Comparison of semiclassical and quantum models of a two-level atom-cavity QED system in the strong coupling regime

References

• Purcell, E.M. Spontaneous Emission Probabilities at Radiofrequencies. Phys. Rev. 1946, 69, 681. doi: 10.1103/PhysRev.69.37
   Web of Science ®Google Scholar
• Casimir, H.B.G.; Polder, D. The Influence of Retardation on the London-van der Waals Forces. Phys. Rev. 1948, 73, 360. doi: 10.1103/PhysRev.73.360
   Web of Science ®Google Scholar
• Drexhage, K.H. J. Luminescence. 1970, 1–2, 693. doi: 10.1016/0022-2313(70)90082-7
   Google Scholar
• Morawitz, H. Superradiant Level Shift and Its Possible Detection in a Transient Optical Experiment. Phys. Rev. A 1973, 7, 1148. doi: 10.1103/PhysRevA.7.1148
   Web of Science ®Google Scholar
• Milonni, P.; Knight, P. Spontaneous Emission Between Mirrors. Opt. Comm. 1973, 9, 119. doi: 10.1016/0030-4018(73)90239-3
   Google Scholar
• Kleppner, D. Inhibited Spontaneous Emission. Phys. Rev. Lett. 1981, 47, 233–235. doi: 10.1103/PhysRevLett.47.233
   Web of Science ®Google Scholar
• Gabrielse, G.; Dehmelt, H. Observation of Inhibited Spontaneous Emission. Phys. Rev. Lett. 1985, 55, 67–70. doi: 10.1103/PhysRevLett.55.67
   PubMed Web of Science ®Google Scholar
• Hulet, R.G.; Hilfer, E.S.; Kleppner, D. Inhibited Spontaneous Emission by a Rydberg Atom. Phys. Rev. Lett. 1985, 55, 2137–2140. doi: 10.1103/PhysRevLett.55.2137
   PubMed Web of Science ®Google Scholar
• Jhe, W.; Anderson, A.; Hinds, E.A.; Meschede, D.; Moiand, L.; Haroche, S. Suppression of Spontaneous Decay at Optical Frequencies: Test of Vacuum-Field Anisotropy in Confined Space. Phys. Rev. Lett. 1987, 58, 666–669. doi: 10.1103/PhysRevLett.58.666
   PubMed Web of Science ®Google Scholar
• Goy, P.; Raimond, J.M.; Haroche, S. Observation of Cavity-Enhanced Single-Atom Spontaneous Emission. Phys. Rev. Lett. 1983, 50, 1903–1906. doi: 10.1103/PhysRevLett.50.1903
   Web of Science ®Google Scholar
• De Martini, F.; Innocenti, G.; Jacobovitz, G.R.; Mataloni, P. Anomalous Spontaneous Emission Time in a Microscopic Optical Cavity. Phys. Rev. Lett. 1987, 59, 2955–2958. doi: 10.1103/PhysRevLett.59.2955
   PubMed Web of Science ®Google Scholar
• Heinzen, D.J.; Childs, J.J.; Thomas, J.E.; Feld, M.S. Phys. Rev. Lett. 1987, 58, 1320. doi: 10.1103/PhysRevLett.58.1320
   PubMed Web of Science ®Google Scholar
• Heinzen, D.J.; Feld, M.S. Vacuum Radiative Level Shift and Spontaneous-Emission Linewidth of an Atom in an Optical Resonator. Phys. Rev. Lett. 1987, 59, 2623–2626. doi: 10.1103/PhysRevLett.59.2623
   PubMed Web of Science ®Google Scholar
• Rempe, G.; Walther, H.; Klein, N. Observation of Quantum Collapse and Revival in a One-Atom Maser. Phys. Rev. Lett. 1987, 58, 353. doi: 10.1103/PhysRevLett.58.353
   PubMed Web of Science ®Google Scholar
• Zhu, Y.; Lezama, A.; Lewenstein, M. Vacuum-Field Dressed-State Pumping. Phys. Rev. Lett. 1988, 61, 1946–1949. doi: 10.1103/PhysRevLett.61.1946
   PubMed Web of Science ®Google Scholar
• Raizen, M.G.; Thompson, R.J.; Brecha, R.J.; Kimble, H.J.; Carmichael, H.J. Normal-mode Splitting and Linewidth Averaging for Two-State Atoms in an Opticalcavity. Phys. Rev. Lett. 1989, 63, 240–243. doi: 10.1103/PhysRevLett.63.240
   PubMed Web of Science ®Google Scholar
• Zhu, Y.; Gauthier, D.J.; Morin, S.E.; Wu, Q.; Carmichael, H.J.; Mossberg, T.W. Vacuum Rabi Splitting as a Feature of Linear-Dispersion Theory: Analysis and Experimental Observations. Phys. Rev. Lett. 1990, 64, 2499. doi: 10.1103/PhysRevLett.64.2499
   PubMed Web of Science ®Google Scholar
• Berman, P.R. Cavity Quantum Electrodynamics; Academic Press: New York, 1994.
