Abstract

We analyze the transmission character of a single-mode cavity containing a resonant two-level atom. Such a simple structure exhibits optical nonlinearity and spatial symmetry breaking, as well as time-reversal symmetry breaking. We perform a detailed analysis in the Purcell regime and find out that there is giant optical nonreciprocity in proper parameter space. Therefore, it is feasible to assemble such a simple atom–cavity structure to realize an acceptable optical nonreciprocal device after carefully designing.

© 2014 Optical Society of America

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    [CrossRef]
  29. W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
    [CrossRef]
  30. J. Volz and A. Rauschenbeutel, “Triggering an optical transistor with one photon,” Science 341, 725–726 (2013).
    [CrossRef]
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    [CrossRef]

2013

K. R. Allahverdyan, A. H. Gevorgyan, R. S. Hakobyan, and T. V. Galstian, “Observation of optical non-reciprocity in a single layer of transparent linear chiral media with asymmetric boundaries,” JETP Lett. 96, 694–698 (2013).
[CrossRef]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-resolved two-pulse excitation of quantum dots coupled to a photonic crystal cavity in the Purcell regime,” Phys. Rev. Lett. 110, 013602 (2013).
[CrossRef]

W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
[CrossRef]

J. Volz and A. Rauschenbeutel, “Triggering an optical transistor with one photon,” Science 341, 725–726 (2013).
[CrossRef]

A. Reiserer, S. Ritter, and G. Rempe, “Nondestructive detection of an optical photon,” Science 342, 1349–1351 (2013).
[CrossRef]

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

2012

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[CrossRef]

C. Wang, X.-L. Zhong, and Z.-Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 1–6 (2012).
[CrossRef]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

C. Wang, “Nonlocal entanglement analysis using quantum dot and microcavity coupled system,” J. Mod. Opt. 59, 962–966 (2012).
[CrossRef]

R. Bose, D. Sridharan, H. Kim, G. S. Solomon, and E. Waks, “Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity,” Phys. Rev. Lett. 108, 227402 (2012).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

2011

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

2010

K. Zhang and Z.-Y. Li, “Transfer behavior of quantum states between atoms in photonic crystal coupled cavities,” Phys. Rev. A 81, 033843 (2010).
[CrossRef]

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef]

2009

H. F. Hofmann and H. Nishitani, “Pulse-shape effects on photon-photon interactions in nonlinear optical quantum gates,” Phys. Rev. A 80, 013822 (2009).
[CrossRef]

G. Manzacca, H. Habibian, K. Hingerl, and G. Cincotti, “Coupled cavity polaritons for switching and slow light applications,” Photon. Nanostr. Fundam. Appl. 7, 39–46 (2009).

2007

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90, 023514 (2007).
[CrossRef]

A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Phys. Rev. A 75, 053823 (2007).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

2006

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef]

2004

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30  dB integrated optical isolator in III/V material,” Electron. Lett. 40, 1293–1294 (2004).
[CrossRef]

R. L. Espinola, T. Izuhara, M.-C. Tsai, J. R. M. Osgood, and H. Dötsch, “Magneto-optical nonreciprocal phase shift in garnet/silicon-on-insulator waveguides,” Opt. Lett. 29, 941–943 (2004).
[CrossRef]

1985

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]

1964

Allahverdyan, K. R.

K. R. Allahverdyan, A. H. Gevorgyan, R. S. Hakobyan, and T. V. Galstian, “Observation of optical non-reciprocity in a single layer of transparent linear chiral media with asymmetric boundaries,” JETP Lett. 96, 694–698 (2013).
[CrossRef]

Aolita, L.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[CrossRef]

Aplet, L. J.

Auffèves-Garnier, A.

A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Phys. Rev. A 75, 053823 (2007).
[CrossRef]

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Baets, R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

Beck, K. M.

W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
[CrossRef]

Bhandare, S.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30  dB integrated optical isolator in III/V material,” Electron. Lett. 40, 1293–1294 (2004).
[CrossRef]

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Bonato, C.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef]

Bose, R.

R. Bose, D. Sridharan, H. Kim, G. S. Solomon, and E. Waks, “Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity,” Phys. Rev. Lett. 108, 227402 (2012).
[CrossRef]

Bouwmeester, D.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef]

Brinkmeyer, E.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

Bücker, R.

W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
[CrossRef]

Carson, J. W.

Chang, D. E.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[CrossRef]

Chen, W.

W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
[CrossRef]

Chen, Y.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Cincotti, G.

G. Manzacca, H. Habibian, K. Hingerl, and G. Cincotti, “Coupled cavity polaritons for switching and slow light applications,” Photon. Nanostr. Fundam. Appl. 7, 39–46 (2009).

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]

Ding, D.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef]

Dionne, G. F.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Doerr, C. R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

Dötsch, H.

Eich, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

Englund, D.

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Espinola, R. L.

Evers, J.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Fan, S.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

Faraon, A.

