Abstract

In a coherently-driven nanocavity QED system, the one-photon blockade via quantum interference is investigated by the modified Lindblad master equation and without using the secular approximation as well. Based on the dressed bases of the Rabi Hamiltonian, a modified Lindblad master equation is obtained, which is valid for any arbitrary degree of the qubit-cavity interaction. It is found that the damping coefficients are very sensitive to interaction strength between the qubit and the cavity mode. How to enhance the one-photon blockade by using the quantum interference effect is discussed with the generalized second-order correlation function and the second-order perturbation in the five-state truncation of the Hilbert space. It is found that, under suitable pump or detection conditions, a strong one-photon blockade can be realized by completely eliminating the two-photon emission. Moreover, even for a strong cavity damping rate, there exhibits a large number of cavity photons by utilizing the quantum interference mechanism.

© 2017 Optical Society of America

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2017 (2)

P. Forn-Dĺłaz, J. J. Garćlła-Ripoll, B. Peropadre, J.-L. Orgiazzi, M. A. Yurtalan, R. Belyansky, C. M. Wilson, and A. Lupascu, “Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime,” Nat. Phys. 13, 39–43 (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]

2016 (5)

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J. J. GarcíaRipoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit QED,” Phys. Rev. B 93, 214501 (2016).
[Crossref]

A. L. Boité, M. J. Hwang, H. Nha, and M. B. Plenio, “Fate of photon blockade in the deep strong-coupling regime,” Phys. Rev. A 94, 033827 (2016).
[Crossref]

B. Y. Zhou and G. X. Li, “Ground-state cooling of a nanomechanical resonator via single-polariton optomechanics in a coupled quantum-dot-cavity system,” Phys. Rev. A 94, 033809 (2016).
[Crossref]

A. Li, T. Chen, Y. H. Zhou, and X. B. Wang, “On-demand single-photon sources via quantum blockade and applications in decoy-state quantum key distribution,” Opt. Lett. 41(9) 1921–1924 (2016).
[Crossref] [PubMed]

Y. Yan, J. P. Zhu, and G. X. Li, “Preparation of a nonlinear coherent state of the mechanical resonator in an optome-chanical microcavity,” Opt. Express 24(12), 13590–13609 (2016)
[Crossref] [PubMed]

2015 (5)

G. W. Lin, Y. H. Qi, X. M. Lin, Y. P. Niu, and S. Q. Gong, “Strong photon blockade with intracavity electromagnetically induced transparency in a blockaded Rydberg ensemble,” Phys. Rev. A 92, 043842 (2015).
[Crossref]

H. Wang, X. Gu, Y. X. Liu, A. Miranowicz, and F. Nori, “Tunable photon blockade in a hybrid system consisting of an optomechanical device coupled to a two-level system,” Phys. Rev. A 92, 033806 (2015).
[Crossref]

H. Z. Shen, Y. H. Zhou, H. D. Liu, G. C. Wang, and X. X. Yi, “Exact optimal control of photon blockade with weakly nonlinear coupled cavities,” Opt. Express 23(25), 32835–32858 (2015)
[Crossref] [PubMed]

J. Tang, W. D. Geng, and X. L. Xu, “Quantun interference induced photon blockade in a coupled single quantum dot-cavity system,” Sci. Rep. 5, 9252 (2015).
[Crossref]

W. W. Deng, G. X. Li, and H. Qin, “Enhancement of the two-photon blockade in a strong-coupling qubit-cavity system,” Phys. Rev. A 91, 043831 (2015).
[Crossref]

2014 (8)

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

X. W. Xu and Y. Li, “Strong photon antibunching of symmetric and antisymmetric modes in weakly nonlinear photonic molecules,” Phys. Rev. A 90, 033809 (2014).
[Crossref]

O. Kyriienko and T. C. H. Liew, “Triggered single-photon emitters based on stimulated parametric scattering in weakly nonlinear systems,” Phys. Rev. A 90, 063805 (2014).
[Crossref]

