Abstract

Broadband homodyne detection of the light transmitted by a Fabry-Perot cavity containing a strongly-coupled 133Cs atom is used to probe the dynamic optical response in a regime where semiclassical theory predicts bistability but strong quantum corrections should apply. While quantum fluctuations destabilize true equilibrium bistability, our observations confirm the existence of metastable states with finite lifetimes and a hysteretic response is apparent when the optical drive is modulated on comparable timescales. Our experiment elucidates remnant semiclassical behavior in the attojoule (∼ 10 photon) regime of single-atom cavity QED, of potential significance for ultra-low power photonic signal processing.

© 2011 OSA

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    [CrossRef] [PubMed]
  3. L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
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    [CrossRef]
  24. M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103173601 (2009).
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    [CrossRef] [PubMed]
  28. 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]
  29. 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]
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    [CrossRef]

2011 (2)

H. Mabuchi, “Coherent-feedback control strategy to suppress spontaneous switching in ultralow power optical bistability,” Appl. Phys. Lett. 98, 193109 (2011).
[CrossRef]

J. Kerckhoff, M. A. Armen, D. S. Pavlichin, and H. Mabuchi, “The dressed atom as binary phase modulator: towards attojoule/edge optical phase-shift keying,” Opt. Express 19, 6478–6486 (2011).
[CrossRef] [PubMed]

2010 (4)

J. Kerckhoff, H. I. Nurdin, D. S. Pavlichin, and H. Mabuchi, “Designing quantum memories with embedded control: Photonic circuits for autonomous quantum error correction,” Phys. Rev. Lett. 105040502 (2010).
[CrossRef] [PubMed]

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

D. A. B. Miller, “Are optical transistors the logical next step?,” Nature Photonics 43–5 (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]

2009 (3)

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photonics 3, 687–695 (2009).
[CrossRef]

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103173601 (2009).
[CrossRef] [PubMed]

2008 (2)

H. Mabuchi, “Derivation of Maxwell-Bloch-type equations by projection of quantum models,” Phys. Rev. A 78, 015801 (2008).
[CrossRef]

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 tunnelling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

2007 (2)

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

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450, 862–865 (2007).
[CrossRef] [PubMed]

2006 (1)

M. A. Armen and H. Mabuchi, “Low-lying bifurcations in cavity quantum electrodynamics,” Phys. Rev. A 73, 063801 (2006).
[CrossRef]

1999 (1)

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

1998 (1)

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

1997 (1)

A. C. Doherty, A. S. Parkins, S. M. Tan, and D. F. Walls, “Motion of a two-level atom in an optical cavity,” Phys. Rev. A 56, 833 (1997).
[CrossRef]

1996 (1)

1991 (2)

S. Ya. Kilin and T. B. Krinitskaya, “Single-atom phase bistability in a fundamental model of quantum optics,” J. Opt. Soc. Am. B 8, 2289 (1991).
[CrossRef]

G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, “Optical bistability and photon statistics in cavity quantum electrodynamics,” Phys. Rev. Lett. 67, 1727 (1991).
[CrossRef] [PubMed]

1990 (3)

H. Gang, C. Z. Ning, and H. Haken, “Codimension-two bifurcations in single-mode optical bistable systems,” Phys. Rev. A 41, 2702 (1990).
[CrossRef] [PubMed]

H. Gang, C. Z. Ning, and H. Haken, “Distribution of subcritical Hopf bifurcations and regular and chaotic attractors in optical bistable systems,” Phys. Rev. A 41, 3975 (1990).
[CrossRef] [PubMed]

A. Barchielli, “Direct and heterodyne detection and other applications of quantum stochastic calculus to quantum optics,” Quantum Opt. 2423–441 (1990).
[CrossRef]

1988 (1)

C. Savage and H. .J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24, 1495–1498 (1988).
[CrossRef]

1986 (1)

1983 (1)

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]

1969 (1)

A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Alton, D. J.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

Aoki, T.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

Armen, M. A.

J. Kerckhoff, M. A. Armen, D. S. Pavlichin, and H. Mabuchi, “The dressed atom as binary phase modulator: towards attojoule/edge optical phase-shift keying,” Opt. Express 19, 6478–6486 (2011).
[CrossRef] [PubMed]

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103173601 (2009).
[CrossRef] [PubMed]

M. A. Armen and H. Mabuchi, “Low-lying bifurcations in cavity quantum electrodynamics,” Phys. Rev. A 73, 063801 (2006).
[CrossRef]

Barchielli, A.

A. Barchielli, “Direct and heterodyne detection and other applications of quantum stochastic calculus to quantum optics,” Quantum Opt. 2423–441 (1990).
[CrossRef]

Brecha, R. J.

