Abstract

We study an intensity-dependent quantum Rabi model that can be written in terms of SU(1,1) group elements and is related to the Buck–Sukumar model for the Bargmann parameter k=1/2. The spectrum seems to present avoided crossings for all valid parameter sets and, thus, may be integrable. For a degenerate qubit, the model is soluble, and we construct an unbroken supersymmetric partner for it. We discuss the classical simulation of the general model in photonic lattices and show that it presents quasi-periodic reconstruction for a given initial state and parameter set.

© 2014 Optical Society of America

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  1. E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
    [CrossRef]
  2. B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).
    [CrossRef]
  3. G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
    [CrossRef]
  4. M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, “Manipulation of photons in a cavity by dispersive atom-field coupling: quantum-nondemolition measurements and generation of Schrödinger cat states,” Phys. Rev. A 45, 5193–5214 (1992).
    [CrossRef]
  5. J. I. Cirac, R. Blatt, A. S. Parkins, and P. Zoller, “Quantum collapse and revival in the motion of a single trapped ion,” Phys. Rev. A 49, 1202–1207 (1994).
    [CrossRef]
  6. J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
    [CrossRef]
  7. A. De and R. Joynt, “Magnetization-noise-induced collapse and revival of Rabi oscillations in circuit-QED,” Phys. Rev. A 87, 042336 (2013).
    [CrossRef]
  8. B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. 81, 132–135 (1981).
    [CrossRef]
  9. W. Vogel and R. L. de Matos Filho, “Nonlinear Jaynes–Cummings dynamics of a trapped ion,” Phys. Rev. A 52, 4214–4217 (1995).
    [CrossRef]
  10. H. Moya-Cessa, F. Soto-Eguibar, J. M. Vargas-Marítnez, R. Juárez-Amaro, and A. Zúñiga-Segundo, “Ion-laser interactions: the most complete solution,” Phys. Rep. 513, 229–261 (2012).
    [CrossRef]
  11. B. M. Rodríguez-Lara, F. Soto-Eguibar, A. Z. Cárdenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices,” Opt. Express 21, 12888–12898 (2013).
    [CrossRef]
  12. C. V. Sukumar and B. Buck, “Some soluble models for periodic decay and revival,” J. Phys. A 17, 885–894 (1984).
    [CrossRef]
  13. S. Singh, “Field statistics in some generalized Jaynes–Cummings models,” Phys. Rev. A 25, 3206–3216 (1982).
    [CrossRef]
  14. V. Bužek, “Light squeezing in the Jaynes–Cummings model with intensity-dependent coupling,” J. Mod. Opt. 36, 1151–1162 (1989).
    [CrossRef]
  15. F. Cordeiro, C. Providencia, J. da Providencia, and S. Nishiyama, “The Buck–Sukumar model described in terms of su(2)⊗su(1,1) coherent states,” J. Phys. A Math. Theor. 40, 12153–12160 (2007).
    [CrossRef]
  16. K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term,” Physica A 275, 463–474 (2000).
    [CrossRef]
  17. P. Shanta, S. Chaturdervi, and V. Srinivasan, “A model which interpolates between the Jaynes–Cummings model and the Buck–Sukumar model,” J. Mod. Opt. 39, 1301–1308 (1992).
    [CrossRef]
  18. C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms,” Physica A 265, 557–564 (1999).
    [CrossRef]
  19. M. Rasetti, “Generalized definition of coherent states and dynamical groups,” Int. J. Theor. Phys. 13, 425–430 (1975).
    [CrossRef]
  20. G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A 18, 1295–1307 (1985).
    [CrossRef]
  21. M. G. Rasetti, G. M. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
    [CrossRef]
  22. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
    [CrossRef]
  23. S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
    [CrossRef]
  24. G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
    [CrossRef]
  25. S. Longhi, “Rectification of light refraction in curved waveguide arrays,” Opt. Lett. 34, 458–460 (2009).
    [CrossRef]
  26. R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
    [CrossRef]
  27. A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
    [CrossRef]
  28. A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
    [CrossRef]
  29. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
    [CrossRef]
  30. S. Longhi and G. D. Valle, “Transparency at the interface between two isospectral crystals,” Europhys. Lett. 102, 40008 (2013).
    [CrossRef]
  31. M.-A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87, 043819 (2013).
    [CrossRef]
  32. A. Zúñiga-Segundo, B. M. Rodríguez-Lara, D. J. Fernández C., and H. M. Moya-Cessa, “Jacobi photonic lattices and their SUSY partners,” Opt. Express 22, 987–994 (2014).
    [CrossRef]
  33. A. O. Barut and R. Raczka, Theory of Group Representations and Applications (PWN Polish Scientific, 1980).
  34. M. Novaes, “Some basics of su(1,1),” Rev. Bras. Ensino Fis. 26, 351–357 (2004).
  35. 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]
  36. D. Ballester, G. Romero, J. J. García-Ripoll, F. Deppe, and E. Solano, “Quantum simulation of the ultrastrong-coupling dynamics in circuit quantum electrodynamics,” Phys. Rev. X 2, 021007 (2012).
    [CrossRef]
  37. C. C. Gerry, “Dynamics of SU(1,1) coherent states,” Phys. Rev. A 31, 2721–2723 (1985).
    [CrossRef]
  38. K. Wódkiewicz and J. H. Eberly, “Coherent states, squeezed fluctuations, and the SU(2) and SU(1,1) groups in quantum-optics applications,” J. Opt. Soc. Am. B 2, 458–466 (1985).
    [CrossRef]
  39. A. O. Barut and L. Girardello, “New ‘coherent’ states associated with non-compact groups,” Commun. Math. Phys. 21, 41–55 (1971).
    [CrossRef]
  40. D. Braak, “Integrability of the Rabi model,” Phys. Rev. Lett. 107, 100401 (2011).
    [CrossRef]
  41. S. A. Chilingaryan and B. M. Rodríguez-Lara, “The quantum Rabi model for two qubits,” J. Phys. A Math. Theor. 46, 335301 (2013).
    [CrossRef]
  42. A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum Rabi model,” Phys. Rev. Lett. 108, 163601 (2012).
    [CrossRef]
  43. B. M. Rodríguez-Lara, F. Soto-Eguibar, A. Z. Cárdenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices: reply to comment,” Opt. Express 22, 1784–1787 (2014).
    [CrossRef]
  44. S. Longhi, “Quantum simulation of decoherence in optical waveguide lattices,” Opt. Lett. 38, 4884–4887 (2013).
    [CrossRef]
  45. B. M. Rodríguez-Lara, F. Soto-Eguibar, and D. N. Christodoulides, “An introduction to arrays of coupled waveguides,” arXiv: 1311.3694 (2013).
  46. F. Beaudoin, J. M. Gambetta, and A. Blais, “Dissipation and ultrastrong coupling in circuit QED,” Phys. Rev. A 84, 043832 (2011).
    [CrossRef]
  47. A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, “Photon blockade in the ultrastrong coupling regime,” Phys. Rev. Lett. 109, 193602 (2012).
    [CrossRef]
  48. A. W. Chin, Á. Rivas, S. F. Huelga, and M. B. Plenio, “Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials,” J. Math. Phys. 51, 092109 (2010).
    [CrossRef]