G. H. Hovsepyan, A. R. Shahinyan, and G. Y. Kryuchkyan, “Multiphoton blockades in pulsed regimes beyond stationary limits,” Phys. Rev. A 90, 013839 (2014).
[Crossref]

A. Rundquist, M. Bajcsy, A. Majumdar, T. Sarmiento, K. Fischer, K. G. Lagoudakis, S. Buckley, A. Y. Piggott, and J. Vučković, “Nonclassical higher-order photon correlations with a quantum dot strongly coupled to a photonic-crystal nanocavity,” Phys. Rev. A 90, 023846 (2014).
[Crossref]

D. Gerace and V. Savona, “Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity,” Phys. Rev. A 89, 031803 (2014).
[Crossref]

O. Kyriienko, I. A. Shelykh, and T. C. H. Liew, “Tunable single-photon emission from dipolaritons,” Phys. Rev. A 90, 033807 (2014).
[Crossref]

Y. X. Liu, X. W. Xu, A. Miranowicz, and F. Nori, “From blockade to transparency: Controllable photon transmission through a circuit-QED system,” Phys. Rev. A 89, 043818 (2014).
[Crossref]

2013 (8)

A. Miranowicz, M. Paprzycka, Y. X. Liu, J. Bajer, and F. Nori, “Two-photon and three-photon blockades in driven nonlinear systems,” Phys. Rev. A 87, 023809 (2013).
[Crossref]

A. Majumdar and D. Gerace, “Single-photon blockade in doubly resonant nanocavities with second-order nonlinearity,” Phys. Rev. B 87, 235319 (2013).
[Crossref]

H. Flayac and V. Savona, “Input-output theory of the unconventional photon blockade,” Phys. Rev. A 88, 033836(2013).
[Crossref]

S. Ferretti, V. Savona, and D. Gerace, “Optimal antibunching in passive photonic devices based on coupled nonlinear resonators,” New J. Phys. 15, 025012 (2013).
[Crossref]

A. Ridolfo, S. Savasta, and M. J. Hartmann, “Nonclassical radiation from thermal cavities in the ultrastrong coupling regime,” Phys. Rev. Lett. 110, 163601 (2013).
[Crossref] [PubMed]

W. W. Deng and G. X. Li, “Emission spectrum of a qubit in Rabi model in strong coupling regime,” Eur. Phys. J. D 67, 91 (2013).
[Crossref]

W. W. Deng and G. X. Li, “Influences of counter-rotating wave terms on the trace distance of quantum states in the Rabi model,” J. Phys. B: At. Mol. Opt. Phys. 46, 035505 (2013).
[Crossref]

W. W. Deng and G. X. Li, “Berry phase of the Rabi model beyond the rotating-wave approximation,” J. Phys. B: At. Mol. Opt. Phys. 46, 224018 (2013).
[Crossref]

2012 (4)

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]

G. Scalari, C. Maissen, D. Turcinkova, D. Hagenmüler, 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. He, C. Wang, Q. H. Chen, X. Z. Ren, T. Liu, and K. L. Wang, “First-order corrections to the rotating-wave approximation in the Jaynes-Cummings model,” Phys. Rev. A 86, 033837 (2012).
[Crossref]

A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vučković, “Loss-enabled sub-poissonian light generation in a bimodal nanocavity,” Phys. Rev. Lett. 108, 183601 (2012).
[Crossref] [PubMed]

2011 (10)

M. Bamba, A. Imamoǧlu, I. Carusotto, and C. Ciuti, “Origin of strong photon antibunching in weakly nonlinear photonic molecules,” Phys. Rev. A 83, 021802 (2011).
[Crossref]

P. Nataf and C. Ciuti, “Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED,” Phys. Rev. Lett. 107, 190402 (2011).
[Crossref] [PubMed]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Cavity-free photon blockade induced by many-body bound states,” Phys. Rev. Lett. 107, 223601 (2011).
[Crossref] [PubMed]