G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, “Optical bistability and photon statistics in cavity quantum electrodynamics,” Phys. Rev. Lett. 67, 1727 (1991).
[CrossRef] [PubMed]

Carmichael, H. .J.

C. Savage and H. .J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24, 1495–1498 (1988).
[CrossRef]

Carmichael, H. J.

H. J. Carmichael in Frontiers in Quantum Optics, edited by E. R. Pike and S. Sarkar (Adam Hilger, Bristol, 1986).

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

Chapman, M. S.

Chow, J. M.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

Daneu, V.

A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Dayan, B.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

Devoret, M. H.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

DiCarlo, L.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

Doherty, A. C.

A. C. Doherty, A. S. Parkins, S. M. Tan, and D. F. Walls, “Motion of a two-level atom in an optical cavity,” Phys. Rev. A 56, 833 (1997).
[CrossRef]

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]

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 tunnelling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Faraon, A.

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 tunnelling 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]

Frunzio, L.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photonics 3, 687–695 (2009).
[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 tunnelling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Gambetta, J. M.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

Gang, H.

H. Gang, C. Z. Ning, and H. Haken, “Codimension-two bifurcations in single-mode optical bistable systems,” Phys. Rev. A 41, 2702 (1990).
[CrossRef] [PubMed]

H. Gang, C. Z. Ning, and H. Haken, “Distribution of subcritical Hopf bifurcations and regular and chaotic attractors in optical bistable systems,” Phys. Rev. A 41, 3975 (1990).
[CrossRef] [PubMed]

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, Berlin, 2004).

Girvin, S. M.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

Goldhar, J.

A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Haken, H.

H. Gang, C. Z. Ning, and H. Haken, “Distribution of subcritical Hopf bifurcations and regular and chaotic attractors in optical bistable systems,” Phys. Rev. A 41, 3975 (1990).
[CrossRef] [PubMed]

H. Gang, C. Z. Ning, and H. Haken, “Codimension-two bifurcations in single-mode optical bistable systems,” Phys. Rev. A 41, 2702 (1990).
[CrossRef] [PubMed]

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]

Hood, C. J.

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[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, C. W. Wong, M. Yu, and D. L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Johnson, B. R.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

Kerckhoff, J.

J. Kerckhoff, M. A. Armen, D. S. Pavlichin, and H. Mabuchi, “The dressed atom as binary phase modulator: towards attojoule/edge optical phase-shift keying,” Opt. Express 19, 6478–6486 (2011).
[CrossRef] [PubMed]

J. Kerckhoff, H. I. Nurdin, D. S. Pavlichin, and H. Mabuchi, “Designing quantum memories with embedded control: Photonic circuits for autonomous quantum error correction,” Phys. Rev. Lett. 105040502 (2010).
[CrossRef] [PubMed]

Kilin, S. Ya.

Kimble, H. .J.

Kimble, H. J.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, “Optical bistability and photon statistics in cavity quantum electrodynamics,” Phys. Rev. Lett. 67, 1727 (1991).
[CrossRef] [PubMed]

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]

Krinitskaya, T. B.

Kurnit, N. A.

A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Kwong, D. L.

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

Lee, W. D.

G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, “Optical bistability and photon statistics in cavity quantum electrodynamics,” Phys. Rev. Lett. 67, 1727 (1991).
[CrossRef] [PubMed]

Lugiato, L. A.

L. A. Lugiato, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1984), Vol. XXI.

Lynn, T. W.

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

Mabuchi, H.

H. Mabuchi, “Coherent-feedback control strategy to suppress spontaneous switching in ultralow power optical bistability,” Appl. Phys. Lett. 98, 193109 (2011).
[CrossRef]

J. Kerckhoff, M. A. Armen, D. S. Pavlichin, and H. Mabuchi, “The dressed atom as binary phase modulator: towards attojoule/edge optical phase-shift keying,” Opt. Express 19, 6478–6486 (2011).
[CrossRef] [PubMed]

J. Kerckhoff, H. I. Nurdin, D. S. Pavlichin, and H. Mabuchi, “Designing quantum memories with embedded control: Photonic circuits for autonomous quantum error correction,” Phys. Rev. Lett. 105040502 (2010).
[CrossRef] [PubMed]

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103173601 (2009).
[CrossRef] [PubMed]

H. Mabuchi, “Derivation of Maxwell-Bloch-type equations by projection of quantum models,” Phys. Rev. A 78, 015801 (2008).
[CrossRef]

M. A. Armen and H. Mabuchi, “Low-lying bifurcations in cavity quantum electrodynamics,” Phys. Rev. A 73, 063801 (2006).
[CrossRef]

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]

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. 103173601 (2009).
[CrossRef] [PubMed]

Miller, D. A. B.

