Abstract

We investigate theoretically the model of two “qubits” system (one qubit having an auxiliary level) interacting with a single-mode resonator in the ultrastrong coupling regime. We show that a single photon could simultaneously excite two qubits without breaking the parity symmetry of system by properly encoding the excited states of qubits. The optimal parameter regime for achieving high probability approaching one is identified in the case of ignoring the system dissipation. Moreover, using experimentally feasible parameters, we also analyze the dissipation dynamics of the system, and present the realization of two-qubit excitation induced by single-photon. This work offers an alternative approach to realize the single-photon-induced two qubits excitation, which should advance the development of single-photon quantum technologies and have potential applications in quantum information science.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Dissipative preparation of distributed steady entanglement: an approach of unilateral qubit driving

Zhao Jin, Shi-Lei Su, Ai-Dong Zhu, Hong-Fu Wang, and Shou Zhang
Opt. Express 25(1) 88-101 (2017)

Preparation of two-qubit steady entanglement through driving a single qubit

Li-Tuo Shen, Rong-Xin Chen, Zhen-Biao Yang, Huai-Zhi Wu, and Shi-Biao Zheng
Opt. Lett. 39(20) 6046-6049 (2014)

Distributed manipulation of two-qubit entanglement with coupled continuous variables

Li-Tuo Shen, Rong-Xin Chen, Huai-Zhi Wu, and Zhen-Biao Yang
J. Opt. Soc. Am. B 32(2) 297-302 (2015)

References

  • View by:
  • |
  • |
  • |

  1. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1992).
  2. S. M. Dutra, Cavity quantum electrodynamics: the strange theory of light in a box (John Wiley & Sons, Inc, 2005).
  3. S. Haroche, “Nobel lecture: Controlling photons in a box and exploring the quantum to classical boundry,” Rev. Mod. Phys. 85, 1083 (2013).
    [Crossref]
  4. S. Haroche, M. Brune, and J. M. Raimond, “Atomic clocks for controlling light fields,” Phys. Today 66(1), 27 (2013).
    [Crossref]
  5. P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
    [Crossref]
  6. G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
    [Crossref]
  7. T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. García-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrostrong-coupling regime,” Nat. Phys. 6, 772–776 (2010).
    [Crossref]
  8. T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Phys. Rev. Lett. 106, 196405 (2011).
    [Crossref] [PubMed]
  9. M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
    [Crossref] [PubMed]
  10. G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
    [Crossref] [PubMed]
  11. S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
    [Crossref]
  12. M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
    [Crossref]
  13. C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
    [Crossref]
  14. T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. García-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nat. Phys. 6, 772–776 (2010).
    [Crossref]
  15. P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
    [Crossref]
  16. P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
    [Crossref] [PubMed]
  17. A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
    [Crossref] [PubMed]
  18. P. Zhao, X. S. Tan, H. F. Yu, S. L. Zhu, and Y. Yu, “Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange,” https://arXiv:1706.08083 (2017).
  19. S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Phys. Rev. A 81, 042311 (2010).
    [Crossref]
  20. F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
    [Crossref]
  21. F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
    [Crossref]
  22. K. K. W. Ma and C. K. Law, “Three-photon resonance and adiabatic passage in the large-detuning Rabi model,” Phys. Rev. A 92, 023842 (2015).
    [Crossref]
  23. L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
    [Crossref] [PubMed]
  24. J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
    [Crossref] [PubMed]
  25. M. H. Devoret and R. J. Schoelkopf, “Superconducting Circuits for Quantum Information: An Outlook,” Science 339, 1169–1174 (2013).
    [Crossref] [PubMed]
  26. S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
    [Crossref] [PubMed]
  27. M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
    [Crossref] [PubMed]
  28. Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
    [Crossref]
  29. M. O. Scully, “Collective Lamb Shift in Single Photon Dicke Superradiance,” Phys. Rev. Lett. 102, 143601 (2009).
    [Crossref] [PubMed]
  30. R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
    [Crossref] [PubMed]
  31. Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
    [Crossref]
  32. G. Y. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, “Circuit QED with fluxonium qubits: Theory of the dispersive regime,” Phys. Rev. B 87, 024501 (2013).
    [Crossref]
  33. L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
    [Crossref]
  34. S. De Liberato, D. Gerace, I. Carusotto, and C. Ciut, “Extracavity quantum vacuum radiation from a single qubit,” Phys. Rev. A 80, 053810 (2009).
    [Crossref]
  35. Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
    [Crossref]
  36. X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
    [Crossref]
  37. X. Cao, J. Q. You, H. Zheng, and F. Nori, “A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation,” New J. Phys. 13, 073002 (2011).
    [Crossref]
  38. R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
    [Crossref] [PubMed]
  39. A. Ridolfo, S. Savasta, and M. J. Hartmann, “Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 110, 163601 (2015).
    [Crossref]
  40. L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
    [Crossref]
  41. J. F. Huang and C. K. Law, “Photon emission via vacuum-dressed intermediate states under ultrastrong coupling,” Phys. Rev. A 89, 033827 (2014).
    [Crossref]
  42. Y. J. Zhao, Y. L. Liu, Y. X. Liu, and F. Nori, “Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields,” Phys. Rev. A 91, 053820 (2015).
    [Crossref]
  43. J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
    [Crossref]
  44. D. Braak, “Integrability of the Rabi Model,” Phys. Rev. Lett. 107, 100401 (2011).
    [Crossref] [PubMed]
  45. M. J. Hwang, R. Puebla, and M. B. Plenio, “Quantum Phase Transition and Universal Dynamics in the Rabi Model,” Phys. Rev. Lett. 115, 180404 (2015).
    [Crossref] [PubMed]
  46. 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]
  47. F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
    [Crossref]
  48. J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, “Rabi Oscillations in a Large Josephson-Junction Qubit Phys,” Rev. Lett. 89, 117901 (2002).
    [Crossref]
  49. J. Joo, J. Bourassa, A. Blais, and B. C. Sanders, “Electromagnetically Induced Transparency with Amplification in Superconducting Circuits,” Phys. Rev. Lett. 105, 073601 (2010).
    [Crossref] [PubMed]
  50. J. Q. You, X. Hu, S. Ashhab, and F. Nori, “Low-decoherence flux qubit,” Phys. Rev. B 75, 140515 (2007).
    [Crossref]
  51. M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
    [Crossref] [PubMed]
  52. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
    [Crossref]
  53. X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
    [Crossref]
  54. J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
    [Crossref]
  55. A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon Blockade in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 109, 193602 (2012).
    [Crossref] [PubMed]