A. J. Hoffman, S. J. Srinivasan, S. Schmidt, L. Spietz, J. Aumentado, H. E. Türeci, and A. A. Houck, “Dispersive photon blockade in a superconducting circuit,” Phys. Rev. Lett. 107, 053602 (2011).
[Crossref] [PubMed]

M. Koch, C. Sames, M. Balbach, H. Chibani, A. Kubanek, K. Murr, T. Wilk, and G. Rempe, “Three-Photon correlations in a strongly driven atom-cavity system,” Phys. Rev. Lett. 107, 023601 (2011).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
[Crossref]

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J. Hausinger and M. Grifoni, “Qubit-oscillator system under ultrastrong coupling and extreme driving,” Phys. Rev. A 83, 030301 (2011).
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F. Beaudoin, J. M. Gambetta, and A. Blais, “Dissipation and ultrastrong coupling in circuit QED,” Phys. Rev. A 84, 043832 (2011).
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2010 (11)

S. S. Shamailov, A. S. Parkins, M. J. Collett, and H. J. Carmichael, “Multi-photon blockade and dressing of the dressed states,” Opt. Commun. 283, 766–772 (2010).
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Y. Todorov, A. M. Andrews, R. Colombelli, S. DeLiberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultra-strong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
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Q. H. Chen, Y. Yang, T. Liu, and K. L. Wang, “Entanglement dynamics of two independent Jaynes-Cummings atoms without the rotating-wave approximation,” Phys. Rev. A 82, 052306 (2010).
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C. J. Zhao and H. Zheng, “Interference between driving and dissipation in the spin-boson model: Effect of counter-rotating terms,” Phys. Rev. A 82, 043844 (2010).
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C. J. Gan and H. Zheng, “Dynamics of a two-level system coupled to a quantum oscillator: transformed rotating-wave approximation,” Eur. Phys. J. D 59, 473 (2010).
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P. Nataf and C. Ciuti, “Vacuum degeneracy of a circuit QED system in the ultrastrong coupling regime,” Phys. Rev. Lett. 104, 023601 (2010).
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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).
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D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vučković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104, 073904 (2010).
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T. C. H. Liew and V. Savona, “Single photons from coupled quantum modes,” Phys. Rev. Lett. 104, 183601 (2010).
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I. Lizuain, J. Casanova, J. J. Garcia-Ripoll, J. G. Muga, and E. Solano, “Zeno physics in ultrastrong-coupling circuit QED,” Phys. Rev. A 81, 062131 (2010).
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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).
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2009 (6)

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. DeLiberato, C. Ciuti, A. Tredicucci, A. Leiten-storfer, and R. Huber, “Sub-cycle switch-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
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A. A. Anappara, S. DeLiberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
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M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. Oconnell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quantum states in a superconducting resonator,” Nature 459, 546–549 (2009).
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M. D. Lahaye, J. Suh, P. M. Echternach, K. C. Schwab, and M. L. Roukes, “Nanomechanical measurements of a superconducting qubit,” Nature 459, 960–964 (2009).
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J. L. ÓBrien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687 (2009).
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V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
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2008 (3)

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–893 (2008).
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H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
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H. Zheng, S. Y. Zhu, and M. S. Zubairy, “Quantum zeno and anti-Zeno effects: Without the rotating-wave approximation,” Phys. Rev. Lett. 101, 200404 (2008).
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2007 (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

2005 (3)

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
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E. K. Irish, J. Gea-Banacloche, I. Martin, and K. C. Schwab, “Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator,” Phys. Rev. B 72, 195410 (2005).
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2004 (1)

A. T. Sornborger, A. N. Cleland, and M. R. Geller, “Superconducting phase qubit coupled to a nanomechanical resonator: Beyond the rotating-wave approximation,” Phys. Rev. A 70, 052315 (2004).
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2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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1937 (1)

I. I. Rabi, “Space quantization in a gyrating magnetic field,” Phys. Rev. 51, 652 (1937).
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C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
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Anappara, A. A.

