, A.

Scheuer, J.

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled resonator optical waveguides: toward the slowing and storage of light,” Opt. Photon. News 16(2), 36–40 (2005).
[CrossRef]

Schreck, M.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Shen, J. T.

Shen, J.-T.

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom,” Phys. Rev. A 79, 023838 (2009).
[CrossRef]

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

Shields, B.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Solomon, G. S.

C. Santori, J. V. David Fattal, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594–597 (2002).
[CrossRef]

Stenholm, S.

M. Havukainen and S. Stenholm, “An open-systems approach to calculating time-dependent spectra,” J. Mod. Opt. 45, 1699–1716 (1998).
[CrossRef]

Tian, L.

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Tucker, R. S.

J. B. Khurgin and R. S. Tucker, Slow Light: Science and Applications (CRC Press, 2008), Vol. 140.

Vahala, K. J.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Vuckovic, J.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Walls, D. F.

P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
[CrossRef]

Wandt, M.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Wodkiewicz, K.

Wolff, S.

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Xu, Y.

Yamamoto, Y.

C. Santori, J. V. David Fattal, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594–597 (2002).
[CrossRef]

Yariv, A.

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled resonator optical waveguides: toward the slowing and storage of light,” Opt. Photon. News 16(2), 36–40 (2005).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Zoller, P.

W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[CrossRef]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, “Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs,” Phys. Rev. A 46, 4382–4396 (1992).
[CrossRef]

P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
[CrossRef]

C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, 2004), Vol. 56.

J. Lightwave Technol. (1)

J. Mod. Opt. (2)

J. E. Heebner and R. W. Boyd, “Slow and stopped light ‘slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002).
[CrossRef]

M. Havukainen and S. Stenholm, “An open-systems approach to calculating time-dependent spectra,” J. Mod. Opt. 45, 1699–1716 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Nano Lett. (1)

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef]

Nat. Nanotechnol. (1)

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One-and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7, 69–74 (2011).
[CrossRef]

Nat. Photonics (2)

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
[CrossRef]

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

Nature (1)

C. Santori, J. V. David Fattal, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594–597 (2002).
[CrossRef]

Opt. Lett. (2)

Opt. Photon. News (1)

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled resonator optical waveguides: toward the slowing and storage of light,” Opt. Photon. News 16(2), 36–40 (2005).
[CrossRef]

Phys. Rev. A (10)

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

G. Cui and M. G. Raymer, “Emission spectra and quantum efficiency of single-photon sources in the cavity-qed strong-coupling regime,” Phys. Rev. A 73, 053807 (2006).
[CrossRef]

A. Auffèves, B. Besga, J.-M. Gérard, and J.-P. Poizat, “Spontaneous emission spectrum of a two-level atom in a very-high-q cavity,” Phys. Rev. A 77, 063833 (2008).
[CrossRef]

L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801–R6804 (1992).
[CrossRef]

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[CrossRef]

P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
[CrossRef]

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

J.-T. Shen and S. Fan, “Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom,” Phys. Rev. A 79, 023838 (2009).
[CrossRef]

W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[CrossRef]

R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, “Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs,” Phys. Rev. A 46, 4382–4396 (1992).
[CrossRef]

Phys. Rev. Lett. (6)

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

H. J. Carmichael, “Quantum trajectory theory for cascaded open systems,” Phys. Rev. Lett. 70, 2273–2276 (1993).
[CrossRef]

C. W. Gardiner, “Driving a quantum system with the output field from another driven quantum system,” Phys. Rev. Lett. 70, 2269–2272 (1993).
[CrossRef]

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 67901 (2002).
[CrossRef]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

A. Aspect, G. Roger, S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji, “Time correlations between the two sidebands of the resonance fluorescence triplet,” Phys. Rev. Lett. 45, 617–620 (1980).
[CrossRef]

Rev. Mod. Phys. (3)

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998).
[CrossRef]

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Science (2)

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992–1994 (2004).
[CrossRef]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Other (5)

This is a recent experiment in the single-photon regime using a single atom inside a single cavity, where the nonlinearity introduced by the presence of the atom is exploited to change an incoming laser beam of light (with Poissonian photon-number statistics) into reflected light that is antibunched, characteristic of single photons.

J. B. Khurgin and R. S. Tucker, Slow Light: Science and Applications (CRC Press, 2008), Vol. 140.

H. J. Carmichael, Statistical Methods in Quantum Optics (Springer, 2007), Vol. 2.

H. Carmichael, An Open Systems Approach to Quantum Optics (Springer, 1993).

C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, 2004), Vol. 56.

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Figures (12)

Fig. 1.
Fig. 1.

Empty lossless ring resonator with one mode, coupled to an optical fiber. The main text discusses classical and quantum descriptions of this system.

Fig. 2.
Fig. 2.

Initially excited two-level atom can emit a photon into one of two counterpropagating modes of a lossy ring resonator. The photon leaks out at a rate κ1 and is detected by one of two frequency-selective detectors with spectral width Γ.

Fig. 3.
Fig. 3.