2014 (2)

2013 (8)

B. M. Rodríguez-Lara, F. Soto-Eguibar, A. Z. Cárdenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices,” Opt. Express 21, 12888–12898 (2013).
[CrossRef]

S. Longhi, “Quantum simulation of decoherence in optical waveguide lattices,” Opt. Lett. 38, 4884–4887 (2013).
[CrossRef]

A. De and R. Joynt, “Magnetization-noise-induced collapse and revival of Rabi oscillations in circuit-QED,” Phys. Rev. A 87, 042336 (2013).
[CrossRef]

R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

S. Longhi and G. D. Valle, “Transparency at the interface between two isospectral crystals,” Europhys. Lett. 102, 40008 (2013).
[CrossRef]

M.-A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87, 043819 (2013).
[CrossRef]

S. A. Chilingaryan and B. M. Rodríguez-Lara, “The quantum Rabi model for two qubits,” J. Phys. A Math. Theor. 46, 335301 (2013).
[CrossRef]

2012 (4)

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum Rabi model,” Phys. Rev. Lett. 108, 163601 (2012).
[CrossRef]

D. Ballester, G. Romero, J. J. García-Ripoll, F. Deppe, and E. Solano, “Quantum simulation of the ultrastrong-coupling dynamics in circuit quantum electrodynamics,” Phys. Rev. X 2, 021007 (2012).
[CrossRef]

H. Moya-Cessa, F. Soto-Eguibar, J. M. Vargas-Marítnez, R. Juárez-Amaro, and A. Zúñiga-Segundo, “Ion-laser interactions: the most complete solution,” Phys. Rep. 513, 229–261 (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]

2011 (3)

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

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

S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
[CrossRef]

2010 (3)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (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]