2017 (2)

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

2016 (2)

P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
[Crossref] [PubMed]

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

2015 (5)

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

K. K. W. Ma and C. K. Law, “Three-photon resonance and adiabatic passage in the large-detuning Rabi model,” Phys. Rev. A 92, 023842 (2015).
[Crossref]

A. Ridolfo, S. Savasta, and M. J. Hartmann, “Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 110, 163601 (2015).
[Crossref]

Y. J. Zhao, Y. L. Liu, Y. X. Liu, and F. Nori, “Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields,” Phys. Rev. A 91, 053820 (2015).
[Crossref]

M. J. Hwang, R. Puebla, and M. B. Plenio, “Quantum Phase Transition and Universal Dynamics in the Rabi Model,” Phys. Rev. Lett. 115, 180404 (2015).
[Crossref] [PubMed]

2014 (5)

L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
[Crossref]

J. F. Huang and C. K. Law, “Photon emission via vacuum-dressed intermediate states under ultrastrong coupling,” Phys. Rev. A 89, 033827 (2014).
[Crossref]

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

2013 (6)

S. Haroche, “Nobel lecture: Controlling photons in a box and exploring the quantum to classical boundry,” Rev. Mod. Phys. 85, 1083 (2013).
[Crossref]

S. Haroche, M. Brune, and J. M. Raimond, “Atomic clocks for controlling light fields,” Phys. Today 66(1), 27 (2013).
[Crossref]

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[Crossref]

G. Y. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, “Circuit QED with fluxonium qubits: Theory of the dispersive regime,” Phys. Rev. B 87, 024501 (2013).
[Crossref]

R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
[Crossref] [PubMed]

M. H. Devoret and R. J. Schoelkopf, “Superconducting Circuits for Quantum Information: An Outlook,” Science 339, 1169–1174 (2013).
[Crossref] [PubMed]

2012 (5)

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
[Crossref]

A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon Blockade in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 109, 193602 (2012).
[Crossref] [PubMed]

2011 (5)

D. Braak, “Integrability of the Rabi Model,” Phys. Rev. Lett. 107, 100401 (2011).
[Crossref] [PubMed]

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

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

X. Cao, J. Q. You, H. Zheng, and F. Nori, “A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation,” New J. Phys. 13, 073002 (2011).
[Crossref]

2010 (12)

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[Crossref]

X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
[Crossref]

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
[Crossref] [PubMed]

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

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

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

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Phys. Rev. A 81, 042311 (2010).
[Crossref]

J. Joo, J. Bourassa, A. Blais, and B. C. Sanders, “Electromagnetically Induced Transparency with Amplification in Superconducting Circuits,” Phys. Rev. Lett. 105, 073601 (2010).
[Crossref] [PubMed]

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
[Crossref]

2009 (4)

