Abstract

Polarization-dependent photon switch is one of the most important ingredients in building future large-scale all-optical quantum network. We present a scheme for a single-photon switch in a one-dimensional coupled-resonator waveguide, where Na Λ-type three-level atoms are individually embedded in each of the resonator. By tuning the interaction between atom and field, we show that an initial incident photon with a certain polarization can be transformed into its orthogonal polarization state. Finally, we use the fidelity as a figure of merit and numerically evaluate the performance of our photon switch scheme in varieties of system parameters, such as number of atoms, energy detuning and dipole couplings.

© 2013 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  33. Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A83, 013825 (2011).
    [CrossRef]
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    [CrossRef]
  36. A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
    [CrossRef]
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    [CrossRef] [PubMed]
  38. T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A69, 063810 (2004).
    [CrossRef]

2012 (4)

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A86, 023824 (2012).
[CrossRef]

M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A85, 053840 (2012).
[CrossRef]

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
[CrossRef] [PubMed]

2011 (6)

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett.106, 160501 (2011).
[CrossRef] [PubMed]

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A83, 013825 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A83, 063828 (2011).
[CrossRef]

Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett.107, 173902 (2011).
[CrossRef] [PubMed]

D. Roy, “Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparency,” Phys. Rev. Lett.106, 053601 (2011).
[CrossRef] [PubMed]

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A84, 063832 (2011).
[CrossRef]

2010 (5)

D. Roy, “Few-photon optical diode,” Phys. Rev. B81, 155117 (2010).
[CrossRef]

D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys.12, 043052 (2010).
[CrossRef]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett.104, 023602 (2010).
[CrossRef]

L. Chirolli, G. Burkard, S. Kumar, and D. P. DiVincenzo, “Superconducting resonators as beam splitters for linear-optics quantum computation,” Phys. Rev. Lett.104, 230502 (2010).
[CrossRef] [PubMed]

2009 (1)

T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A80, 033823 (2009).
[CrossRef]

2008 (8)

T. S. Tsoi and C. K. Law, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A78, 063832 (2008).
[CrossRef]

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A77, 013831 (2008).
[CrossRef]

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel’ev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys.80, 1201–1213 (2008).
[CrossRef]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A78, 063827 (2008).
[CrossRef]

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A78, 053806 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett.101, 100501 (2008).
[CrossRef] [PubMed]

H. J. Kimble, “The quantum internet,” Nature453, 1023–1030 (2008).
[CrossRef] [PubMed]

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

2007 (5)

J.-T. Shen and S. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett.98, 153003 (2007).
[CrossRef] [PubMed]

J.-T. Shen and S. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A76, 062709 (2007).
[CrossRef]

M. Orrit, “Quantum light switch,” Nat. Phys.3, 755–756 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3, 807–812 (2007).
[CrossRef]

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

2006 (3)

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2, 849–855 (2006).
[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys.2, 856–861 (2006).
[CrossRef]

2005 (3)

J. T. Shen and S. Fan, “Coherent single photon Transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett.95, 213001 (2005).
[CrossRef] [PubMed]

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys.68, 1129–1179 (2005).
[CrossRef]

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

2004 (1)

T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A69, 063810 (2004).
[CrossRef]

2003 (1)

M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys.75, 457–472 (2003).
[CrossRef]

2001 (1)

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Ansmann, M.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Bertet, P.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Bialczak, R. C.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel’ev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys.80, 1201–1213 (2008).
[CrossRef]

Bliokh, Y. P.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel’ev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys.80, 1201–1213 (2008).
[CrossRef]

Bradford, M.

Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett.107, 173902 (2011).
[CrossRef] [PubMed]

Brandão, F. G. S. L.

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2, 849–855 (2006).
[CrossRef]

Brune, M.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Buckley, S.

S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
[CrossRef] [PubMed]

Burkard, G.

L. Chirolli, G. Burkard, S. Kumar, and D. P. DiVincenzo, “Superconducting resonators as beam splitters for linear-optics quantum computation,” Phys. Rev. Lett.104, 230502 (2010).
[CrossRef] [PubMed]

Busch, K.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A83, 063828 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett.104, 023602 (2010).
[CrossRef]

Chang, D. E.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3, 807–812 (2007).
[CrossRef]

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

Chang, Y.

