Abstract

In this paper we present an experimentally feasible scheme to simulate a generalized Lipkin-Meskov-Glick model in a Bose-Einstein condensate coupled dispersively with an ultrahigh-finesse optical cavity. This obtained Hamiltonian has a unique advantage in that all parameters can be controlled independently by using Feshbach resonance technique, a pump laser along cavity axis and an external driving laser. By the proper choice of parameters, the macroscopic quantum coherent effect with a large amplitude can be successfully achieved. Comparing with the exist schemes, our proposal has a cleaner, perhaps significantly improved to observe this whole coherent effect. Finally, we predict a novel interaction-induced topological transition, which is an abrupt variation from π to zero of the Berry phase.

© 2009 Optical Society of America

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  1. A. Kitaev,"Anyons in an exactly solved model and beyond" Ann. Phys. 321, 2-111 (2006).
    [CrossRef]
  2. L. M. Duan, E. Demler, and M. D. Lukin, "Controlling spin exchange interactions of ultracold atoms in optical lattices," Phys. Rev. Lett. 91, 090402 (2003).
    [CrossRef] [PubMed]
  3. J. J. Garcia-Ripoll, M. A. Martin-Delgando, and J. I. Cirac, "Implementation of spin Hamiltonians in optical lattices," Phys. Rev. Lett. 93, 250405 (2004).
    [CrossRef]
  4. M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
    [CrossRef]
  5. H. J. Lipkin, N. Meshkov, and A. J. Glick, "Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory," Nucl. Phys. A 62, 188-198 (1965).
    [CrossRef]
  6. R. Botet, R. Jullien, and P. Pfeuty, "Size scaling for infinitely coordinated systems," Phys. Rev. Lett. 49, 478-481 (1982).
    [CrossRef]
  7. R. Botet and R. Jullien, "Large-size critical behavior of infinitely coordinated systems," Phys. Rev. B 28, 3955-3967 (1983).
    [CrossRef]
  8. S. Dusuel and J. Vidal, "Finite-size scaling exponents of the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 93, 237204 (2004).
    [CrossRef] [PubMed]
  9. S. Dusuel and J. Vidal, "Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model," Phys. Rev. B 71, 224420 (2005).
    [CrossRef]
  10. P. Ribeiro, J. Vidal, and R. Mosseri, "Thermodynamical Limit of the Lipkin-Meshkov-Glick Model," Phys. Rev. Lett. 99, 050402 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. C. Maschler and H. Ritsch, "Cold atom dynamics in a quantum optical lattice potential," Phys. Rev. Lett. 95, 260401 (2005).
    [CrossRef]
  17. J. Larson, B. Damski, G. Morigi, and M. Lewenstein, "Mott-Insulator states of ultracold atoms in optical resonators," Phys. Rev. Lett. 100, 050401 (2008).
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    [CrossRef]
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    [CrossRef]
  21. G. Chen, X. G. Wang, J. -Q. Liang, and Z. D. Wang, "Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity," Phys. Rev. A 78, 023634 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. G. J. Miburn, J. Corney, E. M. Wright, and D. F. Walls, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. A 55, 4318-4324 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
  26. S. Morrison and A. S. Parkins, "Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model with proposed realization in optical cavity QED," Phys. Rev. Lett. 100, 040403 (2008).
    [CrossRef] [PubMed]
  27. A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
    [CrossRef] [PubMed]
  28. A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
    [CrossRef] [PubMed]
  29. G. Chen and J. -Q. Liang, "Unconventional quantum phase transition in the finite-size Lipkin-Meshkov-Glick model," New J. Phys. 8, 297 (2006).
    [CrossRef]
  30. W. Wernsdorfer and R. Sessoli, "Quantum phase interference and parity effects in magnetic molecular clusters" Science 284, 133-135 (1999).
    [CrossRef] [PubMed]
  31. R. Lu, M. Zhang, J. L. Zhu, and L. You, "Effect of even and odd numbers of atoms in a condensate inside a double-well potential," Phys. Rev. A 78, 011605(R) (2008).
    [CrossRef]
  32. W. M. Zhang, D. H. Feng, and R. Gilmore, "Coherent states: theory and some applications," Rev. Mod. Phys. 62, 867-927 (1990).
    [CrossRef]
  33. E. Fradkin, "Field Theories of Condensed Matter Systems," (MA: Addison-Wesley, Reading, 1992) Chap. 5.
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    [CrossRef]