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

M. O. Scully, “Collective Lamb Shift in Single Photon Dicke Superradiance,” Phys. Rev. Lett. 102, 143601 (2009).
[Crossref] [PubMed]

S. De Liberato, D. Gerace, I. Carusotto, and C. Ciut, “Extracavity quantum vacuum radiation from a single qubit,” Phys. Rev. A 80, 053810 (2009).
[Crossref]

2008 (2)

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

2007 (2)

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

J. Q. You, X. Hu, S. Ashhab, and F. Nori, “Low-decoherence flux qubit,” Phys. Rev. B 75, 140515 (2007).
[Crossref]

2005 (1)

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]

2002 (1)

J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, “Rabi Oscillations in a Large Josephson-Junction Qubit Phys,” Rev. Lett. 89, 117901 (2002).
[Crossref]

Ai, Q.

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[Crossref]

Anappara, A. A.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Ansmann, M.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Ashhab, S

X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
[Crossref]

Ashhab, S.

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Phys. Rev. A 81, 042311 (2010).
[Crossref]

J. Q. You, X. Hu, S. Ashhab, and F. Nori, “Low-decoherence flux qubit,” Phys. Rev. B 75, 140515 (2007).
[Crossref]

Aumentado, J.

J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, “Rabi Oscillations in a Large Josephson-Junction Qubit Phys,” Rev. Lett. 89, 117901 (2002).
[Crossref]

Ballarini, D.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Beck, M.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

Bernu, J.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Bialczak, R. C.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Biasiol, G.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Blais, A.

J. Joo, J. Bourassa, A. Blais, and B. C. Sanders, “Electromagnetically Induced Transparency with Amplification in Superconducting Circuits,” Phys. Rev. Lett. 105, 073601 (2010).
[Crossref] [PubMed]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Bourassa, J.

J. Joo, J. Bourassa, A. Blais, and B. C. Sanders, “Electromagnetically Induced Transparency with Amplification in Superconducting Circuits,” Phys. Rev. Lett. 105, 073601 (2010).
[Crossref] [PubMed]

Braak, D.

D. Braak, “Integrability of the Rabi Model,” Phys. Rev. Lett. 107, 100401 (2011).
[Crossref] [PubMed]

Brune, M.

S. Haroche, M. Brune, and J. M. Raimond, “Atomic clocks for controlling light fields,” Phys. Today 66(1), 27 (2013).
[Crossref]

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Cao, X.

X. Cao, J. Q. You, H. Zheng, and F. Nori, “A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation,” New J. Phys. 13, 073002 (2011).
[Crossref]

Cao, X. F.

X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
[Crossref]

Carusotto, I.

S. De Liberato, D. Gerace, I. Carusotto, and C. Ciut, “Extracavity quantum vacuum radiation from a single qubit,” Phys. Rev. A 80, 053810 (2009).
[Crossref]

Casanova, J.

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
[Crossref]

Castellano, F.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Charpentier, C.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Cibella, S.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Ciut, C.

S. De Liberato, D. Gerace, I. Carusotto, and C. Ciut, “Extracavity quantum vacuum radiation from a single qubit,” Phys. Rev. A 80, 053810 (2009).
[Crossref]

Ciuti, C.

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Cleland, A. N.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1992).

Couet, S.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
[Crossref] [PubMed]

Creedon, D. L.

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

Cui, W.

X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
[Crossref]

De Liberato, S.

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

S. De Liberato, D. Gerace, I. Carusotto, and C. Ciut, “Extracavity quantum vacuum radiation from a single qubit,” Phys. Rev. A 80, 053810 (2009).
[Crossref]

Deléglise, S.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Deppe, F.

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

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

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Devoret, M. H.

M. H. Devoret and R. J. Schoelkopf, “Superconducting Circuits for Quantum Information: An Outlook,” Science 339, 1169–1174 (2013).
[Crossref] [PubMed]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

DiVincenzo, D. P.

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

Dotsenko, I.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1992).

Dutra, S. M.

S. M. Dutra, Cavity quantum electrodynamics: the strange theory of light in a box (John Wiley & Sons, Inc, 2005).

Ebbesen, T. W.

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

Evers, J.

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[Crossref]

Faist, J.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Fan, Y.

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

Farr, W. G.

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

Fedorov, A.

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

Feng, W.

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[Crossref]

Feofanov, A. K.

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

Ferguson, D. G.

G. Y. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, “Circuit QED with fluxonium qubits: Theory of the dispersive regime,” Phys. Rev. B 87, 024501 (2013).
[Crossref]

Forn-Díaz, P.

P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
[Crossref] [PubMed]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

Fuse, T.

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

Gambetta, J.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Gambetta, J. M.

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

Gambino, S.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

García-Ripoll, J. J.

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
[Crossref]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

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

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

Garziano, L.

