Abstract

We use a single 133Cs atom strongly coupled to an optical resonator to induce random binary phase modulation of a near infra-red, ∼ 500pW laser beam, with each modulation edge caused by the dissipation of a single photon (≈ 0.23aJ) by the atom. While our ability to deterministically induce phase edges with an additional optical control beam is limited thus far, theoretical analysis of an analogous, solid-state system indicates that efficient external control should be achievable in demonstrated nanophotonic systems.

© 2011 OSA

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  1. X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
    [CrossRef]
  2. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
    [CrossRef]
  3. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
    [CrossRef]
  4. K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
    [CrossRef]
  5. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Ch. 6 in Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004).
  6. H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372 (2002).
    [CrossRef] [PubMed]
  7. P. Berman, ed., Cavity Quantum Electrodynamics (San Diego: Academic Press, 1994).
  8. P. Alsing and H. J. Carmichael, “Spontaneous dressed-state polarization of a coupled atom and cavity mode,” Quantum Opt. 3, 13–32 (1991).
    [CrossRef]
  9. M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103, 173601 (2009).
    [CrossRef] [PubMed]
  10. H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, “Real-time detection of individual atoms falling through a high-finesse optical cavity,” Opt. Lett. 21, 1393–1395 (1996).
    [CrossRef] [PubMed]
  11. O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models (Springer Science+Business Media, New York, 2005).
  12. L. R. Welch, “Hidden Markov models and the Baum-Welch algorithm,” IEEE Information Theory Society Newsletter Vol. 53, No. 4 (December2003).
  13. A. J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Trans. Inform. Theory 13260–269 (1967).
    [CrossRef]
  14. S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
    [CrossRef]
  15. H. Carmichael, An Open Systems Approach to Quantum Optics (Springer, Berlin, 1993).
  16. A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
    [CrossRef] [PubMed]
  17. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
    [CrossRef]
  18. E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89 (1963).
    [CrossRef]

2010

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
[CrossRef] [PubMed]

2009

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103, 173601 (2009).
[CrossRef] [PubMed]

2008

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

2007

X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

2003

L. R. Welch, “Hidden Markov models and the Baum-Welch algorithm,” IEEE Information Theory Society Newsletter Vol. 53, No. 4 (December2003).

2002

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372 (2002).
[CrossRef] [PubMed]

1999

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
[CrossRef]

1996

1991

P. Alsing and H. J. Carmichael, “Spontaneous dressed-state polarization of a coupled atom and cavity mode,” Quantum Opt. 3, 13–32 (1991).
[CrossRef]

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

1967

A. J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Trans. Inform. Theory 13260–269 (1967).
[CrossRef]

1963

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

Alsing, P.

P. Alsing and H. J. Carmichael, “Spontaneous dressed-state polarization of a coupled atom and cavity mode,” Quantum Opt. 3, 13–32 (1991).
[CrossRef]

Armen, M. A.

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103, 173601 (2009).
[CrossRef] [PubMed]

Baets, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Cappé, O.

O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models (Springer Science+Business Media, New York, 2005).

Carmichael, H.

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

Carmichael, H. J.

P. Alsing and H. J. Carmichael, “Spontaneous dressed-state polarization of a coupled atom and cavity mode,” Quantum Opt. 3, 13–32 (1991).
[CrossRef]

Chapman, M. S.

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Ch. 6 in Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004).

Cummings, F. W.

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

de Vries, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Doherty, A. C.

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372 (2002).
[CrossRef] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Ch. 6 in Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004).

Englund, D.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Faraon, A.

A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
[CrossRef] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Fushman, I.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Geluk, E.-J.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Ch. 6 in Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004).

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Husko, C.

X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Huybrechts, K.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Jaynes, E. T.

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

Kim, H.

A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
[CrossRef] [PubMed]

Kimble, H. J.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Kumar, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Kwon, D.-L.

X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Liu, L.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Mabuchi, H.

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103, 173601 (2009).
[CrossRef] [PubMed]

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372 (2002).
[CrossRef] [PubMed]

H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, “Real-time detection of individual atoms falling through a high-finesse optical cavity,” Opt. Lett. 21, 1393–1395 (1996).
[CrossRef] [PubMed]

Majumder, A.

A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
[CrossRef] [PubMed]

Matsuo, S.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Miller, A. E.

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103, 173601 (2009).
[CrossRef] [PubMed]

Morthier, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Moulines, E.

O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models (Springer Science+Business Media, New York, 2005).

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Notomi, M.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Nozaki, K.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Petroff, P.

A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
[CrossRef] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Regreny, P.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Roelkens, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Rydén, T.

O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models (Springer Science+Business Media, New York, 2005).

Sato, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Shinya, A.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Spuesens, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Stoltz, N.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Tan, S. M.

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
[CrossRef]

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Turchette, Q. A.

Van Thourhout, D.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

Viterbi, A. J.

A. J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Trans. Inform. Theory 13260–269 (1967).
[CrossRef]

Vuckovic, J.

A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
[CrossRef] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Welch, L. R.

L. R. Welch, “Hidden Markov models and the Baum-Welch algorithm,” IEEE Information Theory Society Newsletter Vol. 53, No. 4 (December2003).

Wong, C. W.

X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Yang, X.

X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Yu, M.

X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 3197 (1983).
[CrossRef]

Appl. Phys. Lett.

X. Yang, C. Husko, M. Yu, D.-L. Kwon, and C. W. Wong, “Observation of femtojoule optical bistability in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

IEEE Information Theory Society Newsletter

L. R. Welch, “Hidden Markov models and the Baum-Welch algorithm,” IEEE Information Theory Society Newsletter Vol. 53, No. 4 (December2003).