A. W. Chin, Á. Rivas, S. F. Huelga, and M. B. Plenio, “Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials,” J. Math. Phys. 51, 092109 (2010).
[CrossRef]

2009 (2)

S. Longhi, “Rectification of light refraction in curved waveguide arrays,” Opt. Lett. 34, 458–460 (2009).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

2008 (3)

A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
[CrossRef]

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

2007 (1)

F. Cordeiro, C. Providencia, J. da Providencia, and S. Nishiyama, “The Buck–Sukumar model described in terms of su(2)⊗su(1,1) coherent states,” J. Phys. A Math. Theor. 40, 12153–12160 (2007).
[CrossRef]

2004 (1)

M. Novaes, “Some basics of su(1,1),” Rev. Bras. Ensino Fis. 26, 351–357 (2004).

2000 (1)

K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term,” Physica A 275, 463–474 (2000).
[CrossRef]

1999 (1)

C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms,” Physica A 265, 557–564 (1999).
[CrossRef]

1995 (1)

W. Vogel and R. L. de Matos Filho, “Nonlinear Jaynes–Cummings dynamics of a trapped ion,” Phys. Rev. A 52, 4214–4217 (1995).
[CrossRef]

1994 (1)

J. I. Cirac, R. Blatt, A. S. Parkins, and P. Zoller, “Quantum collapse and revival in the motion of a single trapped ion,” Phys. Rev. A 49, 1202–1207 (1994).
[CrossRef]

1993 (1)

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).
[CrossRef]

1992 (2)

M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, “Manipulation of photons in a cavity by dispersive atom-field coupling: quantum-nondemolition measurements and generation of Schrödinger cat states,” Phys. Rev. A 45, 5193–5214 (1992).
[CrossRef]

P. Shanta, S. Chaturdervi, and V. Srinivasan, “A model which interpolates between the Jaynes–Cummings model and the Buck–Sukumar model,” J. Mod. Opt. 39, 1301–1308 (1992).
[CrossRef]

1989 (2)

V. Bužek, “Light squeezing in the Jaynes–Cummings model with intensity-dependent coupling,” J. Mod. Opt. 36, 1151–1162 (1989).
[CrossRef]

M. G. Rasetti, G. M. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
[CrossRef]

1987 (1)

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

1985 (3)

G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A 18, 1295–1307 (1985).
[CrossRef]

C. C. Gerry, “Dynamics of SU(1,1) coherent states,” Phys. Rev. A 31, 2721–2723 (1985).
[CrossRef]

K. Wódkiewicz and J. H. Eberly, “Coherent states, squeezed fluctuations, and the SU(2) and SU(1,1) groups in quantum-optics applications,” J. Opt. Soc. Am. B 2, 458–466 (1985).
[CrossRef]

1984 (1)

C. V. Sukumar and B. Buck, “Some soluble models for periodic decay and revival,” J. Phys. A 17, 885–894 (1984).
[CrossRef]

1982 (1)

S. Singh, “Field statistics in some generalized Jaynes–Cummings models,” Phys. Rev. A 25, 3206–3216 (1982).
[CrossRef]

1981 (1)

B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. 81, 132–135 (1981).
[CrossRef]

1975 (1)

M. Rasetti, “Generalized definition of coherent states and dynamical groups,” Int. J. Theor. Phys. 13, 425–430 (1975).
[CrossRef]

1971 (1)

A. O. Barut and L. Girardello, “New ‘coherent’ states associated with non-compact groups,” Commun. Math. Phys. 21, 41–55 (1971).
[CrossRef]

1963 (1)

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Agarwal, G. S.

A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
[CrossRef]

Ballester, D.

D. Ballester, G. Romero, J. J. García-Ripoll, F. Deppe, and E. Solano, “Quantum simulation of the ultrastrong-coupling dynamics in circuit quantum electrodynamics,” Phys. Rev. X 2, 021007 (2012).
[CrossRef]

Barut, A. O.

A. O. Barut and L. Girardello, “New ‘coherent’ states associated with non-compact groups,” Commun. Math. Phys. 21, 41–55 (1971).
[CrossRef]

A. O. Barut and R. Raczka, Theory of Group Representations and Applications (PWN Polish Scientific, 1980).

Baur, M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Beaudoin, F.

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

Bianchetti, R.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Blais, A.

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

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its n nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Blatt, R.

J. I. Cirac, R. Blatt, A. S. Parkins, and P. Zoller, “Quantum collapse and revival in the motion of a single trapped ion,” Phys. Rev. A 49, 1202–1207 (1994).
[CrossRef]

Braak, D.