Time evolution of probabilities of finding the single excitation in the atom, the cavity counterclockwise (1cc) mode, the cavity clockwise (1c) mode, and the right fiber and left fiber continuum modes. (a) Strong coupling regime: |g|/κ1=5, Δc1/κ1=(ωc1ωeg)/κ1=0.5. The oscillatory behavior in the plots is the manifestation of the single-photon Rabi oscillation. (b) Weak coupling regime: |g|/κ1=0.25, Δc1/κ1=(ωc1ωeg)/κ1=0.5. Here we see the nonoscillatory, monotonically decaying behavior for the atomic probability. Note that after sufficiently long times, κ1t10, the probability of finding the photon in the left and right fiber modes approaches 0.5, while all other probabilities die out.

Fig. 4.
Fig. 4.

Emission spectra (as functions of Δk in units of κ1) recorded by a detector with bandwidth Γ/κ1=0.25. (a) Strong coupling regime, Δ/κ1=0.5, and varying values of |g|/κ1. Note that the single-photon Rabi splitting equals 22|g|. The asymmetry in the heights of the peaks is due to a nonzero detuning between atom and cavity (which breaks the symmetry under ωkωk). (b) Emission spectra with varying values of |g|/κ1 remaining in the weak coupling regime and Δ/κ1=0.5.

Fig. 5.
Fig. 5.

Empty ring resonator driven by an atom–cavity system. The input of the second cavity equals the output field of the first cavity, delayed by a time τd.

Fig. 6.
Fig. 6.

Probabilities of finding the excitation in the atom, in the first cavity clockwise–counterclockwise modes, in the second cavity (Cav2), and in the left–right fibers. (a) Strong coupling regime, with |g|/κ1=|g|/κ2=5. Note here that the populations in left and right fiber modes are identical, so only one curve is visible. (b) is an enlargement of (a). It shows the photon time delay (of about 0.24κ1) between the cavities. (c) Weak coupling regime, with parameters |g|/κ1=|g|/κ2=0.25, Δ1/κ1=Δ2/κ2=0.5. This plot’s differences from Fig. 3 are due to the presence of the second cavity and are more clearly present in the weak coupling regime than in the strong coupling regime.

Fig. 7.
Fig. 7.

(a) Comparison of the time-dependent spectrum as defined by either Eq. (18) or Eq. (19), recorded at κt=5.5 for |g|/κ1=|g|/κ2=5, Δ1/κ1=0.5, and Δ2/κ2=7.32. Notice the role of integration is just to smooth out wiggles and change the scale of the plot a little. Other features (in which we are more interested) remain the same. We now focus on the time-integrated version of the spectrum. (b) Integrated time-dependent spectra recorded at different times for the same parameters as in (a), with Γ/κ1=0.25. Note that the peak on the right does not show considerable growth until κ1t=3.6. In fact, we also see a “hole-burning” effect at earlier times for positive Δk: there is one peak, but with the center frequencies removed (delayed).

Fig. 8.
Fig. 8.

Array of four ring resonators driven by ring-atom system.

Fig. 9.
Fig. 9.

(a) Probabilities of finding photon in atom, in first cavity clockwise–counterclockwise modes, in second through fifth cavities, and in left–right fibers in the weak coupling regime |g|/κ1==|g|/κ5=0.25, Δ1/κ1=0.5, Δ2/κ2==Δ5/κ5=0.12. The successive delays in finding the photon in the different cavities are clearly visible. These delays are caused by the photon being trapped in each of the cavities for some time, and is in addition to the trivial delays caused by the propagation time between the cavities. In both regimes the photon can be trapped for times 15κ11 in total. (b) Time-integrated spectra (recorded at κ1t=6 with a detector with spectral width Γ=0.25κ1) detected by Da detector in the strong coupling regime |g|/κ1==|g|/κ5=5, Δ1/κ1=0.5, Δ2/κ2==Δ5/κ5=7.32. Emission spectra are shown for two, three, four, and five cavities. Note the “hole-burning” effect in the right peak in the spectrum. It is caused by the delay of the central frequency components of that peak.

Fig. 10.
Fig. 10.

Raman-type transition driven by laser and cavity. The atom starts in the state |g, and may be (with some probability between 0 and 1) transferred to the state |e by absorbing a laser photon and emitting a photon into the cavity.

Fig. 11.
Fig. 11.

(a) Probabilities of finding the atom in the ground state, or an excitation in the first or second cavity, in the strong coupling regime with |g|/κ=2, Δc1/κ=Δc2/κ=0.25, δ/κ=1.5, assuming a Gaussian laser pulse with the form exp(t2/2τL2). (b) Integrated time-dependent spectra in the strong coupling regime, for the same parameters, with Γ=0.25κ. We note that changing the detunings (Δc1, δ) from positive to negative values would shift the graph toward the left; moreover, the heights of the left and right peaks would be interchanged.

Fig. 12.
Fig. 12.