D. A. B. Miller, “Are optical transistors the logical next step?,” Nature Photonics 43–5 (2010).
[CrossRef]

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]

Ning, C. Z.

H. Gang, C. Z. Ning, and H. Haken, “Distribution of subcritical Hopf bifurcations and regular and chaotic attractors in optical bistable systems,” Phys. Rev. A 41, 3975 (1990).
[CrossRef] [PubMed]

H. Gang, C. Z. Ning, and H. Haken, “Codimension-two bifurcations in single-mode optical bistable systems,” Phys. Rev. A 41, 2702 (1990).
[CrossRef] [PubMed]

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]

Nurdin, H. I.

J. Kerckhoff, H. I. Nurdin, D. S. Pavlichin, and H. Mabuchi, “Designing quantum memories with embedded control: Photonic circuits for autonomous quantum error correction,” Phys. Rev. Lett. 105040502 (2010).
[CrossRef] [PubMed]

O’Brien, J. L.

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photonics 3, 687–695 (2009).
[CrossRef]

Ostby, E.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

Painter, O.

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450, 862–865 (2007).
[CrossRef] [PubMed]

Parkins, A. S.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

A. C. Doherty, A. S. Parkins, S. M. Tan, and D. F. Walls, “Motion of a two-level atom in an optical cavity,” Phys. Rev. A 56, 833 (1997).
[CrossRef]

Pavlichin, D. S.

J. Kerckhoff, M. A. Armen, D. S. Pavlichin, and H. Mabuchi, “The dressed atom as binary phase modulator: towards attojoule/edge optical phase-shift keying,” Opt. Express 19, 6478–6486 (2011).
[CrossRef] [PubMed]

J. Kerckhoff, H. I. Nurdin, D. S. Pavlichin, and H. Mabuchi, “Designing quantum memories with embedded control: Photonic circuits for autonomous quantum error correction,” Phys. Rev. Lett. 105040502 (2010).
[CrossRef] [PubMed]

Petroff, P.

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 tunnelling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Reed, M. D.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

Regal, C. A.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

Rempe, G.

G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, “Optical bistability and photon statistics in cavity quantum electrodynamics,” Phys. Rev. Lett. 67, 1727 (1991).
[CrossRef] [PubMed]

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]

Savage, C.

C. Savage and H. .J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24, 1495–1498 (1988).
[CrossRef]

Schoelkopf, R. J.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

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]

Smith, S. D.

Srinivasan, K.

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450, 862–865 (2007).
[CrossRef] [PubMed]

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 tunnelling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Strogatz, S. H.

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Perseus, Cambridge, MA, 1994).

Sun, L.

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

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A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).
[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]

A. C. Doherty, A. S. Parkins, S. M. Tan, and D. F. Walls, “Motion of a two-level atom in an optical cavity,” Phys. Rev. A 56, 833 (1997).
[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]

Thompson, R. J.

G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, “Optical bistability and photon statistics in cavity quantum electrodynamics,” Phys. Rev. Lett. 67, 1727 (1991).
[CrossRef] [PubMed]

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Vahala, K. J.

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photonics 3, 687–695 (2009).
[CrossRef]

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 tunnelling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Walls, D. F.

A. C. Doherty, A. S. Parkins, S. M. Tan, and D. F. Walls, “Motion of a two-level atom in an optical cavity,” Phys. Rev. A 56, 833 (1997).
[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]

Wong, C. W.

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

Yang, X.

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

Yu, M.

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

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, Berlin, 2004).

Appl. Opt. (1)

Appl. Phys. B (1)

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. (3)

H. Mabuchi, “Coherent-feedback control strategy to suppress spontaneous switching in ultralow power optical bistability,” Appl. Phys. Lett. 98, 193109 (2011).
[CrossRef]

A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its applications,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

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

IEEE J. Quantum Electron. (1)

C. Savage and H. .J. Carmichael, “Single-atom optical bistability,” IEEE J. Quantum Electron. 24, 1495–1498 (1988).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

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

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

Nature (2)

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Preparation and measurement of three-qubit entanglement in a superconducting circuit,” Nature 467, 574–578 (2010).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450, 862–865 (2007).
[CrossRef] [PubMed]

Nature Photonics (3)

D. A. B. Miller, “Are optical transistors the logical next step?,” Nature Photonics 43–5 (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]

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photonics 3, 687–695 (2009).
[CrossRef]

Nature Physics (1)

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 tunnelling and blockade,” Nature Physics 4, 859–863 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (5)