IEEE Trans. Inform. Theory

A. J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Trans. Inform. Theory 13260–269 (1967).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt.

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
[CrossRef]

Nature Photonics

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nature Photonics 4, 182–187 (2010).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photonics 4, 477–483 (2010).
[CrossRef]

Nature Physics

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103, 173601 (2009).
[CrossRef] [PubMed]

A. Faraon, A. Majumder, H. Kim, P. Petroff, and J. Vučković, “Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity,” Phys. Rev. Lett. 104, 047402 (2010).
[CrossRef] [PubMed]

Proc. IEEE

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

Quantum Opt.

P. Alsing and H. J. Carmichael, “Spontaneous dressed-state polarization of a coupled atom and cavity mode,” Quantum Opt. 3, 13–32 (1991).
[CrossRef]

Science

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372 (2002).
[CrossRef] [PubMed]

Other

P. Berman, ed., Cavity Quantum Electrodynamics (San Diego: Academic Press, 1994).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Ch. 6 in Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004).

O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models (Springer Science+Business Media, New York, 2005).

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

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Figures (4)

Fig. 1.
Fig. 1.

a, A representative phase-quadrature, optical homodyne measurement of the field transmitted by a resonator containing a strongly coupled two-level system is displayed in blue with a 20MHz bandwidth, calibrated by the cavity quantum electrodynamical (cQED) parameters, according to strong-driving, theoretical predictions. Red overlay is the decoded binary signal produced by the Viterbi algorithm with hidden Markov model parameters obtained via expectation maximization (see text). b, A histogram of the photocurrent data segment in a, displaying a dual-Gaussian distribution consistent with binary phase modulation and with theoretical predictions. c, Dual histograms of the photocurrent data, each taking counts only when the Viterbi path occupies the positive or negative state.

Fig. 2.
Fig. 2.

Both plots depict contours of the likelihood functions of hidden Markov model transition rates for low ↔ high switching. The most likely rate-pairs inferred from data taken from individual atom transit segments are indicated by grey dots, with the diameter of each dot representing the duration of the corresponding data segment. The grey bars represent the intervals over which the likelihood of the individual transits’ rate-pairs are at least 1/3 of their maximum. The red cross locates the most likely rate-pair, given an aggregated segment formed from the individual transit measurements, with the red oval enclosing the region of rate-pair likelihoods that are at least 1/3 of the maximum. The teal cross and oval represent the same likelihood contours produced from simulated data. a, Likelihood contours using a ‘near-detuned’ system, with atomic detuning Δ/2π = 9MHz, and a probe strength corresponding to 〈〉 = 14 photons in an empty cavity, for which a symmetric switching rate-pair slightly greater than γ /2 is expected. b, The same as a, except using a ‘far-detuned’ system with Δ/2π = 40MHz, 〈〉 = 19, for which an asymmetric switching model is anticipated.

Fig. 3.
Fig. 3.

a, Simulated photocurrent segment assuming cQED parameters demonstrated in [16], a 11μ W probe and perfect detection efficiency at a 10GHz detection bandwidth. The time axis is calibrated in terms of the quantum dot (Qdot) dephasing rate of γ /2π = 0.1GHz and the photocurrent axis is calibrated by the ratio g 0/κ({g 0,κ}/2π = {20,40}GHz in [16]). b, Simulated photocurrent segment assuming the same system, plus a .27μ W cw ‘control’ beam detuned by the magnitude of the Qdot-field coupling Hamiltonian, i.e., by −400GHz relative to the probe beam. Even this weak control probe induces an order of magnitude more flops than the intrinsic spontaneous emission dynamics, corresponding to less than 100aJ dissipated by the control probe per induced edge.

Fig. 4.
Fig. 4.

Data points represent inferred ‘total γ ’ (mean rate at which transitions in either direction occur) for various control beam parameters. The thin lines track the most likely total γ and the confidence interval represents the range of γ values with at least 1/3 the maximum likelihood. The green, blue and red data points depict the total γ as a function of control power for a control probe detuned by −375MHz, −425MHz, and −525MHz from the signal probe, respectively. The colored shaded regions represent linear best fits of the corresponding confidence intervals based on a simulated data set with perfect detection efficiency and duration several times that of the experimental data. The apparent positive, constant bias in the experimental γ relative to simulation for control powers at least equal to the probe’s is perhaps due to enhanced opto-mechanical motion induced by a strong control beam. Although the effect of the control is marginal in both experiment and simulation, as anticipated for this atomic system, the results are consistent with the basic concept of external, optical controllability explained in the text and illustrated more convincingly in a Qdot-photonic crystal simulation in Fig. 3.

Equations (3)

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H = Δ σ σ + Θ a a + i g ( r ) ( a σ a σ ) + i E ( a a )
d | ψ c ( t ) = ( i H + κ a a + γ σ σ ) | ψ c ( t ) d t + ( 2 κ ψ c ( t ) | a + a | ψ c ( t ) d t + d W t ( 1 ) ) 2 κ a | ψ c ( t ) + ( 2 γ ψ c ( t ) | σ + σ | ψ c ( t ) d t + d W t ( 2 ) ) 2 γ σ | ψ c ( t )
d Q ( t ) = η ( 2 κ ψ c ( t ) | a + a | ψ c ( t ) d t + d W t ( 1 ) ) + 1 η d W t ( 3 )

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