(a) Probabilities of finding the atom in the ground state, or an excitation in the first or second cavity, in the weak coupling regime, with parameters |g|/κ=0.25, Δc1/κ=Δc2/κ=0.25, δ/κ=0.5, and τL=10/κ. (b) Integrated time-dependent spectra (recorded with bandwidth Γ/κ1=0.25) emitted by cavity driven by Raman atom–cavity system recorded at different times for the same parameters.

Equations (43)

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aout=t+eiϕ1teiϕain,
aout=κ/2+i(ωωc)κ/2i(ωωc)ain
κτ=r2;ϕ=(ωωc)τ,
db^(ω)/dt=iωb^(ω)+κ1/2πa^1,
b^(ω)=exp(i(ω(tt0)))b^0(ω)+κ1/2πt0tdtexp(i(ω(tt)))a^1(t).
b^in(t)12πdωexp(iω(tt0))b^0(ω).
H^s=ωegσ^σ^++ωc1(a^1a^1+b^b^)+(ga^1σ^+g*a^1σ^+)+(g*b^σ^+gb^σ^+)iκ1(a^1a^ina^ina^1+b^b^inb^inb^).
a^out=a^in+κ1a^1,
b^out=b^in+κ1b^.
|ψJ^j|ψΠj.
Pj(t)=ψ|J^jJ^j|ψdtΠjdt,
H^NH=H^sij=a,bJ^jJ^j/2.
id|ψ˜(t)dt=H^NH|ψ˜(t).
|ψ˜(t)=ce(t)|e,0,0+c1(t)|g,1,0+c2(t)|g,0,1,
sCe(s)+igC1(s)+ig*C2(s)=1,
(s+iΔ+κ12)C1(s)+ig*Ce(s)=0,
(s+iΔ+κ12)C2(s)+igCe(s)=0
ce(t)=2e(κ14+iΔ2)tα((iΔ+κ1)sinh(αt)+αcosh(αt)),
c1(t)=2ig*α(2e(κ14+iΔ2)tsinh(αt)),
c2(t)=2igα(2e(κ14+iΔ2)tsinh(αt)),
α=κ12+4iκ1Δ4Δ232g24.
ρ^(t)=|ψ˜(t)ψ˜(t)|+P(t)|g,0,0g,0,0|.
Pe(t)=Tr[ρ^(t)|e,0,0e,0,0|]=|ce(t)|2,
P1(t)=Tr[ρ^(t)|g,1,0g,1,0|]=|c1(t)|2,
P2(t)=Tr[ρ^(t)|g,0,1g,0,1|]=|c2(t)|2,
Pk1(t)=κ10tTr[ρ(t)a^1a^1]dt=κ10t|c1(t)|2dt,
Pk2(t)t=κ10tTr[ρ(t)b^b^]dt=κ10t|c2(t)|2dt.
N(t;Δk,Γ)=Γ0t0te(ΓiΔk)(tt1)e(Γ+iΔk)(tt2)×a^out(t1)a^out(t2)dt1dt2.
NS(t;Δk,Γ)=0tN(t;Δk,Γ)dt.
PDa(Δk)=4|g|2κ1Γ[4|g|22Δk(Δk+Δ)]2+κ12Δk2.
a^in(2)(t)=a^out(1)(t),
a^out(2)=a^in(2)+κ2a^2.
J^a=κ1a^1+κ2a^2+a^in(1).
H^H=H^A+H^Biκ1κ22(a^2a^1a^2a^1),
H^B=ωc2a^2a^2.
H^AH=i2(κ1a^1a^1+κ1b^b^+κ2a^2a^2)iκ1κ22(a^2a^1+a^2a^1).
H^NH=H^A+H^Bi2(κ1a^1a^1+κ1b^b^+κ2a^2a^2)iκ1κ2a^2a^1.
|ψ˜(t)=ce(t)|e,0,0,0+c1(t)|g,1,0,0+c2(t)|g,0,1,0+c3(t)|g,0,0,1.
c3(t)=igκα(8|g|2+2iκΔ)[4αe(iΔ+κ2)t4e(κ/4+iΔ/2)t{(2iΔκ)sinh(αt)4e(κ/4+iΔ/2)tαcosh(αt)}],
H^NH=ωegσ^σ^++ωcb^b^+(ga^1σ^+g*a^1σ^+)+(g*b^σ^+gb^σ^+)+i=15(ωciiκi2)a^ia^iii=14j=i+15κiκja^ja^i.
J^a=a^out(5)=j=25κja^j.
H^=ωeg|ee|+ωig|ii|+ωc1a^1a^1+ωc1b^b^+ωc2a^2a^2+2(Ω(t)eiωLt|gi|+Ω*(t)eiωLt|ig|)+(ga^1|ie|+g*a^1|ei|)+(g*b^|ie|+gb^|ei|),
H^=Δc1a^1a^1+Δc1b^b^+Δc2a^2a^2|Ω(t)|24δ|gg||g|2δa^1a^1|ee||g|2δb^b^|ee|(g*Ω(t)2δ|ge|a^1+gΩ(t)*2δ|eg|a^1)(gΩ(t)*2δ|ge|b^+g*Ω(t)2δ|eg|b^),

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