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A83, 013825 (2011).
[CrossRef]

Chen, T. W.

T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A69, 063810 (2004).
[CrossRef]

Cheng, M. T.

M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A85, 053840 (2012).
[CrossRef]

Chirolli, L.

L. Chirolli, G. Burkard, S. Kumar, and D. P. DiVincenzo, “Superconducting resonators as beam splitters for linear-optics quantum computation,” Phys. Rev. Lett.104, 230502 (2010).
[CrossRef] [PubMed]

Cleland, A. N.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Cole, J. H.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys.2, 856–861 (2006).
[CrossRef]

Demler, E. A.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3, 807–812 (2007).
[CrossRef]

Ding, M. T.

M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A85, 053840 (2012).
[CrossRef]

DiVincenzo, D. P.

L. Chirolli, G. Burkard, S. Kumar, and D. P. DiVincenzo, “Superconducting resonators as beam splitters for linear-optics quantum computation,” Phys. Rev. Lett.104, 230502 (2010).
[CrossRef] [PubMed]

Dong, H.

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A78, 063827 (2008).
[CrossRef]

Dotsenko, I.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

Eto, Y.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett.106, 160501 (2011).
[CrossRef] [PubMed]

Fan, S.

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A84, 063832 (2011).
[CrossRef]

J.-T. Shen and S. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A76, 062709 (2007).
[CrossRef]

J.-T. Shen and S. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett.98, 153003 (2007).
[CrossRef] [PubMed]

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

J. T. Shen and S. Fan, “Coherent single photon Transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett.95, 213001 (2005).
[CrossRef] [PubMed]

Freilikher, V.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel’ev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys.80, 1201–1213 (2008).
[CrossRef]

Gao, Y. B.

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A77, 013831 (2008).
[CrossRef]

Gleyzes, S.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

Gong, Z. R.

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A83, 013825 (2011).
[CrossRef]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A78, 053806 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett.101, 100501 (2008).
[CrossRef] [PubMed]

Greentree, A. D.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys.2, 856–861 (2006).
[CrossRef]

Haroche, S.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Hartmann, M. J.

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2, 849–855 (2006).
[CrossRef]

Hemmer, P. R.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

Hijlkema, M.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

Hofheinz, M.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Hollenberg, L. C. L.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys.2, 856–861 (2006).
[CrossRef]

Ian, H.

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A78, 053806 (2008).
[CrossRef]

Kimble, H. J.

H. J. Kimble, “The quantum internet,” Nature453, 1023–1030 (2008).
[CrossRef] [PubMed]

Kocabas, S. E.

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A84, 063832 (2011).
[CrossRef]

Kozuma, M.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett.106, 160501 (2011).
[CrossRef] [PubMed]

Kuhn, A.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

Kumar, S.

L. Chirolli, G. Burkard, S. Kumar, and D. P. DiVincenzo, “Superconducting resonators as beam splitters for linear-optics quantum computation,” Phys. Rev. Lett.104, 230502 (2010).
[CrossRef] [PubMed]

Law, C. K.

T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A80, 033823 (2009).
[CrossRef]

T. S. Tsoi and C. K. Law, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A78, 063832 (2008).
[CrossRef]

T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A69, 063810 (2004).
[CrossRef]

Leung, P. T.

T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A69, 063810 (2004).
[CrossRef]

Li, Y.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A86, 023824 (2012).
[CrossRef]

Liao, J. Q.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

Liu, Y. X.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A78, 063827 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett.101, 100501 (2008).
[CrossRef] [PubMed]

Longo, P.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A83, 063828 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett.104, 023602 (2010).
[CrossRef]

Lounis, B.

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys.68, 1129–1179 (2005).
[CrossRef]

Lucero, E.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Lukin, M. D.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3, 807–812 (2007).
[CrossRef]

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys.75, 457–472 (2003).
[CrossRef]

Luo, Y. Q.

M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A85, 053840 (2012).
[CrossRef]

Ma, X. S.

M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A85, 053840 (2012).
[CrossRef]

Martinis, J. M.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Neeley, M.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Noguchi, A.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett.106, 160501 (2011).
[CrossRef] [PubMed]

Nogues, G.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Nori, F.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel’ev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys.80, 1201–1213 (2008).
[CrossRef]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A78, 063827 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett.101, 100501 (2008).
[CrossRef] [PubMed]

O’Connell, A. D.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Orrit, M.