M. A. Armen and H. Mabuchi, “Low-lying bifurcations in cavity quantum electrodynamics,” Phys. Rev. A 73, 063801 (2006).
[CrossRef]

A. C. Doherty, A. S. Parkins, S. M. Tan, and D. F. Walls, “Motion of a two-level atom in an optical cavity,” Phys. Rev. A 56, 833 (1997).
[CrossRef]

H. Gang, C. Z. Ning, and H. Haken, “Codimension-two bifurcations in single-mode optical bistable systems,” Phys. Rev. A 41, 2702 (1990).
[CrossRef] [PubMed]

H. Gang, C. Z. Ning, and H. Haken, “Distribution of subcritical Hopf bifurcations and regular and chaotic attractors in optical bistable systems,” Phys. Rev. A 41, 3975 (1990).
[CrossRef] [PubMed]

H. Mabuchi, “Derivation of Maxwell-Bloch-type equations by projection of quantum models,” Phys. Rev. A 78, 015801 (2008).
[CrossRef]

Phys. Rev. Lett. (5)

M. A. Armen, A. E. Miller, and H. Mabuchi, “Spontaneous dressed-state polarization in the strong driving regime of cavity QED,” Phys. Rev. Lett. 103173601 (2009).
[CrossRef] [PubMed]

J. Kerckhoff, H. I. Nurdin, D. S. Pavlichin, and H. Mabuchi, “Designing quantum memories with embedded control: Photonic circuits for autonomous quantum error correction,” Phys. Rev. Lett. 105040502 (2010).
[CrossRef] [PubMed]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

T. Aoki, A. S. Parkins, D. J. Alton, C. A. Regal, B. Dayan, E. Ostby, K. J. Vahala, and H. J. Kimble, “Efficient Routing of Single Photons by One Atom and a Microtoroidal Cavity,” Phys. Rev. Lett. 102, 083601 (2009).
[CrossRef] [PubMed]

G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, “Optical bistability and photon statistics in cavity quantum electrodynamics,” Phys. Rev. Lett. 67, 1727 (1991).
[CrossRef] [PubMed]

Quantum Opt. (1)

A. Barchielli, “Direct and heterodyne detection and other applications of quantum stochastic calculus to quantum optics,” Quantum Opt. 2423–441 (1990).
[CrossRef]

Other (6)

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

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

C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, Berlin, 2004).

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Perseus, Cambridge, MA, 1994).

L. A. Lugiato, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1984), Vol. XXI.

H. J. Carmichael in Frontiers in Quantum Optics, edited by E. R. Pike and S. Sarkar (Adam Hilger, Bristol, 1986).

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Figures (7)

Fig. 1
Fig. 1

(a) Steady state intracavity mode amplitude α from the semiclassical Maxwell-Bloch Equations (MBEs) as a function of drive amplitude E for the experimental cQED system with {Θ,Δ} = {−1.1,.7}κ mode-drive and atom-drive detunings. Blue (green) indicates dynamically stable (unstable) solutions, predicting true amplitude bistability for drives in the interval E = [1.5,2.3]κ. (b) Wigner quasi-probability functions of the steady state cavity field from the quantum model as a function of drive amplitude for the same parameters as (a). (c) Sample trace of amplitude quadrature homodyne measurement of the transmitted field during an atom transit with the drive turned on at t = 2μs and held at E = 2.6κ. The slight decrease in signal variance between 2 and 14μs is likely due to a gradual decrease in the coupling rate g from a initial, near-maximal value as the atom moves through the cavity mode.

Fig. 2
Fig. 2

(a) Amplitude quadrature photocurrent data segment taken from the 14 – 19μs interval in Fig. 1(c). The histogram of the data points in this segment are presented on the right, revealing a distribution that well-fits the expected normal distribution of photocurrents when our cavity is empty. (b) High-variance photocurrent segment taken from the 2–7μs interval in Fig. 1(c), when the atom should be near-maximally coupled to the cavity mode. Faint, but sharp transitions between high and low outputs and a seemingly bimodal distribution are visible in this single shot measurement. (c–d) Two more high variance segments from two different experimental runs with the same parameters. (e) A typical 5μs amplitude quadrature segment simulated using quantum trajectory techniques, assuming perfect detection efficiency, with a clearly bimodal output. (f) The same simulated realization as (e), but with calibrated detection inefficiency yields a signal that resembles (b–d) in both visibility and time scale for the large fluctuations.