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
[Crossref]

Geiser, M.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Genco, A.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Genet, C.

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

Gerace, D.

S. De Liberato, D. Gerace, I. Carusotto, and C. Ciut, “Extracavity quantum vacuum radiation from a single qubit,” Phys. Rev. A 80, 053810 (2009).
[Crossref]

Gigli, G.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Girvin, S. M.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Goryachev, M.

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

Gross, R.

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

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

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1992).

Günter, G.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Hagenmüller, D.

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

Harmans, C. J. P. M.

P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
[Crossref] [PubMed]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

Haroche, S.

S. Haroche, M. Brune, and J. M. Raimond, “Atomic clocks for controlling light fields,” Phys. Today 66(1), 27 (2013).
[Crossref]

S. Haroche, “Nobel lecture: Controlling photons in a box and exploring the quantum to classical boundry,” Rev. Mod. Phys. 85, 1083 (2013).
[Crossref]

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Hartmann, M. J.

A. Ridolfo, S. Savasta, and M. J. Hartmann, “Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 110, 163601 (2015).
[Crossref]

R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
[Crossref] [PubMed]

A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon Blockade in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 109, 193602 (2012).
[Crossref] [PubMed]

Hees, J.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Hocke, F.

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

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

Hofheinz, M.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Houck, A. A.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Hu, X.

J. Q. You, X. Hu, S. Ashhab, and F. Nori, “Low-decoherence flux qubit,” Phys. Rev. B 75, 140515 (2007).
[Crossref]

Huang, J. F.

J. F. Huang and C. K. Law, “Photon emission via vacuum-dressed intermediate states under ultrastrong coupling,” Phys. Rev. A 89, 033827 (2014).
[Crossref]

Huber, R.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Huebl, H.

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

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

Hümmer, T.

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

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

Hutchison, J. A.

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

Hwang, M. J.

M. J. Hwang, R. Puebla, and M. B. Plenio, “Quantum Phase Transition and Universal Dynamics in the Rabi Model,” Phys. Rev. Lett. 115, 180404 (2015).
[Crossref] [PubMed]

Joo, J.

J. Joo, J. Bourassa, A. Blais, and B. C. Sanders, “Electromagnetically Induced Transparency with Amplification in Superconducting Circuits,” Phys. Rev. Lett. 105, 073601 (2010).
[Crossref] [PubMed]

Kakuyanagi, K.

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Keefe, G. A.

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

Ketchen, M. B.

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

Koch, J.

G. Y. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, “Circuit QED with fluxonium qubits: Theory of the dispersive regime,” Phys. Rev. B 87, 024501 (2013).
[Crossref]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Kockum, A. F.

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

Kofman, A. G.

X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
[Crossref]

Kostylev, M.

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

Kumar, S.

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

Law, C. K.

K. K. W. Ma and C. K. Law, “Three-photon resonance and adiabatic passage in the large-detuning Rabi model,” Phys. Rev. A 92, 023842 (2015).
[Crossref]

J. F. Huang and C. K. Law, “Photon emission via vacuum-dressed intermediate states under ultrastrong coupling,” Phys. Rev. A 89, 033827 (2014).
[Crossref]

Leib, M.

A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon Blockade in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 109, 193602 (2012).
[Crossref] [PubMed]

Leitenstorfer, A.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Leoni, R.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Lerario, G.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Li, Y.

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[Crossref]

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[Crossref]

Liberota, S. D.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Lisenfeld, J.

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

Liu, Y. L.

Y. J. Zhao, Y. L. Liu, Y. X. Liu, and F. Nori, “Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields,” Phys. Rev. A 91, 053820 (2015).
[Crossref]

Liu, Y. X.

Y. J. Zhao, Y. L. Liu, Y. X. Liu, and F. Nori, “Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields,” Phys. Rev. A 91, 053820 (2015).
[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]

Lizuain, I.

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
[Crossref]

Lü, X. Y.

X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
[Crossref]

Lucero, E.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Ma, K. K. W.

K. K. W. Ma and C. K. Law, “Three-photon resonance and adiabatic passage in the large-detuning Rabi model,” Phys. Rev. A 92, 023842 (2015).
[Crossref]

Macha, P.

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

Macrì, V.

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

Maissen, C.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

Majer, J.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Mangione, F.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Manucharyan, V. E.

G. Y. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, “Circuit QED with fluxonium qubits: Theory of the dispersive regime,” Phys. Rev. B 87, 024501 (2013).
[Crossref]

Marcos, D.

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

Mariantoni, M.

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Martinis, J. M.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, “Rabi Oscillations in a Large Josephson-Junction Qubit Phys,” Rev. Lett. 89, 117901 (2002).
[Crossref]

Marx, A.

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

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

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Mazzeo, M.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Meno, T.