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

Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Brune, M.

M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, “Manipulation of photons in a cavity by dispersive atom-field coupling: quantum-nondemolition measurements and generation of Schrödinger cat states,” Phys. Rev. A 45, 5193–5214 (1992).
[CrossRef]

Buck, B.

C. V. Sukumar and B. Buck, “Some soluble models for periodic decay and revival,” J. Phys. A 17, 885–894 (1984).
[CrossRef]

B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. 81, 132–135 (1981).
[CrossRef]

Bužek, V.

V. Bužek, “Light squeezing in the Jaynes–Cummings model with intensity-dependent coupling,” J. Mod. Opt. 36, 1151–1162 (1989).
[CrossRef]

Cárdenas, A. Z.

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]

Chaturdervi, S.

P. Shanta, S. Chaturdervi, and V. Srinivasan, “A model which interpolates between the Jaynes–Cummings model and the Buck–Sukumar model,” J. Mod. Opt. 39, 1301–1308 (1992).
[CrossRef]

Chilingaryan, S. A.

S. A. Chilingaryan and B. M. Rodríguez-Lara, “The quantum Rabi model for two qubits,” J. Phys. A Math. Theor. 46, 335301 (2013).
[CrossRef]

Chin, A. W.

A. W. Chin, Á. Rivas, S. F. Huelga, and M. B. Plenio, “Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials,” J. Math. Phys. 51, 092109 (2010).
[CrossRef]

Christodoulides, D.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

Christodoulides, D. N.

M.-A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87, 043819 (2013).
[CrossRef]

R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
[CrossRef]

B. M. Rodríguez-Lara, F. Soto-Eguibar, and D. N. Christodoulides, “An introduction to arrays of coupled waveguides,” arXiv: 1311.3694 (2013).

Cirac, J. I.

J. I. Cirac, R. Blatt, A. S. Parkins, and P. Zoller, “Quantum collapse and revival in the motion of a single trapped ion,” Phys. Rev. A 49, 1202–1207 (1994).
[CrossRef]

Coppa, A.

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Cordeiro, F.

F. Cordeiro, C. Providencia, J. da Providencia, and S. Nishiyama, “The Buck–Sukumar model described in terms of su(2)⊗su(1,1) coherent states,” J. Phys. A Math. Theor. 40, 12153–12160 (2007).
[CrossRef]

Crespi, A.

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum Rabi model,” Phys. Rev. Lett. 108, 163601 (2012).
[CrossRef]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

D’Ariano, G.

G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A 18, 1295–1307 (1985).
[CrossRef]

D’Ariano, G. M.

M. G. Rasetti, G. M. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
[CrossRef]

da Providencia, J.

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Figures (2)

Fig. 1.
Fig. 1.

Spectra for the positive (red solid lines) and negative (blue dashed lines) parity subspaces of the model H^± with k=1/2, that is, the BSM plus counter-rotating terms, for variable qubit frequency ω0 with a fixed coupling parameter (a) g=0.2ω and (b) g=0.45ω. The insets show typical avoided crossings.

Fig. 2.
Fig. 2.

Numerical simulation of evolution under H^+ with an initial state |0,e and parameter set {ω,ω0,g,k}={ω,3ω/4,4ω/10,1/2}. (a) Intensity at the zeroth waveguide, (b) mean photon number equivalent to the intensity barycenter, and (c) mean atomic excitation energy equivalent to the total intensity in odd waveguides minus the total intensity in even waveguides.

Equations (12)

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H^JC=ωn^+ω02σ^z+g(a^σ^++a^σ^),
H^BS=ωn^+ω02σ^z+g(a^n^σ^++n^a^σ^),
H^RBS=ωn^+ω02σ^z+g(a^n^+n^a^)σ^x,
H^=ωn^+ω02σ^z+g(n^+2ka^+a^n^+2k)σ^x,k>0,
H^±=ωK^0±ω02(1)K^0+g(K^++K^)ωk±ω02(1)k,k>0
H^±=ωK^0±ω02(1)K^0+g(K^++K^).
H^0=ωK^0+g(K^++K^).
A^A^=ωK^0+g(K^++K^)kω24g2,
A^A^=ωK˜0+g(K˜++K˜)+(12k)ω24g2,
S(ξ)A^A^S(ξ)=ω24g2n^,Ωj=ω24g2j,
S(ξ)A^A^S(ξ)=ω24g2(n^+1),Ωj(p)=ω24g2(j+1),
izEj(±)=nj(±)Ej(±)+γj1Ej1(±)+γjEj+1(±),E|j|=0.

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