Abstract

We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in a driven three-level superconducting artificial system which is a dressed-state system resulting from the coupling of a superconducting charge qubit (an artificial atom) and a transmission line resonator. In the frame of the dressed-state approach and steady-state approximation, we study the linear absorption of the dressed artificial system to a weak probe signal in depth. In light of the spectrum-decomposition method and some other restrictions, we obtain the explicit conditions for the dressed-state realization of EIT and ATS and present a corresponding “phase diagram”. In contrast to usual bare systems, these conditions given in the dressed system have an extra dependency on the qubit-resonator parameters. And by varying the qubit’s Josephson coupling energy we demonstrate a transition from EIT to ATS.

© 2015 Optical Society of America

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  1. K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [Crossref] [PubMed]
  2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [Crossref]
  3. O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
    [Crossref]
  4. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [Crossref] [PubMed]
  5. M. Fleischhauer and A. S. Manka, “Propagation of laser pulses and coherent population transfer in dissipative three-level systems: an adiabatic dressed-state picture,” Phys. Rev. A 54, 794–803 (1996).
    [Crossref] [PubMed]
  6. C. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions: Basic Principles and Applications (Wiley, 1998).
    [Crossref]
  7. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
    [Crossref] [PubMed]
  8. J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
    [Crossref] [PubMed]
  9. J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58, 42–47 (2005).
    [Crossref]
  10. J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
    [Crossref] [PubMed]
  11. T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
    [Crossref]
  12. Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
    [Crossref] [PubMed]
  13. Y. X. Liu, C. Yang, H. Sun, and X. Wang, “Coexistence of single- and multi-photon processes due to longitudinal couplings between superconducting flux qubits and external fields”, New J. Phys. 16, 015301 (2014).
    [Crossref]
  14. G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
    [Crossref] [PubMed]
  15. Y. X. Liu, C. P. Sun, and F. Nori, “Scalable superconducting qubit circuits using dressed states,” Phys. Rev. A 74, 052321 (2006).
    [Crossref]
  16. H. C. Li, G. Q. Ge, and S. B. Feng, “Dressed Zeno effect in circuit quantum electrodynamics,” Phys. Rev. A 89, 062119 (2014).
    [Crossref]
  17. G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
    [Crossref]
  18. G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
    [Crossref] [PubMed]
  19. S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
    [Crossref]
  20. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [Crossref]
  21. P. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
    [Crossref] [PubMed]
  22. B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
    [Crossref] [PubMed]
  23. P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level system,” J. Mod. Opt. 55, 3159–3171 (2008).
    [Crossref]
  24. T.Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81, 053836 (2010).
    [Crossref]
  25. A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
    [Crossref]
  26. K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
    [Crossref] [PubMed]
  27. J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
    [Crossref] [PubMed]

2014 (3)

Y. X. Liu, C. Yang, H. Sun, and X. Wang, “Coexistence of single- and multi-photon processes due to longitudinal couplings between superconducting flux qubits and external fields”, New J. Phys. 16, 015301 (2014).
[Crossref]

H. C. Li, G. Q. Ge, and S. B. Feng, “Dressed Zeno effect in circuit quantum electrodynamics,” Phys. Rev. A 89, 062119 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

2013 (3)

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

2011 (3)

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
[Crossref] [PubMed]

P. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
[Crossref] [PubMed]

2010 (2)

T.Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81, 053836 (2010).
[Crossref]

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

2008 (3)

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level system,” J. Mod. Opt. 55, 3159–3171 (2008).
[Crossref]

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[Crossref] [PubMed]

2006 (1)

Y. X. Liu, C. P. Sun, and F. Nori, “Scalable superconducting qubit circuits using dressed states,” Phys. Rev. A 74, 052321 (2006).
[Crossref]

2005 (3)

Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
[Crossref] [PubMed]

J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58, 42–47 (2005).
[Crossref]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

2004 (2)

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

2001 (1)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

1996 (1)

M. Fleischhauer and A. S. Manka, “Propagation of laser pulses and coherent population transfer in dissipative three-level systems: an adiabatic dressed-state picture,” Phys. Rev. A 54, 794–803 (1996).
[Crossref] [PubMed]

1992 (1)

O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
[Crossref]

1991 (1)

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

1955 (1)

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
[Crossref]

Abi-Salloum, T.Y.