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Fedotov, V. A.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Freude, W.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

Fushman, I.

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Galstian, T. V.

K. R. Allahverdyan, A. H. Gevorgyan, R. S. Hakobyan, and T. V. Galstian, “Observation of optical non-reciprocity in a single layer of transparent linear chiral media with asymmetric boundaries,” JETP Lett. 96, 694–698 (2013).
[CrossRef]

Gardiner, C. W.

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-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Phys. Rev. A 75, 053823 (2007).
[CrossRef]

Gevorgyan, A. H.

K. R. Allahverdyan, A. H. Gevorgyan, R. S. Hakobyan, and T. V. Galstian, “Observation of optical non-reciprocity in a single layer of transparent linear chiral media with asymmetric boundaries,” JETP Lett. 96, 694–698 (2013).
[CrossRef]

Gong, Q.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Gudat, J.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef]

Gullans, M.

W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
[CrossRef]

Guo, M.-J.

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S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30  dB integrated optical isolator in III/V material,” Electron. Lett. 40, 1293–1294 (2004).
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T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
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L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
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C. Wang, X.-L. Zhong, and Z.-Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 1–6 (2012).
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K. Zhang and Z.-Y. Li, “Transfer behavior of quantum states between atoms in photonic crystal coupled cavities,” Phys. Rev. A 81, 033843 (2010).
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G. Manzacca, H. Habibian, K. Hingerl, and G. Cincotti, “Coupled cavity polaritons for switching and slow light applications,” Photon. Nanostr. Fundam. Appl. 7, 39–46 (2009).

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J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-resolved two-pulse excitation of quantum dots coupled to a photonic crystal cavity in the Purcell regime,” Phys. Rev. Lett. 110, 013602 (2013).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
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J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-resolved two-pulse excitation of quantum dots coupled to a photonic crystal cavity in the Purcell regime,” Phys. Rev. Lett. 110, 013602 (2013).
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H. F. Hofmann and H. Nishitani, “Pulse-shape effects on photon-photon interactions in nonlinear optical quantum gates,” Phys. Rev. A 80, 013822 (2009).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30  dB integrated optical isolator in III/V material,” Electron. Lett. 40, 1293–1294 (2004).
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C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
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Petroff, P.

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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
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A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Phys. Rev. A 75, 053823 (2007).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
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V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90, 023514 (2007).
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J. Volz and A. Rauschenbeutel, “Triggering an optical transistor with one photon,” Science 341, 725–726 (2013).
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T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
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V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

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L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
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S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30  dB integrated optical isolator in III/V material,” Electron. Lett. 40, 1293–1294 (2004).
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J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-resolved two-pulse excitation of quantum dots coupled to a photonic crystal cavity in the Purcell regime,” Phys. Rev. Lett. 110, 013602 (2013).
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M. O. Scully, Quantum Optics (Cambridge University, 1997).

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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Sih, V.

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-resolved two-pulse excitation of quantum dots coupled to a photonic crystal cavity in the Purcell regime,” Phys. Rev. Lett. 110, 013602 (2013).
[CrossRef]

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A. Auffèves-Garnier, C. Simon, J.-M. Gérard, and J.-P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,” Phys. Rev. A 75, 053823 (2007).
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R. Bose, D. Sridharan, H. Kim, G. S. Solomon, and E. Waks, “Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity,” Phys. Rev. Lett. 108, 227402 (2012).
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R. Bose, D. Sridharan, H. Kim, G. S. Solomon, and E. Waks, “Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity,” Phys. Rev. Lett. 108, 227402 (2012).
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D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
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W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
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C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

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J. Volz and A. Rauschenbeutel, “Triggering an optical transistor with one photon,” Science 341, 725–726 (2013).
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T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

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D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
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W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
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R. Bose, D. Sridharan, H. Kim, G. S. Solomon, and E. Waks, “Low-photon-number optical switching with a single quantum dot coupled to a photonic crystal cavity,” Phys. Rev. Lett. 108, 227402 (2012).
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D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 2007).

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C. Wang, X.-L. Zhong, and Z.-Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 1–6 (2012).
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D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

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X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not—an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335, 38 (2012).
[CrossRef]

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T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90, 023514 (2007).
[CrossRef]

Zhang, H.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30  dB integrated optical isolator in III/V material,” Electron. Lett. 40, 1293–1294 (2004).
[CrossRef]

Zhang, J.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Zhang, J.-X.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef]

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K. Zhang and Z.-Y. Li, “Transfer behavior of quantum states between atoms in photonic crystal coupled cavities,” Phys. Rev. A 81, 033843 (2010).
[CrossRef]

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X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

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V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
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C. Wang, X.-L. Zhong, and Z.-Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 1–6 (2012).
[CrossRef]

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D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
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Figures (5)

Fig. 1.
Fig. 1.