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. DeLiberato, C. Ciuti, A. Tredicucci, A. Leiten-storfer, and R. Huber, “Sub-cycle switch-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref] [PubMed]

A. A. Anappara, S. DeLiberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
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Andrews, A. M.

Y. Todorov, A. M. Andrews, R. Colombelli, S. DeLiberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultra-strong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
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Ansmann, M.

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

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).
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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).
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Aumentado, J.

A. J. Hoffman, S. J. Srinivasan, S. Schmidt, L. Spietz, J. Aumentado, H. E. Türeci, and A. A. Houck, “Dispersive photon blockade in a superconducting circuit,” Phys. Rev. Lett. 107, 053602 (2011).
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Bajcsy, M.

A. Rundquist, M. Bajcsy, A. Majumdar, T. Sarmiento, K. Fischer, K. G. Lagoudakis, S. Buckley, A. Y. Piggott, and J. Vučković, “Nonclassical higher-order photon correlations with a quantum dot strongly coupled to a photonic-crystal nanocavity,” Phys. Rev. A 90, 023846 (2014).
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A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vučković, “Loss-enabled sub-poissonian light generation in a bimodal nanocavity,” Phys. Rev. Lett. 108, 183601 (2012).
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Bajer, J.

A. Miranowicz, M. Paprzycka, Y. X. Liu, J. Bajer, and F. Nori, “Two-photon and three-photon blockades in driven nonlinear systems,” Phys. Rev. A 87, 023809 (2013).
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Balbach, M.

M. Koch, C. Sames, M. Balbach, H. Chibani, A. Kubanek, K. Murr, T. Wilk, and G. Rempe, “Three-Photon correlations in a strongly driven atom-cavity system,” Phys. Rev. Lett. 107, 023601 (2011).
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Bamba, M.

M. Bamba, A. Imamoǧlu, I. Carusotto, and C. Ciuti, “Origin of strong photon antibunching in weakly nonlinear photonic molecules,” Phys. Rev. A 83, 021802 (2011).
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H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Cavity-free photon blockade induced by many-body bound states,” Phys. Rev. Lett. 107, 223601 (2011).
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Bastard, G.

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
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Baur, M.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
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Baust, A.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J. J. GarcíaRipoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit QED,” Phys. Rev. B 93, 214501 (2016).
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Beaudoin, F.

F. Beaudoin, J. M. Gambetta, and A. Blais, “Dissipation and ultrastrong coupling in circuit QED,” Phys. Rev. A 84, 043832 (2011).
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Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
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Beck, M.

G. Scalari, C. Maissen, D. Turcinkova, D. Hagenmüler, 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).
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Beltram, F.

A. A. Anappara, S. DeLiberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
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Belyansky, R.

P. Forn-Dĺłaz, J. J. Garćlła-Ripoll, B. Peropadre, J.-L. Orgiazzi, M. A. Yurtalan, R. Belyansky, C. M. Wilson, and A. Lupascu, “Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime,” Nat. Phys. 13, 39–43 (2017).
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Bialczak, R. C.

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

A. A. Anappara, S. DeLiberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
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G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. DeLiberato, C. Ciuti, A. Tredicucci, A. Leiten-storfer, and R. Huber, “Sub-cycle switch-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref] [PubMed]

Birnbaum, K. M.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
[Crossref] [PubMed]

Blais, A.

F. Beaudoin, J. M. Gambetta, and A. Blais, “Dissipation and ultrastrong coupling in circuit QED,” Phys. Rev. A 84, 043832 (2011).
[Crossref]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
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Boca, A.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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Boité, A. L.

A. L. Boité, M. J. Hwang, H. Nha, and M. B. Plenio, “Fate of photon blockade in the deep strong-coupling regime,” Phys. Rev. A 94, 033827 (2016).
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Boozer, A. D.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
[Crossref] [PubMed]

Bozyigit, D.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Braak, D.

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

Buckley, S.