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Menzel, E. P.

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

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

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Merkel, S. T.

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

Mooij, J. E.

P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
[Crossref] [PubMed]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

Motzoi, F.

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

Nam, S.

J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, “Rabi Oscillations in a Large Josephson-Junction Qubit Phys,” Rev. Lett. 89, 117901 (2002).
[Crossref]

Neeley, M.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Nevou, L.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Niemczyk, T.

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

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

Nori, F.

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

Y. J. Zhao, Y. L. Liu, Y. X. Liu, and F. Nori, “Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields,” Phys. Rev. A 91, 053820 (2015).
[Crossref]

X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
[Crossref]

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

X. Cao, J. Q. You, H. Zheng, and F. Nori, “A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation,” New J. Phys. 13, 073002 (2011).
[Crossref]

S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Phys. Rev. A 81, 042311 (2010).
[Crossref]

X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
[Crossref]

J. Q. You, X. Hu, S. Ashhab, and F. Nori, “Low-decoherence flux qubit,” Phys. Rev. B 75, 140515 (2007).
[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]

O’Connell, A. D.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Patanè, S.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Plenio, M. B.

M. J. Hwang, R. Puebla, and M. B. Plenio, “Quantum Phase Transition and Universal Dynamics in the Rabi Model,” Phys. Rev. Lett. 115, 180404 (2015).
[Crossref] [PubMed]

Puebla, R.

M. J. Hwang, R. Puebla, and M. B. Plenio, “Quantum Phase Transition and Universal Dynamics in the Rabi Model,” Phys. Rev. Lett. 115, 180404 (2015).
[Crossref] [PubMed]

Raimond, J. M.

S. Haroche, M. Brune, and J. M. Raimond, “Atomic clocks for controlling light fields,” Phys. Today 66(1), 27 (2013).
[Crossref]

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Reichl, C.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

Ridolfo, A.

A. Ridolfo, S. Savasta, and M. J. Hartmann, “Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 110, 163601 (2015).
[Crossref]

L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
[Crossref]

R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
[Crossref] [PubMed]

A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon Blockade in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 109, 193602 (2012).
[Crossref] [PubMed]

Röhlsberger, R.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
[Crossref] [PubMed]

Romero, G.

P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
[Crossref] [PubMed]

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
[Crossref]

Rothwell, M. B.

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

Rozen, J. R.

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

Rüffer, R.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
[Crossref] [PubMed]

Sahoo, B.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
[Crossref] [PubMed]

Saito, S.

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Sanders, B. C.

J. Joo, J. Bourassa, A. Blais, and B. C. Sanders, “Electromagnetically Induced Transparency with Amplification in Superconducting Circuits,” Phys. Rev. Lett. 105, 073601 (2010).
[Crossref] [PubMed]

Sank, D.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Sanvitto, D.

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Savasta, S.

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

A. Ridolfo, S. Savasta, and M. J. Hartmann, “Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 110, 163601 (2015).
[Crossref]

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
[Crossref]

R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
[Crossref] [PubMed]

A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon Blockade in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 109, 193602 (2012).
[Crossref] [PubMed]

Sayrin, C.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

Scalari, G.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

Schlage, K.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
[Crossref] [PubMed]

Schoelkopf, R. J.

M. H. Devoret and R. J. Schoelkopf, “Superconducting Circuits for Quantum Information: An Outlook,” Science 339, 1169–1174 (2013).
[Crossref] [PubMed]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Schuh, D.

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

Schuster, D. I.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Schwartz, T.

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

Schwarz, M. J.

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

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

Scully, M. O.

M. O. Scully, “Collective Lamb Shift in Single Photon Dicke Superradiance,” Phys. Rev. Lett. 102, 143601 (2009).
[Crossref] [PubMed]

Sell, A.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Semba, K.

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Solano, E.

P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
[Crossref] [PubMed]

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

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

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

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
[Crossref]

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Sorna, L.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Stassi, R.

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
[Crossref]

R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
[Crossref] [PubMed]

Stefano, O. D.

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Stefano, O. Di

L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
[Crossref]

R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
[Crossref] [PubMed]

Steffen, M.

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

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. A 86, 023824 (2012).
[Crossref]

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[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]

Takayanagi, T.

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Tan, X. S.

P. Zhao, X. S. Tan, H. F. Yu, S. L. Zhu, and Y. Yu, “Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange,” https://arXiv:1706.08083 (2017).

Tanaka, H.

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Tobar, M. E.

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

Trcinková, D.

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

Tredicucci, A.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

Urbina, C.

J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, “Rabi Oscillations in a Large Josephson-Junction Qubit Phys,” Rev. Lett. 89, 117901 (2002).
[Crossref]

Valmorra, F.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Wang, H.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

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. A 86, 023824 (2012).
[Crossref]

Wegscheider, W.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[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]

Wenner, J.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

Wilhelm, F. K.