Fig. 3
Fig. 3

(a–c) Wigner function representations of the expected steady state photocurrent distributions, using calibrated detection efficiencies and bandwidths, for three sets of detuning and drive parameters. Marginal distributions of homodyne measurements of any quadrature may be obtained by integrating these representations over the perpendicular quadrature (see Appendix B). (d–f) Histograms represent the phase- (απ/2) and amplitude-quadrature (α0) photocurrent distributions from ensembles of the highest-variance segments. The histograms are compared with theoretically expected distributions obtained from corresponding Wigner functions (a–c), respectively.

Fig. 4
Fig. 4

The autocorrelation function for the same aggregated amplitude quadrature photocurrent data presented as a histogram in figure 3(d) is displayed in black. Blue crosses represent the autocorrelation of photocurrents simulated by quantum trajectory methods [26] for identical parameters, as in Fig. 2(f). The stability of these quasi-bistable signals is enhanced relative to linearly scaled empty cavity transmission data taken after the atom is lost (red pluses, also presented with a 20MHz analog bandwidth and scaled to match the 0 and 10μs autocorrelation of the high-variance ‘experiment’ signal), and the κ−1 = 17ns cavity decay time (dashed orange line) characterizing the intracavity field relaxation of the empty resonator. We attribute the elevated and noisy autocorrelation of the atom-cavity transmission data at ≳ 1μs timescales to dynamic fluctuations in g, as in Fig 3.

Fig. 5
Fig. 5

(a–b) Single-shot, amplitude quadrature measurements as the drive amplitude is swept at .25MHz and 1MHz, respectively. Black traces are 20MHz bandwidth photocurrents while the green, dashed traces represent the instantaneous drive amplitude. (c–d) Dashed red (blue) traces portray the same photocurrent data in (a) and (b), respectively, as a function of the instantaneous, increasing (decreasing) drive amplitude. Error bars represent sample mean and sample standard deviation of the same photocurrents within non-overlapping drive amplitude intervals. Red and blue regions represent theoretically expected photocurrent mean and sample variance as a function of instantaneous drive (see Appendix B). (e–f) Only the sample means of 3 additional single shot measurements of similar duration are plotted in each figure as a function of the instantaneous drive amplitude, as in (c) and (d), overlaying the same theoretically expected photocurrent statistics.

Fig. 6
Fig. 6

The essential optical and electro-optical components that define and stabilize the science cavity resonance frequency, drive the cQED system, detect individual atom transits, and perform homodyne detection of the cQED transmitted field, as explained in the text.

Fig. 7
Fig. 7

Reproduction of several figures in the main article replacing experimental data with simulated photocurrent data produced by quantum trajectory methods. (a), Simulated amplitude quadrature photocurrent data with {Θ,Δ,E} = {−1.1,.7,2.6}κ, 20MHz analog bandwidth and perfect detection efficiency. (b), Same quantum trajectory realization as (a), but with the 20MHz bandwidth photocurrent simulated with η = .2 efficiency. (c), Histogram of simulated inefficient photocurrents in comparison to the expected distribution derived from master equation based techniques. (d), Sample mean and sample standard deviation of simulated photocurrents from fifty 1MHz AM cycles, overlaying master equation-based predictions.

Equations (12)

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

H = Δ σ σ + Θ a a + i g ( a σ a σ ) + i E ( a a ) ,
d dt O = i [ H , O ] + 2 κ ( a O a 1 2 a a O 1 2 O a a ) + 2 γ ( σ O σ 1 2 σ σ O 1 2 O σ σ ) O .
Φ T [ β s ] = 𝒯 exp { 0 T β s d B out , s 0 T β s * d B out , s }
W t ( α ) = 1 π 2 d 2 β e α β * α * β Tr [ e τ ( 1 2 | β | 2 + ) ρ t ]
P t ( α θ ) = d α θ + π / 2 W t ( α ) .
Φ θ , T [ k ] = 𝒯 exp { i 0 T k s d Y θ , s } ,
I t 1 I t n = ( i ) n n k t 1 k t n Φ θ , T [ k ] | k = 0 .
I t = Tr [ i 0 ρ t ]
I t I t = δ ( t t ) T r [ 0 exp { ( t t ) } 0 ρ t ] .
t = τ T r [ i 0 ρ t ] t 2 = τ τ 2 T r [ 0 2 ρ t ]
d | ψ c ( t ) = ( i H + κ a a + γ σ σ ) | ψ c ( t ) d t + ( 2 κ a + a c d t + d W t ( 1 ) ) 2 κ a | ψ c ( t ) + ( 2 γ σ + σ c d t + d W t ( 2 ) ) 2 γ σ | ψ c ( t )
d Y t = η ( 2 κ a + a c d t + d W t ( 1 ) ) + 1 η d W t ( 3 )

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