   Google Scholar
• Haroche, S. Cavity Quantum Electrodynamics. In Fundamental Systems in Quantum Optics; Dalibard, J., Raimond, J.-M., Zinn-Justin, J., Eds.; Elsevier Science Publishers, 1992; pp 767.
   Google Scholar
• Haroche, S.; Raimond, J.-M. Exploring the Quantum: Atoms, Cavities and Photons; Oxford University Press: NewYork, 2006.
   Google Scholar
• Kimble, H.J. Strong Interactions of Single Atoms and Photons in Cavity QED. Physica Scripta. 1998, T76, 127–137. doi: 10.1238/Physica.Topical.076a00127
   Web of Science ®Google Scholar
• Imamoglu, A.; Schmidt, H.; Woods, G.; Deutsch, M. Strongly Interacting Photons in a Nonlinear Cavity. Phys. Rev. Lett. 1997, 79, 1467–1470. doi: 10.1103/PhysRevLett.79.1467
   Web of Science ®Google Scholar
• Birnbaum, K.M.; Boca, A.; Miller, R.; Boozer, A.D.; Northup, T.E.; Kimble, H.J. Photon Blockade Inan Optical Cavity with One Trapped Atom. Nature. 2005, 436, 87–90. doi: 10.1038/nature03804
   PubMed Web of Science ®Google Scholar
• Kubanek, A.; Ourjoumtsev, A.; Schuster, I.; Koch, M.; Pinkse, P.W.H.; Murr, K.; Rempe, G. Two-Photon Gateway in One-Atom Cavity Quantum Electrodynamics. Phys. Rev. Lett. 2008, 101, 203602–203605. doi: 10.1103/PhysRevLett.101.203602
   PubMed Web of Science ®Google Scholar
• Schuster, I.; Kubanek, A.; Fuhrmanek, A.; Puppe, T.; Pinkse, P.W.H.; Murr, K.; Rempe, G. Nonlinear Spectroscopy of Photons Bound to one Atom. Nat. Phys. 2008, 4, 382–385. doi: 10.1038/nphys940
   Web of Science ®Google Scholar
• Khitrova, G.; Gibbs, H.M.; Kira, M.; Koch, S.W.; Scherer, A. Vacuum Rabi Splitting in Semiconductors. Nat. Phys. 2006, 2, 81–90. doi: 10.1038/nphys227
   Web of Science ®Google Scholar
• Schneebeli, L.; Kira, M.; Koch, S.W. Characterization of Strong Light-Matter Coupling in Semiconductor Quantum-Dot Microcavities via Photon-Statistics Spectroscopy. Phys. Rev. Lett. 2008, 101, 097401. doi: 10.1103/PhysRevLett.101.097401
   PubMed Web of Science ®Google Scholar
• Blais, A.; Huang, R.-S.; Wallraff, A.; Girvin, S.M.; Schoelkopf, R.J. Cavity Quantum Electrodynamics for Superconducting Electrical Circuits: An Architecture for Quantum Computation. Phys. Rev. A. 2004, 69, 0623201–06232014. doi: 10.1103/PhysRevA.69.062320
   Web of Science ®Google Scholar
• Wallraff, A.; Schuster, D.I.; Blais, A.; Frunzio, L.; Huang, R.S.; Majer, J.; Kumar, S.; Girvin, S.M.; Schoelkopf, R.J. Strong Coupling of a Single Photon to a Superconducting Qubit Using Circuit Quantum Electrodynamics. Nature. 2004, 431, 162–167. doi: 10.1038/nature02851
   PubMed Web of Science ®Google Scholar
• Frunzio, L.; Wallraff, A.; Schuster, D.; Majer, J.; Schoelkopf, R. Fabrication and Characterization of Supercon-Ducting Circuit QED Devices for Quantum Computation. IEEE Trans. Appl. Supercond. 2005, 15, 860–863. doi: 10.1109/TASC.2005.850084