M. Orrit, “Quantum light switch,” Nat. Phys.3, 755–756 (2007).
[CrossRef]

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys.68, 1129–1179 (2005).
[CrossRef]

Osnaghi, S.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Peaudecerf, B.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

Plenio, M. B.

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2, 849–855 (2006).
[CrossRef]

Raimond, J. M.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Rauschenbeutel, A.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A64, 050301(R)(2001).
[CrossRef]

Rempe, G.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

Rephaeli, E.

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A84, 063832 (2011).
[CrossRef]

Rivoire, K.

S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
[CrossRef] [PubMed]

Roy, D.

D. Roy, “Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparency,” Phys. Rev. Lett.106, 053601 (2011).
[CrossRef] [PubMed]

D. Roy, “Few-photon optical diode,” Phys. Rev. B81, 155117 (2010).
[CrossRef]

Rybarczyk, T.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

Savel’ev, S.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel’ev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys.80, 1201–1213 (2008).
[CrossRef]

Sayrin, C.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

Schmitteckert, P.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A83, 063828 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett.104, 023602 (2010).
[CrossRef]

Shen, J. T.

Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett.107, 173902 (2011).
[CrossRef] [PubMed]

J. T. Shen and S. Fan, “Coherent single photon Transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett.95, 213001 (2005).
[CrossRef] [PubMed]

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

Shen, J.-T.

J.-T. Shen and S. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett.98, 153003 (2007).
[CrossRef] [PubMed]

J.-T. Shen and S. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A76, 062709 (2007).
[CrossRef]

Shen, Y.

Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett.107, 173902 (2011).
[CrossRef] [PubMed]

Song, Z.

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A77, 013831 (2008).
[CrossRef]

Sorensen, A. S.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

Sørensen, A. S.

D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys.12, 043052 (2010).
[CrossRef]

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3, 807–812 (2007).
[CrossRef]

Specht, H. P.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

Sun, C. P.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A86, 023824 (2012).
[CrossRef]

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A83, 013825 (2011).
[CrossRef]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A78, 063827 (2008).
[CrossRef]

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A77, 013831 (2008).
[CrossRef]

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A78, 053806 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett.101, 100501 (2008).
[CrossRef] [PubMed]

Tahan, C.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys.2, 856–861 (2006).
[CrossRef]

Tsoi, T. S.

T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A80, 033823 (2009).
[CrossRef]

T. S. Tsoi and C. K. Law, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A78, 063832 (2008).
[CrossRef]

Ueda, M.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett.106, 160501 (2011).
[CrossRef] [PubMed]

Vuckovic, J.

S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
[CrossRef] [PubMed]

Wang, H.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Wang, Z. H.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A86, 023824 (2012).
[CrossRef]

Weber, B.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

Webster, S. C.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

Weig, E. M.

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Witthaut, D.

D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys.12, 043052 (2010).
[CrossRef]

Zhang, P.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A86, 023824 (2012).
[CrossRef]

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett.106, 160501 (2011).
[CrossRef] [PubMed]

Zhao, G. X.

M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A85, 053840 (2012).
[CrossRef]

Zhou, D. L.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A86, 023824 (2012).
[CrossRef]

Zhou, L.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A78, 063827 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett.101, 100501 (2008).
[CrossRef] [PubMed]

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A78, 053806 (2008).
[CrossRef]

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A77, 013831 (2008).
[CrossRef]

Zhou, X.