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

Wu, R.

X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
[Crossref]

Yoshihara, F.

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

You, J. Q.

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

X. Cao, J. Q. You, H. Zheng, and F. Nori, “A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation,” New J. Phys. 13, 073002 (2011).
[Crossref]

X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
[Crossref]

J. Q. You, X. Hu, S. Ashhab, and F. Nori, “Low-decoherence flux qubit,” Phys. Rev. B 75, 140515 (2007).
[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, H. F.

P. Zhao, X. S. Tan, H. F. Yu, S. L. Zhu, and Y. Yu, “Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange,” https://arXiv:1706.08083 (2017).

Yu, T. M.

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

Yu, Y.

P. Zhao, X. S. Tan, H. F. Yu, S. L. Zhu, and Y. Yu, “Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange,” https://arXiv:1706.08083 (2017).

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. A 86, 023824 (2012).
[Crossref]

Zhao, P.

P. Zhao, X. S. Tan, H. F. Yu, S. L. Zhu, and Y. Yu, “Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange,” https://arXiv:1706.08083 (2017).

Zhao, Y. J.

Y. J. Zhao, Y. L. Liu, Y. X. Liu, and F. Nori, “Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields,” Phys. Rev. A 91, 053820 (2015).
[Crossref]

Zheng, H.

X. Cao, J. Q. You, H. Zheng, and F. Nori, “A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation,” New J. Phys. 13, 073002 (2011).
[Crossref]

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[Crossref]

X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
[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. A 86, 023824 (2012).
[Crossref]

Zhu, G. Y.

G. Y. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, “Circuit QED with fluxonium qubits: Theory of the dispersive regime,” Phys. Rev. B 87, 024501 (2013).
[Crossref]

Zhu, S. L.

P. Zhao, X. S. Tan, H. F. Yu, S. L. Zhu, and Y. Yu, “Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange,” https://arXiv:1706.08083 (2017).

Zhu, S. Y.

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[Crossref]

Zueco, D.

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

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

ACS Photonics (1)

S. Gambino, M. Mazzeo, A. Genco, O. D. Stefano, S. Savasta, S. Patanè, D. Ballarini, F. Mangione, G. Lerario, D. Sanvitto, and G. Gigli, “Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime,” ACS Photonics 1 (10), 1042–1048 (2014).
[Crossref]

Nat. Phys. (4)

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

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

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44–47 (2017).
[Crossref]

F. Deppe, M. Mariantoni, E. P. Menzel, A. Marx, S. Saito, K. Kakuyanagi, H. Tanaka, T. Meno, K. Semba, T. Takayanagi, E. Solano, and R. Gross, “Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED,” Nat. Phys. 4, 686–691 (2008).
[Crossref]

Nature (4)

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
[Crossref] [PubMed]

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

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorna, S. D. Liberota, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber, “Sub-cycle Swith-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

New J. Phys. (2)

X. Cao, J. Q. You, H. Zheng, and F. Nori, “A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation,” New J. Phys. 13, 073002 (2011).
[Crossref]

X. Y. Lü, S Ashhab, W. Cui, R. Wu, and F. Nori, “Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity,” New J. Phys. 14, 073041 (2012).
[Crossref]

Phys. Rev. A (14)

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
[Crossref]

S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Phys. Rev. A 81, 042311 (2010).
[Crossref]

L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, “Vacuum-induced symmetry breaking in a superconducting quantum circuit,” Phys. Rev. A 90, 043817 (2014).
[Crossref]

J. F. Huang and C. K. Law, “Photon emission via vacuum-dressed intermediate states under ultrastrong coupling,” Phys. Rev. A 89, 033827 (2014).
[Crossref]

Y. J. Zhao, Y. L. Liu, Y. X. Liu, and F. Nori, “Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields,” Phys. Rev. A 91, 053820 (2015).
[Crossref]

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[Crossref]

L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, “Multiphoton quantum Rabi oscillations in ultrastrong cavity QED,” Phys. Rev. A 92, 063830 (2015).
[Crossref]

S. De Liberato, D. Gerace, I. Carusotto, and C. Ciut, “Extracavity quantum vacuum radiation from a single qubit,” Phys. Rev. A 80, 053810 (2009).
[Crossref]

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[Crossref]

X. F. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori, “Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation,” Phys. Rev. A 82, 022119 (2010).
[Crossref]

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime,” Phys. Rev. A 95, 053824 (2017).
[Crossref]

K. K. W. Ma and C. K. Law, “Three-photon resonance and adiabatic passage in the large-detuning Rabi model,” Phys. Rev. A 92, 023842 (2015).
[Crossref]