   Web of Science ®Google Scholar
• Koch, J.; Yu, T.M.; Gambetta, J.; Houck, A.A.; Schuster, D.I.; Majer, J.; Blais, A.; Devoret, M.H.; Girvin, S.M.; Schoelkopf, R.J. Charge-insensitive Qubit Design Derived from the Cooper Pair box. Phys. Rev. A. 2007, 76, 042319. doi: 10.1103/PhysRevA.76.042319
   Web of Science ®Google Scholar
• Bouchiat, V.; Vion, D.; Joyez, P.; Esteve, D.; Devoret, M.H. Quantum Coherence with a Single Cooper Pair. Physica Scripta. 1998, T76, 165–170. doi: 10.1238/Physica.Topical.076a00165
   Web of Science ®Google Scholar
• Mooij, J.E.; Orlando, T.P.; Levitov, L.; Tian, L.; vander Wal, C.H.; Lloyd, S. Josephson Persistent-Current Qubit. Science. 1999, 285, 1036–1039. doi: 10.1126/science.285.5430.1036
   PubMed Web of Science ®Google Scholar
• Martinis, J.M.; Nam, S.; Aumentado, J.; Urbina, C. Rabi Oscillations in a Large Josephson-Junction Qubit. Phys. Rev. Lett. 2002, 89, 117901. doi: 10.1103/PhysRevLett.89.117901
   PubMed Web of Science ®Google Scholar
• A. Kitaev, Protected Qubit Based on a Superconducting Current Mirror. ArXiv cond-mat/0609441 2006.
   Google Scholar
• Manucharyan, V.E.; Koch, J.; Glazman, L.I.; Devoret, M.H. Fluxonium: Single Cooper-Pair Circuit Free of Charge Offset. Science. 2009, 326, 113–116. doi: 10.1126/science.1175552
   PubMed Web of Science ®Google Scholar
• Romero, G.; Ballester, D.; Wang, Y.M.; Scarani, V.; Solano, E. Ultrafast Quantum Gates in Circuit QED. Phys. Rev. Lett. 2012, 108, 1205011–1205014. doi: 10.1103/PhysRevLett.108.120501
   Web of Science ®Google Scholar
• Togan, E.; Chu, Y.; Trifonov, A.S.; Jiang, L.; Maze, J.; Childress, L.; Dutt, M.V.G., et al. Quantum Entanglement Between an Optical Photon and a Solid-State Spin Qubit. Nature. 2010, 466, 730–734. doi: 10.1038/nature09256
   PubMed Web of Science ®Google Scholar
• Mirza, I.M.; van Enk, S.J.; Kimble, H.J. Single-photon Time-Dependent Spectra in Coupled Cavity Arrays. J. Opt. Soc. Am. B. 2013, 30, 2640–2649. doi: 10.1364/JOSAB.30.002640
   Web of Science ®Google Scholar
• Su, Q.-P.; Yang, C.-P.; Zheng, S.-B. Fast and Simple Scheme for Generating NOON States of Photons in Circuit QED. Sci. Rep. 2014, 4, 3898–3904. doi: 10.1038/srep03898
   PubMed Web of Science ®Google Scholar
• Mirza, I.M. Bi- and Uni-Photon Entanglement in Two-Way Cascaded fiber-Coupled Atom-Cavity Systems. Phys. Lett. A. 2015, 379, 1643–1648. doi: 10.1016/j.physleta.2015.04.035
   Web of Science ®Google Scholar
• Masada, G.; Miyata, K.; Politi, A.; Hashimoto, T.; O’Brien, J.L.; Furusawa, A. Continuous-variable Entanglement on a Chip. Nat. Photonics. 2015, 9, 316–319. doi: 10.1038/nphoton.2015.42