A. Rundquist, M. Bajcsy, A. Majumdar, T. Sarmiento, K. Fischer, K. G. Lagoudakis, S. Buckley, A. Y. Piggott, and J. Vučković, “Nonclassical higher-order photon correlations with a quantum dot strongly coupled to a photonic-crystal nanocavity,” Phys. Rev. A 90, 023846 (2014).
[Crossref]

Carmichael, H. J.

S. S. Shamailov, A. S. Parkins, M. J. Collett, and H. J. Carmichael, “Multi-photon blockade and dressing of the dressed states,” Opt. Commun. 283, 766–772 (2010).
[Crossref]

H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, 2008).
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Carusotto, I.

M. Bamba, A. Imamoǧlu, I. Carusotto, and C. Ciuti, “Origin of strong photon antibunching in weakly nonlinear photonic molecules,” Phys. Rev. A 83, 021802 (2011).
[Crossref]

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

Casanova, J.

I. Lizuain, J. Casanova, J. J. Garcia-Ripoll, J. G. Muga, and E. Solano, “Zeno physics in ultrastrong-coupling circuit QED,” Phys. Rev. A 81, 062131 (2010).
[Crossref]

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Chen, Q. H.

S. He, C. Wang, Q. H. Chen, X. Z. Ren, T. Liu, and K. L. Wang, “First-order corrections to the rotating-wave approximation in the Jaynes-Cummings model,” Phys. Rev. A 86, 033837 (2012).
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Q. H. Chen, Y. Yang, T. Liu, and K. L. Wang, “Entanglement dynamics of two independent Jaynes-Cummings atoms without the rotating-wave approximation,” Phys. Rev. A 82, 052306 (2010).
[Crossref]

Chen, T.

Chibani, H.

M. Koch, C. Sames, M. Balbach, H. Chibani, A. Kubanek, K. Murr, T. Wilk, and G. Rempe, “Three-Photon correlations in a strongly driven atom-cavity system,” Phys. Rev. Lett. 107, 023601 (2011).
[Crossref] [PubMed]

Ciuti, C.

G. Scalari, C. Maissen, D. Turcinkova, D. Hagenmüler, 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).
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P. Nataf and C. Ciuti, “Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED,” Phys. Rev. Lett. 107, 190402 (2011).
[Crossref] [PubMed]

M. Bamba, A. Imamoǧlu, I. Carusotto, and C. Ciuti, “Origin of strong photon antibunching in weakly nonlinear photonic molecules,” Phys. Rev. A 83, 021802 (2011).
[Crossref]

Y. Todorov, A. M. Andrews, R. Colombelli, S. DeLiberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultra-strong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

P. Nataf and C. Ciuti, “Vacuum degeneracy of a circuit QED system in the ultrastrong coupling regime,” Phys. Rev. Lett. 104, 023601 (2010).
[Crossref] [PubMed]

A. A. Anappara, S. DeLiberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. DeLiberato, C. Ciuti, A. Tredicucci, A. Leiten-storfer, and R. Huber, “Sub-cycle switch-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref] [PubMed]

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

Cleland, A. N.

M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. Oconnell, 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]

A. T. Sornborger, A. N. Cleland, and M. R. Geller, “Superconducting phase qubit coupled to a nanomechanical resonator: Beyond the rotating-wave approximation,” Phys. Rev. A 70, 052315 (2004).
[Crossref]

Collett, M. J.

S. S. Shamailov, A. S. Parkins, M. J. Collett, and H. J. Carmichael, “Multi-photon blockade and dressing of the dressed states,” Opt. Commun. 283, 766–772 (2010).
[Crossref]

Colombelli, R.

Y. Todorov, A. M. Andrews, R. Colombelli, S. DeLiberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultra-strong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

da Silva, M. P.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

De Liberato, S.

G. Scalari, C. Maissen, D. Turcinkova, D. Hagenmüler, 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]

DeLiberato, S.