2009 (2)

J. Larson and M. Lewenstein, "Dilute gas of ultracold two-level atoms inside a cavity: generalized Dicke model," New J. Phys. 11, 063027 (2009).
[CrossRef]

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, "Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity," Phys. Rev. A 79, 033401 (2009).
[CrossRef]

2008 (9)

G. Chen, X. G. Wang, J. -Q. Liang, and Z. D. Wang, "Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity," Phys. Rev. A 78, 023634 (2008).
[CrossRef]

J. M. Zhang, W. M. Liu, and D. L. Zhou, "Mean-field dynamics of a Bose Josephson junction in an optical cavity," Phys. Rev. A 78, 043618 (2008).
[CrossRef]

J. Larson, B. Damski, G. Morigi, and M. Lewenstein, "Mott-Insulator states of ultracold atoms in optical resonators," Phys. Rev. Lett. 100, 050401 (2008).
[CrossRef] [PubMed]

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

S. Morrison and A. S. Parkins, "Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model with proposed realization in optical cavity QED," Phys. Rev. Lett. 100, 040403 (2008).
[CrossRef] [PubMed]

P. Ribeiro, J. Vidal, and R. Mosseri, "Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections," Phys. Rev. E 78, 021106 (2008).
[CrossRef]

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, "Entanglement in many-body systems," Rev. Mod. Phys. 80, 517-576 (2008).
[CrossRef]

R. Orus, S. Dusuel, and J. Vidal, "Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 101, 025701 (2008).
[CrossRef] [PubMed]

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, "Cavity optomechanics with a Bose-Einstein condensate," Science 322, 235-238 (2008).
[CrossRef] [PubMed]

2007 (3)

P. Ribeiro, J. Vidal, and R. Mosseri, "Thermodynamical Limit of the Lipkin-Meshkov-Glick Model," Phys. Rev. Lett. 99, 050402 (2007).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

2006 (2)

A. Kitaev,"Anyons in an exactly solved model and beyond" Ann. Phys. 321, 2-111 (2006).
[CrossRef]

G. Chen and J. -Q. Liang, "Unconventional quantum phase transition in the finite-size Lipkin-Meshkov-Glick model," New J. Phys. 8, 297 (2006).
[CrossRef]

2005 (2)

S. Dusuel and J. Vidal, "Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model," Phys. Rev. B 71, 224420 (2005).
[CrossRef]

C. Maschler and H. Ritsch, "Cold atom dynamics in a quantum optical lattice potential," Phys. Rev. Lett. 95, 260401 (2005).
[CrossRef]

2004 (3)

J. J. Garcia-Ripoll, M. A. Martin-Delgando, and J. I. Cirac, "Implementation of spin Hamiltonians in optical lattices," Phys. Rev. Lett. 93, 250405 (2004).
[CrossRef]

S. Dusuel and J. Vidal, "Finite-size scaling exponents of the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 93, 237204 (2004).
[CrossRef] [PubMed]

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

2003 (2)

R. G. Unanyan and M. Fleischhauer, "Decoherence-free generation of many-particle entanglement by adiabatic ground-state transitions," Phys. Rev. Lett. 90, 133601 (2003).
[CrossRef] [PubMed]

L. M. Duan, E. Demler, and M. D. Lukin, "Controlling spin exchange interactions of ultracold atoms in optical lattices," Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

1999 (2)

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

W. Wernsdorfer and R. Sessoli, "Quantum phase interference and parity effects in magnetic molecular clusters" Science 284, 133-135 (1999).
[CrossRef] [PubMed]

1997 (1)

G. J. Miburn, J. Corney, E. M. Wright, and D. F. Walls, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. A 55, 4318-4324 (1997).
[CrossRef]