   Web of Science ®Google Scholar
• Aolita, L.; deMelo, F.; Davidovich, L. Open-system Dynamics of Entanglement: A Key Issues Review. Rep. Prog. Phys. 2015, 78, 4–82. doi: 10.1088/0034-4885/78/4/042001
   Web of Science ®Google Scholar
• Mirza, I.M.; van Enk, S.J. How Nonlinear Optical Effects DegradeHong-Ou-Mandel Like Interference. Opt. Comm. 2015, 343, 172–177. doi: 10.1016/j.optcom.2015.01.018
   Web of Science ®Google Scholar
• Mirza, I.M.; Schotland, J.C. Two-photon Entanglement in Multiqubit Bidirectional-Waveguide QED. Phys. Rev. A. 2016, 94, 0123091–01230912.
   Web of Science ®Google Scholar
• Niemczyk, T.; Deppe, F.; Huebl, H.; Menzeel, E.P.; Hocke, F.; Schwarz, M.J.; Garcia-Rippol, J.J., et al. Circuit Quantum Electrodynamics in the Ultrastrong-Coupling Regime. Nat. Phys. 2010, 6, 772–776. doi: 10.1038/nphys1730
   Web of Science ®Google Scholar
• Reithmaier, J.P.; Sek, G.; Lãűffler, A.; Hofmann, C.; Kuhn, S.; Reitzenstein, S.; Keldysh, L.V.; Kulakovskii, V.D.; Reinecke, T.L.; Forchel, A. Strong Coupling in a Single Quantum Dot Semiconductor Micro-Cavity System. Nature. 2004, 432, 197–200. doi: 10.1038/nature02969
   PubMed Web of Science ®Google Scholar
• Yoshie, T.; Scherer, A.; Hendrickson, J.; Khitrova, G.; Gibbs, H.M.; Rupper, G.; Ell, C.; Shchekin, O.B.; Deppe, D.G. Vacuum Rabi Splitting with a Single Quantum Dot in a Photonic Crystal Nanocavity. Nature. 2004, 432, 200–203. doi: 10.1038/nature03119
   PubMed Web of Science ®Google Scholar
• Peter, E.; Senellart, P.; Martrou, D.; Lemaitre, A.; Hours, J.; Gerard, J.M.; Bloch, J. Exciton-photon Strong-Coupling Regime for a Single Quantum dot Embedded in a Microcavity. Phy. Rev. Lett. 2005, 95, 0674011–0674014. doi: 10.1103/PhysRevLett.95.067401
   Web of Science ®Google Scholar
• Srinivasan, K.; Painter, O. Linear and Nonlinear Optical Spectroscopy of a Strongly Coupled Microdisk-Quantum dot System. Nature. 2007, 450, 862–865. doi: 10.1038/nature06274
   PubMed Web of Science ®Google Scholar
• Hennessy, K.; Badolato, A.; Winger, M.; Gerace, D.; Atature, M.; Gulde, S.; Falt, S.; Hu, E.L.; Imamoglu, A. Quantum Nature of a Strongly Coupled Single Quantum dot-Cavity System. Nature. 2007, 445, 896–899. doi: 10.1038/nature05586
   PubMed Web of Science ®Google Scholar
• Ohta, R.; Ota, Y.; Nomura, M.; Kumagai, N.; Ishida, S.; Iwamoto, S.; Arakawa, Y. Strong Coupling Between a Photonic Crystal Nano-Beam Cavity and a Single Quantum dot. App. Phys. Lett. 2011, 98, 173104. doi: 10.1063/1.3579535
   Web of Science ®Google Scholar
• Dory, C.; Fischer, K.A.; Mãijller, K.; Lagoudakis, K.G.; Sarmiento, T.; Rundquist, A.; Zhang, J.L.; Kelaita, Y.; Vuckovic, J. Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity. Nat. Sci. Rep. 2016, 6, 25172. doi: 10.1038/srep25172