X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, “Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections,” Phys. Rev. Lett.108, 243602 (2012).
[CrossRef] [PubMed]

Nat. Phys. (4)

M. Orrit, “Quantum light switch,” Nat. Phys.3, 755–756 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3, 807–812 (2007).
[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys.2, 856–861 (2006).
[CrossRef]

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2, 849–855 (2006).
[CrossRef]

Nature (1)

H. J. Kimble, “The quantum internet,” Nature453, 1023–1030 (2008).
[CrossRef] [PubMed]

Nature (London) (1)

M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature (London)454, 310–314 (2008).
[CrossRef]

Nature Physics (1)

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Physics3, 253–255 (2007).
[CrossRef]

New J. Phys. (1)

D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys.12, 043052 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (14)

T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A80, 033823 (2009).
[CrossRef]

J.-T. Shen and S. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A76, 062709 (2007).
[CrossRef]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A78, 063827 (2008).
[CrossRef]

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A78, 053806 (2008).
[CrossRef]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A81, 042304 (2010).
[CrossRef]

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A84, 063832 (2011).
[CrossRef]

T. S. Tsoi and C. K. Law, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A78, 063832 (2008).
[CrossRef]

T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A69, 063810 (2004).
[CrossRef]

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A77, 013831 (2008).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic setup of the polarization-dependent photon switch. It consists of a coupled resonator waveguide with Na three-level atoms (a). The coupling between the resonator field and the Λ- type three-level atom is also shown in (b), where |e〉 represents the excitation state, and |H〉 and |V〉 are the degenerate ground states of the atom.

Fig. 2
Fig. 2

The transmission and reflection spectra as a function of the detuning Δ for the system with one atom serves as the scatterer. The values of the four coefficients are all equal to 0.25 at Δ = 0.

Fig. 3
Fig. 3

The transmission and reflection spectra (a) TH, (b) TV, (c) RH, and (d) RV as a function of the detuning Δ with different atom numbers Na, where Na = 2 (red lines), Na = 4 (green lines), and Na = 8 (blue lines).

Fig. 4
Fig. 4

The transmission and reflection spectra (a) TH, (b) TV, (c) RH, (d) RV, and (e) TH + TV + RH + RV as a function of the detuning Δ when the system is interacting with the environment. The red solid lines is for γc = γa = 0, the green dashed lines is for γc = 0.1, γa = 0.2, and the blue dashed lines is for γc = 0.1, γa = 0.4.

Fig. 5
Fig. 5

The as a function of detuning Δ with Na = 1, 2, 4, 8, 16, 32. The red lines represent the fidelity of the system without dissipation. The blue dashed lines represent the fidelity of the system in a more realistic circumstance, in which the atomic decay and the loss of resonators are considered.

Fig. 6
Fig. 6

The transmission spectra (a) TH, (b) TV, and the fidelity (c) as a function of the number of atoms. The blue squares and red circles represent the values of functions with and without dissipation respectively. The other system parameters are chosen as gH = gV = 1, ω = 5, Ω = 6, ξ = −1, γc = 0.15, and γa = 0.3.

Fig. 7
Fig. 7

Phase diagrams of the fidelity spectrum with respect to the detuning Δ and the dipole coupling constants (a) gV and (b) gH with Na = 8.

Fig. 8
Fig. 8

Phase diagram of the fidelity spectrum with respect to the dipole coupling constants gV and gH for Na = 8 and Δ = −1.

Equations (43)