Y. Todorov, A. M. Andrews, R. Colombelli, S. DeLiberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultra-strong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

A. A. Anappara, S. DeLiberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. DeLiberato, C. Ciuti, A. Tredicucci, A. Leiten-storfer, and R. Huber, “Sub-cycle switch-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
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Deng, W. W.

W. W. Deng, G. X. Li, and H. Qin, “Enhancement of the two-photon blockade in a strong-coupling qubit-cavity system,” Phys. Rev. A 91, 043831 (2015).
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W. W. Deng and G. X. Li, “Emission spectrum of a qubit in Rabi model in strong coupling regime,” Eur. Phys. J. D 67, 91 (2013).
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W. W. Deng and G. X. Li, “Influences of counter-rotating wave terms on the trace distance of quantum states in the Rabi model,” J. Phys. B: At. Mol. Opt. Phys. 46, 035505 (2013).
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W. W. Deng and G. X. Li, “Berry phase of the Rabi model beyond the rotating-wave approximation,” J. Phys. B: At. Mol. Opt. Phys. 46, 224018 (2013).
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Deppe, F.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J. J. GarcíaRipoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit QED,” Phys. Rev. B 93, 214501 (2016).
[Crossref]

Dowling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Echternach, P. M.

M. D. Lahaye, J. Suh, P. M. Echternach, K. C. Schwab, and M. L. Roukes, “Nanomechanical measurements of a superconducting qubit,” Nature 459, 960–964 (2009).
[Crossref] [PubMed]

Eder, P.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J. J. GarcíaRipoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit QED,” Phys. Rev. B 93, 214501 (2016).
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Sci. Rep. (1)

J. Tang, W. D. Geng, and X. L. Xu, “Quantun interference induced photon blockade in a coupled single quantum dot-cavity system,” Sci. Rep. 5, 9252 (2015).
[Crossref]

Science (1)

G. Scalari, C. Maissen, D. Turcinkova, D. Hagenmüler, 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]

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H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, 2008).
[Crossref]

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Scheme of the considered coherently-driven nanocavity QED system. There exists a strong coupling qubit-cavity subsystem illustrated by Rabi model, in which the coupling strength g between the qubit and the single cavity mode is comparable to the transition frequency ω0 of qubit, the frequency ω of cavity mode, and the cavity damping rate κ. The cavity mode and qubit are driven simultaneously by driving laser with frequency ωp and pumping laser with frequency ωL, respectively. The coupling strengths from the pumping and driving fields are weak, and satisfy {ε, Ω} ≪ {g, ω, ω0, κ}.
Fig. 2
Fig. 2 Energy level diagram of Rabi model with the five-state truncation without the inter-crossing of the energy levels.
Fig. 3
Fig. 3 (a) The second-order correlation function g(2) (0) and (b) the mean cavity photon number n are functions of cavity-light detuning Δc = ω0ωp in the regime of strong coupling between the qubit and the cavity mode, respectively. The black solid lines show the results of Rabi model with Ω = 0, the blue dashed lines represent the results in the optimized conditions (Ωopt, θopt) = (0.034, − 0.396) for ωp = E10, and the red dash-dotted lines represent the results in the optimized conditions (Ωopt, θopt) = (0.035, 0.373) for ωp = E20. Here g = κ, Δ = ω0ω = 0, ε = 10−2κ, κ = 0.2GHz, γ = 10−3κ and ω0 = 1GHz.
Fig. 4
Fig. 4 The mean cavity photon number n under the optimized conditions (Ωopt, θopt) is a function of cavity-light detuning Δc (= ω0ωp) and cavity-qubit detuning Δ = ω0ω. Here, the other parameters are the same as in Fig. 3.
Fig. 5
Fig. 5 (a) The second-order correlation function g(2)(0) and (b) the mean cavity photon number n are functions of the coupling strength g between the qubit and the single cavity mode in the optimized conditions (Ωopt, θopt). The black solid lines show the results of Rabi model with Ω = 0, The blue dashed lines represent the results of the driving frequency ωp = E20, and the red dash-dotted lines represent the results of the driving frequency ωp = E10. Here ε = 10−1κ, κ = 0.1GHz, γ = 10−2κ, Δ = ω0ω = 0 and ω0 = 1GHz.