Phys. Rev. Applied (1)

M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-Cooperativity Cavity QED with Magnons at Microwave Frequencies,” Phys. Rev. Applied 2, 054002 (2014).
[Crossref]

Phys. Rev. B (3)

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

G. Y. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, “Circuit QED with fluxonium qubits: Theory of the dispersive regime,” Phys. Rev. B 87, 024501 (2013).
[Crossref]

J. Q. You, X. Hu, S. Ashhab, and F. Nori, “Low-decoherence flux qubit,” Phys. Rev. B 75, 140515 (2007).
[Crossref]

Phys. Rev. Lett. (16)

M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, “High-Coherence Hybrid Superconducting Qubit,” Phys. Rev. Lett. 105, 100502 (2010).
[Crossref] [PubMed]

J. Joo, J. Bourassa, A. Blais, and B. C. Sanders, “Electromagnetically Induced Transparency with Amplification in Superconducting Circuits,” Phys. Rev. Lett. 105, 073601 (2010).
[Crossref] [PubMed]

A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon Blockade in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 109, 193602 (2012).
[Crossref] [PubMed]

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep Strong Coupling Regime of the Jaynes-Cummings Model,” Phys. Rev. Lett. 105, 263603 (2010).
[Crossref]

D. Braak, “Integrability of the Rabi Model,” Phys. Rev. Lett. 107, 100401 (2011).
[Crossref] [PubMed]

M. J. Hwang, R. Puebla, and M. B. Plenio, “Quantum Phase Transition and Universal Dynamics in the Rabi Model,” Phys. Rev. Lett. 115, 180404 (2015).
[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]

R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime,” Phys. Rev. Lett. 110, 243601 (2013).
[Crossref] [PubMed]

A. Ridolfo, S. Savasta, and M. J. Hartmann, “Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 110, 163601 (2015).
[Crossref]

L. Garziano, V. Macrì, R. Stassi, O. D. Stefano, F. Nori, and S. Savasta, “One Photon Can Simultaneously Excite Two or More Atoms,” Phys. Rev. Lett. 117, 043601 (2016).
[Crossref] [PubMed]

M. O. Scully, “Collective Lamb Shift in Single Photon Dicke Superradiance,” Phys. Rev. Lett. 102, 143601 (2009).
[Crossref] [PubMed]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in theUltrastong Coupling Regime,” Phys. Rev. Lett. 10, 237001 (2010).
[Crossref]

P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010).
[Crossref]

A. Fedorov, A. K. Feofanov, P. Macha, P. Forn-Díaz, C. J. P. M. Harmans, and J. E. Mooij, “Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point,” Phys. Rev. Lett. 105, 060503 (2010).
[Crossref] [PubMed]

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible Switching of Ultrastrong Light-Molecule Coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong Coupling Regime and Plasmon Polaritons in Parabolic Semiconductor Quantum Wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Phys. Today (1)

S. Haroche, M. Brune, and J. M. Raimond, “Atomic clocks for controlling light fields,” Phys. Today 66(1), 27 (2013).
[Crossref]

Rev. Lett. (1)

J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, “Rabi Oscillations in a Large Josephson-Junction Qubit Phys,” Rev. Lett. 89, 117901 (2002).
[Crossref]

Rev. Mod. Phys. (1)

S. Haroche, “Nobel lecture: Controlling photons in a box and exploring the quantum to classical boundry,” Rev. Mod. Phys. 85, 1083 (2013).
[Crossref]

Sci. Rep. (1)

P. Forn-Díaz, G. Romero, C. J. P. M. Harmans, E. Solano, and J. E. Mooij, “Broken selection rule in the quantum Rabi model,” Sci. Rep. 6, 26720 (2016).
[Crossref] [PubMed]

Science (3)

G. Scalari, C. Maissen, D. Trčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012).
[Crossref] [PubMed]

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science,  328, 1248–1251 (2010).
[Crossref] [PubMed]

M. H. Devoret and R. J. Schoelkopf, “Superconducting Circuits for Quantum Information: An Outlook,” Science 339, 1169–1174 (2013).
[Crossref] [PubMed]

Other (3)

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1992).

S. M. Dutra, Cavity quantum electrodynamics: the strange theory of light in a box (John Wiley & Sons, Inc, 2005).

P. Zhao, X. S. Tan, H. F. Yu, S. L. Zhu, and Y. Yu, “Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange,” https://arXiv:1706.08083 (2017).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic of the system consists of two qubits are strongly coupled to a cavity mode. Here, Δ and λj(j = A, B) are the anharmonicity of qubit A and the qubit-cavity coupling strength, respectively. The cavity frequency is denoted by ωc, qubits frequencies are ωA = ωfg + ωef and ωB.