Scheme of the atom–cavity coupling system. The atomic frequency is ω0 and the cavity-mode frequency ω0+δ. The cavity mode is coupled to the outside modes via two ports labeled 1 and 2 with coupling constants g1 and g2. The atom–cavity coupling strength is Ω.

Fig. 2.
Fig. 2.

(a) Transmittivities of the system T as a function of normalized detuning (Δ+δ)/k with nin=0.52. (b) ΔT as a function of (Δ+δ)/k under different operating power nin. (c) ΔT as a function of (Δ+δ)/k under different atomic dissipation γ1 by setting γ2=0. (d) ΔT as a function of (Δ+δ)/k under different cavitary dissipation γ2 by setting γ1=0. Other parameters are shown in figures.

Fig. 3.
Fig. 3.

Normalized saturation parameter x×k/k1 as a function of (Δ+δ)/k under different input powers in forward input case. We take δ=γ1=γ2=0 for convenience and fix k=40, Ω=4 to fulfill the Purcell regime condition.

Fig. 4.
Fig. 4.

Optimal input power nin-opt as a function of front mirror cavity-loss rate k1 in resonant case. Here Δ=δ=γ1=γ2=0, Ω=4, k=40, and k2=2kk1.

Fig. 5.
Fig. 5.

Optical nonreciprocal property ΔT as function of nin and k1 in the resonant case. Here, Δ=δ=γ1=γ2=0, Ω=4, k=40, and k2=2kk1.

Equations (27)

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H=ω0Sz+(ω0+δ)a+a+kωkbk+bk+lωlcl+cl+kg1(bk+a+a+bk)+lg2(cl+a+a+cl)+Ω(S+a+a+S).
s˙=(iΔγ1)sΓ2t0sk1ΩΓ2t0(2sz)bin,s˙z=[ΓRe(t0)2γ1](sz+12)(k1ΩΓ2t0s*bin+c.c),br=(1k1kt0)bink1kΓ2t0s,bt=k2kΓ2t0sk1k2kt0bin.
sz=1211+x,
x=ninPc.
Pc=kk1[γ1+ΓRe(t0)/2]2+[Δ+ΓIm(t0)/2]2Γ|t0|2.
t=k1k2kt0[1Γt0/2(1+x)(iΔ+γ1+Γt0/2)].
ΔT=|TforwardTbackward|.
CT=10×|log10(Tforward/Tbackward)|.
T=k1k2(k+γ2)2+Δ2.
T=k1k2(k+γ2+Ω2γ1Δ2+γ12)2+[(1Ω2Δ2+γ12)Δ+δ]2.
ΔT=16k1k2nin2k2[k12(kΓ+4k1nin)2k22(kΓ+4k2nin)2].
nin-opt=Ω221(k1/k2)2/3k2(k1/k2)2/3k1.
t=1i[,H].
S˙=iω0SiΩ(2Sz)a,S˙z=iΩS+a+iΩa+S,a˙=i(ω0+δ)aiΩSig1kbkig2lcl,b˙k=iωkbkig1a,c˙l=iωlclig2a.
bk(t)=bk(t0)eiωktig1t0tdua(u)eiωk(tu),cl(t)=cl(t0)eiωltig2t0tdua(u)eiωl(tu).
bin(t)=1τkkbk(t0)eiωk(tt0),bin(t)=1τlkcl(t0)eiωl(tt0),
jeiωjt=δ(t)τj.
kbk(t)=τkbin(t)i2g1τka(t),kcl(t)=τlbin(t)i2g2τla(t).
br(t)=1τkkbk(t0)eiωk(tt0),bt(t)=1τlkcl(t0)eiωl(tt0),
kbk(t)=τkbr(t)+i2g1τka(t),kcl(t)=τlbt(t)+i2g2τla(t).
br=binik1a.br=binik2a,
S˙=iΔSiΩ(2Sz)a,S˙z=iΩS+a+iΩa+S,a˙=i(Δ+δ)akaiΩSik1binik2bin,br=binigk1a,br=binik2a.
S˙=iΔSiΩ(2Sz)aγ1S,S˙z=iΩS+a+iΩa+Sγ1(2Sz+1),a˙=i(Δ+δ)akaiΩSik1binik2binγ2a,br=binik1a,br=bt=ik2a.
a=iΩsik1bini(Δ+δ)+k+γ2.
s˙=(iΔγ1)sΓ2t0sk1ΩΓ2t0(2sz)bin,s˙z=[ΓRe(t0)2γ1](sz+12)(k1ΩΓ2t0s+bin+c.c),br=(1k1kt0)bink1kΓ2t0s,bt=k2kΓ2t0sk1k2kt0bin.
t0=1/(1+iΔ+δk+γ2k).
s˙=(iΔγ1)sΓ2t0sk1ΩΓ2t0(2sz)bin,s˙z=[ΓRe(t0)2γ1](sz+12)(k1ΩΓ2t0s*bin+c.c),br=(1k1kt0)bink1kΓ2t0s,bt=k2kΓ2t0sk1k2kt0bin.

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