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H CRW = ω s = H , V j = 1 N a j , s a j , s + ξ s = H , V j = 1 N ( a j , s a j + 1 , s + a j + 1 , s a j , s ) ,
H I , j = Ω | e j , j e | + s = H , V g s ( a j , s | s j , j e | + a j , s | e j , j s | ) ,
| E = j = N N s = H , V u j s | j s | s 1 + u 1 e | 0 | e 1 ,
ω u j s + ξ ( u j + 1 s + u j 1 s ) + δ j , 1 g s u 1 e = E u j s ,
Ω u 1 e + s g s u 1 s = E u 1 e .
ω u j s + ξ ( u j + 1 s + u j 1 s ) + δ j , 1 g s ω ( E ) ( g H u 1 H + g V u 1 V ) = E u j s .
u j H = { e i k j + r H e i k j , j < 1 t H e i k j , j > 1
u j V = { r V e i k j , j < 1 t V e i k j , j > 1
E = ω + 2 ξ cos k ,
u 1 H = e i k + r H e i k = t H e i k ,
u 1 V = r V e i k = t V e i k .
ω u 1 H + ξ ( t H e i k 2 + 1 + r H ) + ω ( E ) ( g H 2 u 1 H + g H g V u 1 V ) = E k u 1 H ,
ω u 1 V + ξ ( t V e i k 2 + r V ) + ω ( E ) ( g V g H u 1 H + g V 2 u 1 V ) = E k u 1 V .
t H = 2 i ξ Δ sin k + g V 2 2 i ξ Δ sin k + g H 2 + g V 2 ,
r H = g H 2 e 2 i k 2 i ξ Δ sin k + g H 2 + g V 2 ,
t V = r V e 2 i k = g V g H 2 i ξ Δ sin k + g H 2 + g V 2 .
| E = j = N N u j H | j H | H + j = N N l = 1 N a u j , l V | j V | V l + l = 1 N a u l e | 0 | e ,
| H = j = 1 N a | H j , | V l = j = 1 , j 1 N a | H j | V l , | e = j = 1 , j l N a | H j | e l .
ω u j H + ξ ( u j + 1 H + u j 1 H ) + l = 1 N a δ j , l g H u l e = E u j H ,
ω u j , l V + ξ ( u j + 1 , l V + u j 1 , l V ) + δ j , l g V u l e = E u j , l V ,
Ω u l e + g H u l H + g V u l , l V = E u l e ,
ω u j H + ξ ( u j + 1 H + u j 1 H ) + l = 1 N a δ j , l ω ( E ) g H ( g H u l H + g V u l , l V ) = E u j H ,
ω u j , l V + ξ ( u j + 1 , l V + u j 1 , l V ) + δ j , l ω ( E ) g V ( g H u l H + g V u l , l V ) = E u j , l V ,
u j H = { e i k j + r H e i k j , j < 1 t H e i k j + r H e i k j , j = 1 , , N a t H e i k j , j > N a
u j V = { r V , l e i k j , j < l t V , l e i k j , j > l
cos k = cos k i ω ( E ) g H 2 sin k 2 i ξ sin k + ω ( E ) g V 2 .
t H = 2 D i sin k ( A 1 B ) 2 D 2 e i k ( N a 1 ) ,
r H = ( A 2 B ) ( A 1 B ) D 2 ( A 1 B ) 2 D 2 e 2 i k ,
t V , l e i k l = r V , l e i k l = 2 i ω ( E ) g V g H e i k sin k { D sin [ k ( l 1 ) ] + ( A 1 B ) sin [ k ( N a l ) ] } sin [ k ( N a 1 ) ] [ 2 ξ i sin k + ω ( E ) g V 2 ] [ ( A 1 B ) 2 D 2 ] ,
A 1 = e i k ω ( E ) ξ g H 2 sin [ k ( N a 2 ) ] sin [ k ( N a 1 ) ] ,
A 2 = e i k ω ( E ) ξ g H 2 sin [ k ( N a 2 ) ] sin [ k ( N a 1 ) ] ,
B = g H 2 g V 2 ω 2 ( E ) 2 i ξ 2 sin k + ξ ω ( E ) g V 2 ,
D = sin k sin [ k ( N a 1 ) ] .
| t H | 2 + | r H | 2 + l = 1 N a ( | t V , l | 2 + | r V , l | 2 ) = 1
cos k L = cos k i ω ( E L ) g H 2 sin k 2 i ξ sin k + ω ( E L ) g V 2 .
T H L = | 2 D L sin k ( A 1 , L B L ) 2 D L 2 | 2 ,
R H L = | ( A 2 , L B L ) ( A 1 , L B L ) D L 2 ( A 1 , L B L ) 2 D L 2 | 2 ,
T V L = R V L = l = 1 N a | 2 ω ( E L ) g V g H sin k { D L sin [ k L ( l 1 ) ] + ( A 1 , L B L ) sin [ k L ( N a l ) ] } sin [ k L ( N a 1 ) ] [ 2 ξ i sin k + ω ( E L ) g V 2 ] [ ( A 1 , L B L ) 2 D L 2 ] | ,
A 1 , L = e i k ω ( E L ) ξ g H 2 sin [ k L ( N a 2 ) ] sin [ k L ( N a 1 ) ] ,
A 2 , L = e i k ω ( E L ) ξ g H 2 sin [ k L ( N a 2 ) ] sin [ k L ( N a 1 ) ] ,
B L = g H 2 g V 2 ω 2 ( E L ) 2 i ξ 2 sin k + ξ ω ( E L ) g V 2 ,
D L = sin k L sin [ k L ( N a 1 ) ] .
= T V T H + T V ,

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