Equations (48)

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H S = H R + H p + H L ,
H R = ω b b + 1 2 ω 0 σ z + g ( b + b ) ( S + + S ) ,
H p = 2 ε cos ( ω p t ) ( b + b ) ,
H L = 2 Ω cos ( ω L t + θ ) ( S + + S ) ,
R = n = 0 E n | ψ n ψ n | ,
p = 2 ε cos ( ω p t ) [ m , n > m Z m n σ m n + H . c . ] ,
L = 2 Ω cos ( ω L t + θ ) [ m , n > m S m n σ m n + H . c . ] ,
Z m n = ψ m | ( b + b ) | ψ n , S m n = ψ m | ( S + + S ) | ψ n .
Z m n = 2 l = 0 [ l + 1 ( c m l c n l + 1 + c m l + 1 c n l ) ] ,
S m n = 2 l = 0 ( c m 2 l c n 2 l + c m 2 l + 1 c n 2 l + 1 ) ( n > m ) .
* p ( t ) = ε [ m , n > m Z m n σ m n e i ω p t + H . c . ] ,
* L ( t ) = Ω [ m , n > m S m n σ m n e i ( ω L t + θ ) + H . c . ] .
H ( t ) = * p ( t ) + * L ( t ) = m , n > m K m n σ m n e i ω p t + H . c . ,
K m n = ε Z m n + Ω S m n e i θ .
S ( t ) = n = 0 E n σ n n + [ m , n > m K m n σ m n e i ω p t + H . c . ] .
ω p = ω L E 10 ( E 20 ) ,
| Ψ ( t ) = n = 0 4 C n | ψ n ,
U = exp { i t [ E 0 σ 00 + ( E 0 + ω p ) ( σ 11 + σ 22 ) + ( E 0 + 2 ω p ) ( σ 33 + σ 44 ) ] } ,
H T = ( E 10 ω p ) σ 11 + ( E 20 ω p ) σ 22 + ( E 30 2 ω p ) σ 33 + ( E 40 2 ω p ) σ 44 + [ m , n > m 4 K m n σ m n + H . c . ] .
ρ ˙ ( t ) = i [ H T , ρ ( t ) ] + c ρ ,
g ( 2 ) ( 0 ) = X ˙ X ˙ X ˙ + X ˙ + X ˙ X ˙ + 2 .
X ˙ + = m , n > m Y m n | m n | ,
g ( 2 ) ( 0 ) = | Y 3 C 3 + Y 4 C 4 | 2 [ | Y 10 C 1 + Y 20 C 2 | 2 + | Y 31 C 3 + Y 41 C 4 | 2 + | Y 32 C 3 + Y 42 C 4 | 2 ] .
{ g , κ } { ε , Ω } .
C 0 { C 1 , C 2 } { C 3 , C 4 } .
i C ˙ 1 = C 0 K 10 + C 1 Λ 10 i C 2 Γ 21 0 , i C ˙ 2 = C 0 K 20 + C 2 Λ 20 i C 1 Γ 12 0 ,
C 1 = Λ 20 K 10 + i Γ 21 0 K 20 Λ 20 Λ 10 + Γ 12 0 Γ 21 0 C 0 , C 2 = Λ 10 K 20 + i Γ 12 0 K 10 Λ 20 Λ 10 + Γ 12 0 Γ 21 0 C 0 ,
i C ˙ 3 = C 1 K 31 + C 2 K 32 + C 3 Λ 31 i C 4 Γ 4 , i C ˙ 4 = C 1 K 41 + C 2 K 42 + C 4 Λ 41 i C 3 Γ 3 ,
C 3 = ( C 1 K 31 + C 2 K 32 ) Λ 41 + i Γ 4 ( C 1 K 41 + C 2 K 42 ) Λ 41 Λ 31 + Γ 3 Γ 4 , C 4 = ( C 1 K 41 + C 2 K 42 ) Λ 31 + i Γ 3 ( C 1 K 31 + C 2 K 32 ) Λ 41 Λ 31 + Γ 3 Γ 4 .