Fig. 2
Fig. 2

(a) Two parity chains describing the dynamical evolution of system decided by the Z2 symmetry. The transition between two states in the same chain may be connected via either rotating or counterrotating terms of Hamiltonian H. The first, second and third indexes in state |A, B, C〉 denote qubits A, B, and resonator, respectively. (b) One of the processes of the effective coupling between the states |g, g, 1〉 and |e, e, 0〉 depicted by the red text in (a). Here, |f, g, 2〉 and |f, e, 1〉 are intermediate states, 2 λ A and 2 λ B are transition matrix elements, the excitation-number-nonconserving processes are represented by arrowed black dashed line.

Fig. 3
Fig. 3

The energy levels E6/ωB and E5/ωB versus the cavity frequency ωc/ωB. Here, we consider a normalized coupling rate λ/ωB = 0.1. we used ωA = ωB, ω/fg = (ωB – Δ)/2 and Δ = 0.4ωB. The black arrows indicate an avoided-level crossing.

Fig. 4
Fig. 4

(a) The fidelities Fa and Fb for ωc at the avoided-crossing point versus Δ/ωB when λA = λB = 0.1ωB. The inset correspond to the fidelities for λA = 0:105ωB and λB = 0:095ωB. (b) The fidelities Fa and Fb versus λ/ωB for ωc at the avoided-crossing point. The system parameters used here are: (a) ωA = ωB, ωfg = (ωB − Δ)/2 and Δ = 0:4ωB; (b) ωA = ωB, ωfg = (ωB − Δ)/2 and Δ = 0.1ωB.

Fig. 5
Fig. 5

Time evolution of the expectation value of the photon number 〈aa〉 (green solid curve), the occupation probability of qubit A in the excited state |eA (red solid curve), and the two-qubit occupation probability in state |e, eAB (black dashed curve). The system parameters used here are λ/ωB = 0.1, ωA = ωB, ωfg = (ωB – Δ)/2, Δ = 0.4ωB, γ f g A = γ g e A / 2 = γ e g B = κ; And κ = 0 for panel (a), κ = 10−5ωB for panel (b) and κ = 10−4ωB for panel (c).

Fig. 6
Fig. 6

The maximum difference D between the two-qubit occupation probability in their excited states P A B e and the mean cavity photon number 〈aa〉 in a period of time versus λ/ωB. The maximum values of the curves are marked in green circles. The system parameters are the same as Figure 5(b) except for: (a) Δ = 0; (b) Δ = −0.4ωB; (c) Δ = 0.4ωB;

Fig. 7
Fig. 7

The effective coupling rate between the states |g, g, 1〉 and |e, e, 0〉 versus λ/ωB and Δ/ωB. The dashed lines correspond to the parameter regime for implementing the energy splitting 2Ωeff/ωB = 5 × 10−4. The system parameters used here are: ωA = ωB, ωfg = (ωB − Δ)/2.

Equations (19)

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

H = H 0 + H I ,
H 0 = ω c a a + ω A | e A e | + ω f g | f A f | + ω B | e B e |
H I = λ A ( a + a ) ( 2 | e A f | + | f A g | + h . c . ) + λ B ( a + a ) ( | e B g | + h . c . ) .
Π = e i π N = e i π [ a a + 2 | e A e | + | f A f | + | e B e | ] ,
H s b = μ , ν α μ , ν ( s μ + s μ ) ( b μ ν + b μ ν ) ,
d ρ d t = i [ ρ , H ] + κ L [ a ] ρ + γ e f A L [ | f A e | ] ρ
+ γ f g A L [ | g A f | ] ρ + γ e g B L [ | g B e | ] ρ ,
L [ O ] = 1 2 ( 2 O ρ O ρ O O O O ρ ) .
X + = E n , E m > E n X n m | φ n φ m | ,
Φ = κ X X + = κ Tr [ ρ ( t ) X X + ] .
C i + = E n , E m > E n C n m i | φ n φ m | ,
C n m 1 = φ n | ( | e A f | + | f A e | ) | φ m ,
C n m 2 = φ n | ( | f A g | + | g A f | ) | φ m ,
C n m 3 = φ n | ( | e B g | + | g B e | ) | φ m ,
d ρ d t = i [ ρ , H ] + μ E n , E m > E n Γ μ n m L [ | φ n φ m | ] ρ ,
Γ 1 n m = κ | φ n | X | φ m | 2 ,
Γ 2 n m = γ e f A | φ n | ( | e A f | + | f A e | ) | φ m | 2 ,
Γ 3 n m = γ f g A | φ n | ( | f A g | + | g A f | ) | φ m | 2 ,
Γ 4 n m = γ e g B | φ n | ( | e B g | + | g B e | ) | φ m | 2 .