1990 (1)

W. M. Zhang, D. H. Feng, and R. Gilmore, "Coherent states: theory and some applications," Rev. Mod. Phys. 62, 867-927 (1990).
[CrossRef]

1984 (1)

M. V. Berry, "Quantum phase factors accompanying adiabatic changes," Proc. R. Soc. London A 392, 45-57 (1984).
[CrossRef]

1983 (1)

R. Botet and R. Jullien, "Large-size critical behavior of infinitely coordinated systems," Phys. Rev. B 28, 3955-3967 (1983).
[CrossRef]

1982 (2)

R. Botet, R. Jullien, and P. Pfeuty, "Size scaling for infinitely coordinated systems," Phys. Rev. Lett. 49, 478-481 (1982).
[CrossRef]

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Nijs, "Quantized Hall conductance in a two-dimensional periodic potential," Phys. Rev. Lett. 49, 405-408 (1982).
[CrossRef]

1965 (1)

H. J. Lipkin, N. Meshkov, and A. J. Glick, "Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory," Nucl. Phys. A 62, 188-198 (1965).
[CrossRef]

Ahufinger, V

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

Amico, L.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, "Entanglement in many-body systems," Rev. Mod. Phys. 80, 517-576 (2008).
[CrossRef]

Berry, M. V.

M. V. Berry, "Quantum phase factors accompanying adiabatic changes," Proc. R. Soc. London A 392, 45-57 (1984).
[CrossRef]

Bloch, I.

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

Botet, R.

R. Botet and R. Jullien, "Large-size critical behavior of infinitely coordinated systems," Phys. Rev. B 28, 3955-3967 (1983).
[CrossRef]

R. Botet, R. Jullien, and P. Pfeuty, "Size scaling for infinitely coordinated systems," Phys. Rev. Lett. 49, 478-481 (1982).
[CrossRef]

Bourdel, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

Brennecke, F.

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, "Cavity optomechanics with a Bose-Einstein condensate," Science 322, 235-238 (2008).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

Cheinet, P.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

Chen, G.

G. Chen, X. G. Wang, J. -Q. Liang, and Z. D. Wang, "Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity," Phys. Rev. A 78, 023634 (2008).
[CrossRef]

G. Chen and J. -Q. Liang, "Unconventional quantum phase transition in the finite-size Lipkin-Meshkov-Glick model," New J. Phys. 8, 297 (2006).
[CrossRef]

Cirac, J. I.

J. J. Garcia-Ripoll, M. A. Martin-Delgando, and J. I. Cirac, "Implementation of spin Hamiltonians in optical lattices," Phys. Rev. Lett. 93, 250405 (2004).
[CrossRef]

Corney, J.

G. J. Miburn, J. Corney, E. M. Wright, and D. F. Walls, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. A 55, 4318-4324 (1997).
[CrossRef]

Cui, F. C.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, "Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity," Phys. Rev. A 79, 033401 (2009).
[CrossRef]

Damski, B

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

Damski, B.

J. Larson, B. Damski, G. Morigi, and M. Lewenstein, "Mott-Insulator states of ultracold atoms in optical resonators," Phys. Rev. Lett. 100, 050401 (2008).
[CrossRef] [PubMed]

Demler, E

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

Demler, E.

L. M. Duan, E. Demler, and M. D. Lukin, "Controlling spin exchange interactions of ultracold atoms in optical lattices," Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

Donner, T.

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, "Cavity optomechanics with a Bose-Einstein condensate," Science 322, 235-238 (2008).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

Duan, L. M.

L. M. Duan, E. Demler, and M. D. Lukin, "Controlling spin exchange interactions of ultracold atoms in optical lattices," Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

Dusuel, S.

R. Orus, S. Dusuel, and J. Vidal, "Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 101, 025701 (2008).
[CrossRef] [PubMed]

S. Dusuel and J. Vidal, "Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model," Phys. Rev. B 71, 224420 (2005).
[CrossRef]

S. Dusuel and J. Vidal, "Finite-size scaling exponents of the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 93, 237204 (2004).
[CrossRef] [PubMed]

Esslinger, T

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

Esslinger, T.