Y 3 C 3 + Y 4 C 4 0.
T ( Ω o p t , θ o p t ) = Y 3 C 3 + Y 4 C 4 = K 31 ( K 10 Λ 20 + i K 20 Γ 21 0 ) ( Y 3 Λ 41 + i Y 4 Γ 3   ) + K 32 ( K 20 Λ 10 + i K 10 Γ 12 0 ) ( Y 3 Λ 41 + i Y 4 Γ 3   ) + K 41 ( K 10 Λ 20 + i K 20 Γ 21 0 ) ( Y 4 Λ 31 + i Y 3 Γ 4   ) + K 42 ( K 20 Λ 10 + i K 10 Γ 12 0 ) ( Y 4 Λ 31 + i Y 3 Γ 4   ) 0.
= ( ω b b + g ( b + b ) ω 0 2 ω 0 2 ω b b g ( b + b ) ) .
| Ψ n = ( Σ l = 0 m c n l | l ± Σ l = 0 m ( 1 ) l c n l | l ) ,
| ψ n = 1 2 l = 0 m c n l { [ 1 ( 1 ) l ] | e , l + [ 1 ± ( 1 ) l ] | g , l } .
c n l + 1 = E ω l ± ω 0 2 ( 1 ) l g l + 1 c n l l l + 1 c n l 1 .
H s B = m n l α l C m n | m n | ( b l e i ν l t + b l e i ν l t ) e i E k j t ,
H s B = s ( t ) B ( t ) + s ( t ) B ( t )
s ( t ) = m , n > m C m n | m n | e i E n m t , B ( t ) = t α l b l e i v l t .
ρ ˙ I ( t ) = 0 t d t B ( t ) B ( t ) [ s ( t ) ρ I ( t ) , s ( t ) ] + H . c . ,
B ( t ) B ( t ) = 0 D ( ω ) | α l | 2 e i v l ( t t ) d ω , ( T = 0 )
c ρ = 1 2 n > m Γ n m c { [ | n m | , | m n | ρ ] + H . c . } 1 2 n > m Γ n m c { [ | n m | , | m n | ρ ] + H . c . } ,
Γ n m c = Γ E n m ω 0 | C m n | 2 , Γ n m c = Γ E n m ω 0 C m n C n m * ,
ρ ˙ 11 = 2 Γ 10 ρ 11 ( Γ 21 0 ρ 21 + c . c . ) , ρ ˙ 22 = 2 Γ 20 ρ 22 ( Γ 12 0 ρ 12 + c . c . ) .
ρ ˙ 33 = 2 ( Γ 31 + Γ 32 ) ρ 33 [ ( Γ 43 1 + Γ 43 2 ) ρ 43 + c . c . ] , ρ ˙ 44 = 2 ( Γ 41 + Γ 42 ) ρ 44 [ ( Γ 34 1 + Γ 34 2 ) ρ 34 + c . c . ] .
Γ n m = γ 2 E n m ω 0 | S m n | 2 + κ 2 E n m ω 0 | Z m n | 2 ,
Γ n m a = γ 2 E n a ω 0 S a n S a m * + κ 2 E n a ω 0 Z a n Z a m * .
ρ ˙ n n = d C n C n * d t = C n * d C n d t + C n d C n * d t = 2 A ρ n n B ( ρ n m + ρ m n ) .
C ˙ 1 = C 1 Γ 10 C 2 Γ 21 0 , C ˙ 2 = C 2 Γ 20 C 1 Γ 12 0 , C ˙ 3 = C 3 ( Γ 31 + Γ 32 ) C 4 ( Γ 43 1 + Γ 43 2 ) , C ˙ 4 = C 4 ( Γ 41 + Γ 42 ) C 3 ( Γ 34 1 + Γ 34 2 ) ,

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