T.Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81, 053836 (2010).
[Crossref]

Anisimov, P.

P. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
[Crossref] [PubMed]

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level system,” J. Mod. Opt. 55, 3159–3171 (2008).
[Crossref]

Astafiev, O. V.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Autler, S. H.

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
[Crossref]

Baur, M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

Bianchetti, R.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

Blais, A.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Chen, J.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Chen, W.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Clarke, J.

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[Crossref] [PubMed]

Coen-Tannoudji, C.

C. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions: Basic Principles and Applications (Wiley, 1998).
[Crossref]

Deppe, F.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Dowling, J. P.

P. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
[Crossref] [PubMed]

Dupont-Rock, J.

C. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions: Basic Principles and Applications (Wiley, 1998).
[Crossref]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Feng, S. B.

H. C. Li, G. Q. Ge, and S. B. Feng, “Dressed Zeno effect in circuit quantum electrodynamics,” Phys. Rev. A 89, 062119 (2014).
[Crossref]

Fink, J. M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

M. Fleischhauer and A. S. Manka, “Propagation of laser pulses and coherent population transfer in dissipative three-level systems: an adiabatic dressed-state picture,” Phys. Rev. A 54, 794–803 (1996).
[Crossref] [PubMed]

Frunzio, L.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

Garcia-Ripoll, J. J.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Ge, G. Q.

H. C. Li, G. Q. Ge, and S. B. Feng, “Dressed Zeno effect in circuit quantum electrodynamics,” Phys. Rev. A 89, 062119 (2014).
[Crossref]

Ginossar, E.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Girvin, S. M.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

Göppl, M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

Grajcar, M.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Gross, R.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Grynberg, G.

C. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions: Basic Principles and Applications (Wiley, 1998).
[Crossref]

Han, S.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Harris, S. E.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

Himmer, T.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Hocke, F.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Huang, R. S.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

Hübner, U.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Huebl, H.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Il’ichev, E.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Inomata, K.

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Ivanov, B. I.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Kang, L.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Kirchmair, G.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Kocharovskaya, O.

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level system,” J. Mod. Opt. 55, 3159–3171 (2008).
[Crossref]

O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
[Crossref]

Koshino, K.

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Kumar, S.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

Leek, P. J.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

Leghtas, Z.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Li, H. C.

H. C. Li, G. Q. Ge, and S. B. Feng, “Dressed Zeno effect in circuit quantum electrodynamics,” Phys. Rev. A 89, 062119 (2014).
[Crossref]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

Liu, Y. X.

Y. X. Liu, C. Yang, H. Sun, and X. Wang, “Coexistence of single- and multi-photon processes due to longitudinal couplings between superconducting flux qubits and external fields”, New J. Phys. 16, 015301 (2014).
[Crossref]

Y. X. Liu, C. P. Sun, and F. Nori, “Scalable superconducting qubit circuits using dressed states,” Phys. Rev. A 74, 052321 (2006).
[Crossref]

Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
[Crossref] [PubMed]

Macha, P.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Majer, J.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

Manka, A. S.

M. Fleischhauer and A. S. Manka, “Propagation of laser pulses and coherent population transfer in dissipative three-level systems: an adiabatic dressed-state picture,” Phys. Rev. A 54, 794–803 (1996).
[Crossref] [PubMed]

Mao, B.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Marx, A.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Menzel, E. P.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Meyer, H.-G.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Mirrahimi, M.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Nakamura, Y.

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Neilinger, P.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Niemczyk, T.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Nigg, S. E.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Nori, F.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
[Crossref] [PubMed]

Y. X. Liu, C. P. Sun, and F. Nori, “Scalable superconducting qubit circuits using dressed states,” Phys. Rev. A 74, 052321 (2006).
[Crossref]

Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
[Crossref] [PubMed]

J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58, 42–47 (2005).
[Crossref]

Oelsner, G.

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

Özdemir, S. K.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Paik, H.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Peng, B.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Qiu, W.

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Sanders, B. C.

P. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
[Crossref] [PubMed]

Schoelkopf, R. J.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

Schuster, D. I.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

Schwarz, M. J.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Solano, E.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Sun, C. P.