   PubMed Web of Science ®Google Scholar
• Englund, D.; Faraon, A.; Fushman, I.; Stoltz, N.; Petroff, P.; Vockovic, J. Controlling Cavity Reflectivity with a Single Quantum Dot. Nature. 2007, 450, 758–761. doi: 10.1038/nature06234
   Web of Science ®Google Scholar
• Chiorescu, I.; Bertet, P.; Semba, K.; Nakamura, Y.; Harmans, C.J.P.M.; Mooij, J.E. Coherent Dynamics of a Flux Qubit Coupled to a Harmonic Oscillator. Nature. 2004, 431, 159–162. doi: 10.1038/nature02831
   PubMed Web of Science ®Google Scholar
• Forn-Diaz, P; Lisenfeld, J; Marcos, D; Garcia-Ripoll, J.J.; Solano, E.; Harmans, C.J.P.M.; Mooij, J.E. Observation of the Block-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime. Phys. Rev. Lett. 2010, 105, 237001–237014. doi: 10.1103/PhysRevLett.105.237001
   PubMed Web of Science ®Google Scholar
• Yoshihara, F; Fuse, T; Ashhab, S; Kakuyanagi, K; Saito, S; Semba, K. Superconducting Qubit-oscillator Circuit beyond the Ultrastrong-Coupling Regime. Nat. Phy. 2017, 13, 44–47. doi: 10.1038/nphys3906
   Web of Science ®Google Scholar
• Cuiti, C.; Bastard, G.; Carusotto, I.. Quantum Vacuum Properties of the Intersubband Cavity Polariton Field. Phy. Rev. B. 2005, 72, 115303. doi: 10.1103/PhysRevB.72.115303
   Web of Science ®Google Scholar
• Anappara, A.A.; De Liberito, D.; Tredicucci, A.; Ciuti, C.; Biasiol, G.; Sorba, L.; Beltram, F. Signatures of the ultrastrong light matter coupling regime. Phys. Rev. B. 2009, 79, 201303. doi: 10.1103/PhysRevB.79.201303
   Web of Science ®Google Scholar
• Devoret, M.H.; Girvin, S.; Schoelkopf, R. Circuit QED: How Strong can the Coupling between a Josephson Junction Atom and a Transmission Line Resonator be. Ann. Phys. 2007, 16, 767. doi: 10.1002/andp.200710261
   Google Scholar
• Forn-Diaz, P.; Lamata, L.; Rico, E.; Kono, J.; Solano, E. arXiv:1804.09275 2018.
   Google Scholar
• Kockum, A.F.; Miranowicz, A.; De Liberato, S.; Savasta, S.; Nori, F. arXiv:1807,11636v1 2018.
   Google Scholar
• Carmichael, H J. Statistical Methods in Quantum Optics; Springer: Heidlberg, Germany, 1999.
   Google Scholar
• Johansson, J.R.; Nation, P.D.; Nori, F. QuTiP: An Open-Source Python Framework for the Dynamics of Open Quantum Systems. Comp. Phys. Comm. 2012, 183, 1760–1772. doi: 10.1016/j.cpc.2012.02.021
   Web of Science ®Google Scholar
• Lukin, M.D.; Fleischhauer, M.; Scully, M.O. Intracavity Electromagnetically Induced Transparency. Opt. Lett. 1998, 23, 295. doi: 10.1364/OL.23.000295
   PubMed Web of Science ®Google Scholar
• Lugiato, L.A. Theory of Optical Bistability. Prog. Optics. 1984, 21, 69–216. doi: 10.1016/S0079-6638(08)70122-7
   Web of Science ®Google Scholar