Y. X. Liu, C. P. Sun, and F. Nori, “Scalable superconducting qubit circuits using dressed states,” Phys. Rev. A 74, 052321 (2006).
[Crossref]

Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
[Crossref] [PubMed]

Sun, G.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Sun, H.

Y. X. Liu, C. Yang, H. Sun, and X. Wang, “Coexistence of single- and multi-photon processes due to longitudinal couplings between superconducting flux qubits and external fields”, New J. Phys. 16, 015301 (2014).
[Crossref]

Terai, H.

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Townes, C. H.

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
[Crossref]

Vlastakis, B.

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Wallraff, A.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

Wang, X.

Y. X. Liu, C. Yang, H. Sun, and X. Wang, “Coexistence of single- and multi-photon processes due to longitudinal couplings between superconducting flux qubits and external fields”, New J. Phys. 16, 015301 (2014).
[Crossref]

Wang, Z.

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Wei, L. F.

Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
[Crossref] [PubMed]

Wen, X.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Wilhelm, F. K.

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[Crossref] [PubMed]

Wu, P.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Xu, W.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Yamamoto, T.

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Yang, C.

Y. X. Liu, C. Yang, H. Sun, and X. Wang, “Coexistence of single- and multi-photon processes due to longitudinal couplings between superconducting flux qubits and external fields”, New J. Phys. 16, 015301 (2014).
[Crossref]

Yang, L.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

You, J. Q.

J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
[Crossref] [PubMed]

J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58, 42–47 (2005).
[Crossref]

Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
[Crossref] [PubMed]

Yu, Y.

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Zueco, D.

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

J. Mod. Opt. (1)

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level system,” J. Mod. Opt. 55, 3159–3171 (2008).
[Crossref]

Nat. Commun. (1)

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Nature (6)

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the JaynesCCummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454315–318 (2008).
[Crossref] [PubMed]

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–166 (2004).
[Crossref] [PubMed]

J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
[Crossref] [PubMed]

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[Crossref] [PubMed]

G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Observation of quantum state collapse and revival due to the single-photon Kerr effect,” Nature 495, 205–209 (2013).
[Crossref] [PubMed]

Nature Phys. (1)

T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Himmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

New J. Phys. (1)

Y. X. Liu, C. Yang, H. Sun, and X. Wang, “Coexistence of single- and multi-photon processes due to longitudinal couplings between superconducting flux qubits and external fields”, New J. Phys. 16, 015301 (2014).
[Crossref]

Phys. Rep. (1)

O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
[Crossref]

Phys. Rev. (2)

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
[Crossref]

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Phys. Rev. A (5)

Y. X. Liu, C. P. Sun, and F. Nori, “Scalable superconducting qubit circuits using dressed states,” Phys. Rev. A 74, 052321 (2006).
[Crossref]

H. C. Li, G. Q. Ge, and S. B. Feng, “Dressed Zeno effect in circuit quantum electrodynamics,” Phys. Rev. A 89, 062119 (2014).
[Crossref]

M. Fleischhauer and A. S. Manka, “Propagation of laser pulses and coherent population transfer in dissipative three-level systems: an adiabatic dressed-state picture,” Phys. Rev. A 54, 794–803 (1996).
[Crossref] [PubMed]

T.Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81, 053836 (2010).
[Crossref]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[Crossref]

Phys. Rev. B (1)

G. Sun, X. Wen, B. Mao, Y. Yu, J. Chen, W. Xu, L. Kang, P. Wu, and S. Han, “Landau-Zener-Stückelberg interference of microwave-dressed states of a superconducting phase qubit,” Phys. Rev. B 83, 180507(R) (2011).
[Crossref]

Phys. Rev. Lett. (5)

G. Oelsner, P. Macha, O. V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, “Dressed-state amplification by a single superconducting qubit,” Phys. Rev. Lett. 110, 053602 (2013).
[Crossref] [PubMed]

P. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
[Crossref] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Y. X. Liu, J. Q. You, L. F. Wei, C. P. Sun, and F. Nori, “Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit,” Phys. Rev. Lett. 95, 087001 (2005).
[Crossref] [PubMed]

K. Koshino, H. Terai, K. Inomata, T. Yamamoto, W. Qiu, Z. Wang, and Y. Nakamura, “Observation of the three-state dressed states in circuit quantum electrodynamics,” Phys. Rev. Lett. 110, 263601 (2013).
[Crossref] [PubMed]

Phys. Today (1)

J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58, 42–47 (2005).
[Crossref]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Other (1)

C. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions: Basic Principles and Applications (Wiley, 1998).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Schematic of a dressed three-level Λ-type system with a probe field ωp and a control field ωc driving the |−, 1〉 |−, 0〉 and |−, 1〉 |+, 0〉 transitions.
Fig. 2
Fig. 2 (a) Peak, EIT and ATS regions divided by two reduced threshold factors 1 − Γ and 2 Γ Γ 1 + 2 Γ . The yellow (green) region denotes the EIT (ATS) regime while the purple area represents single absorption peak. (b) Coupling coefficient sinθ1 sinθ0 of the control field as a function of the Josephson coupling energy EJ for = 0.008ωr.
Fig. 3
Fig. 3 Imaginary part of the matrix element ρ 1 ( 1 ) (red solid line) and two Lorentzians β+ p ) (blue dashed line) and β p ) (black dashed-dotted line) as a function of the probe field detuning Δ p for different values of the Josephson coupling energy EJ. (a) EJ = 1.025ωr and Γ+− = 0.2Γ1−, (b) EJ = 1.005ωr and Γ+− = 0.2Γ1−, (c) EJ = 0.95ωr and Γ+− = 0.2Γ1− and (d) EJ = 1.005ωr and Γ+− = 0.01Γ1−. The other parameters are = 0.008ωr and Ω c = 1.5Γ1−.

Equations (16)

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H = ω r a a + 1 2 E J σ s + ( a σ + a σ + ) ,
| + , n = cos θ n | e , n | + sin θ n | g , n + 1 ,
| , n = sin θ n | e , n + cos θ n | g , n + 1 ,
E ± , n = ( n + 1 2 ) ω r ± 1 2 ( E J ω r ) 2 + 4 2 ( n + 1 ) ,
θ n = 1 2 tan 1 ( 2 n + 1 E J ω r ) .
H 1 = ( Ω c cos ω c t + Ω p cos ω p t ) ( | e g | + | g e | ) .
σ + = n | e , n g , n | = n { sin θ n + 1 cos θ n | , n + 1 , n | + cos θ n + 1 sin θ n | + , n + 1 + , n | + cos θ n cos θ n | + , n + 1 , n | sin θ n + 1 sin θ n | , n + 1 + , n | } .
H T = E , 0 | | + E + , 0 | + + | + E , 1 | 1 1 | ξ p cos ω p t ( | 1 | + | 1 | ) ξ c cos ω c t ( | 1 + | + | + 1 | ) .
H I = Δ p | 1 1 | + ( Δ p Δ c ) | + + | 1 2 ξ p ( | 1 | + | 1 | ) 1 2 ξ c ( | 1 + | + | + 1 | ) ,
ρ 1 ( 1 ) = i ξ p 2 Γ + + i Δ p ( Γ + + i Δ p ) ( Γ 1 + i Δ p ) + | ξ c | 2 / 4 ,
ρ 1 ( 1 ) = β + ( Δ p ) + β ( Δ p ) = 1 2 ( Δ + Δ ) Δ + i Γ + Δ p Δ + 1 2 ( Δ + Δ ) Δ i Γ + Δ p Δ ,
Δ ± = 1 2 [ i ( Γ + + Γ 1 ) ± | ξ c | 2 ( Γ 1 Γ + ) 2 ] .
2 Γ 1 ( Γ 1 Γ + + ξ c 2 / 4 ) Γ + ( 2 Γ 1 2 + 2 Γ + 2 ξ c 2 ) > 0 .
absorption peak : Γ 1 > 2 Γ + , sin θ 1 sin θ 0 Ω c < 2 Γ + Γ + Γ 1 + 2 Γ + ,
EIT dip : Γ 1 > 2 Γ + , 2 Γ + Γ + Γ 1 + 2 Γ + < sin θ 1 sin θ 0 Ω c < Γ 1 Γ + ,
ATS dip : Γ 1 > 2 Γ + , sin θ 1 sin θ 0 Ω c > Γ 1 Γ + .

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