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, "Cavity optomechanics with a Bose-Einstein condensate," Science 322, 235-238 (2008).
[CrossRef] [PubMed]

Fazio, R.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, "Entanglement in many-body systems," Rev. Mod. Phys. 80, 517-576 (2008).
[CrossRef]

Feng, D. H.

W. M. Zhang, D. H. Feng, and R. Gilmore, "Coherent states: theory and some applications," Rev. Mod. Phys. 62, 867-927 (1990).
[CrossRef]

Fleischhauer, M.

R. G. Unanyan and M. Fleischhauer, "Decoherence-free generation of many-particle entanglement by adiabatic ground-state transitions," Phys. Rev. Lett. 90, 133601 (2003).
[CrossRef] [PubMed]

Foling, S.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

Garcia-Ripoll, J. J.

J. J. Garcia-Ripoll, M. A. Martin-Delgando, and J. I. Cirac, "Implementation of spin Hamiltonians in optical lattices," Phys. Rev. Lett. 93, 250405 (2004).
[CrossRef]

Gerbier, F.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

Gilmore, R.

W. M. Zhang, D. H. Feng, and R. Gilmore, "Coherent states: theory and some applications," Rev. Mod. Phys. 62, 867-927 (1990).
[CrossRef]

Glick, A. J.

H. J. Lipkin, N. Meshkov, and A. J. Glick, "Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory," Nucl. Phys. A 62, 188-198 (1965).
[CrossRef]

Greiner, M.

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

Gritsev, V.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

Hansch, T W.

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

Immanuel Bloch, F.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

Jullien, R.

R. Botet and R. Jullien, "Large-size critical behavior of infinitely coordinated systems," Phys. Rev. B 28, 3955-3967 (1983).
[CrossRef]

R. Botet, R. Jullien, and P. Pfeuty, "Size scaling for infinitely coordinated systems," Phys. Rev. Lett. 49, 478-481 (1982).
[CrossRef]

K¨ohl, M.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

Kitaev, A.

A. Kitaev,"Anyons in an exactly solved model and beyond" Ann. Phys. 321, 2-111 (2006).
[CrossRef]

Kohmoto, M.

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Nijs, "Quantized Hall conductance in a two-dimensional periodic potential," Phys. Rev. Lett. 49, 405-408 (1982).
[CrossRef]

Kreim, S.

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

Larson, J.

J. Larson and M. Lewenstein, "Dilute gas of ultracold two-level atoms inside a cavity: generalized Dicke model," New J. Phys. 11, 063027 (2009).
[CrossRef]

J. Larson, B. Damski, G. Morigi, and M. Lewenstein, "Mott-Insulator states of ultracold atoms in optical resonators," Phys. Rev. Lett. 100, 050401 (2008).
[CrossRef] [PubMed]

Lewenstein, M.

J. Larson and M. Lewenstein, "Dilute gas of ultracold two-level atoms inside a cavity: generalized Dicke model," New J. Phys. 11, 063027 (2009).
[CrossRef]

J. Larson, B. Damski, G. Morigi, and M. Lewenstein, "Mott-Insulator states of ultracold atoms in optical resonators," Phys. Rev. Lett. 100, 050401 (2008).
[CrossRef] [PubMed]

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

Liang, J. -Q.

G. Chen, X. G. Wang, J. -Q. Liang, and Z. D. Wang, "Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity," Phys. Rev. A 78, 023634 (2008).
[CrossRef]

G. Chen and J. -Q. Liang, "Unconventional quantum phase transition in the finite-size Lipkin-Meshkov-Glick model," New J. Phys. 8, 297 (2006).
[CrossRef]

Lipkin, H. J.

H. J. Lipkin, N. Meshkov, and A. J. Glick, "Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory," Nucl. Phys. A 62, 188-198 (1965).
[CrossRef]

Liu, W. M.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, "Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity," Phys. Rev. A 79, 033401 (2009).
[CrossRef]

J. M. Zhang, W. M. Liu, and D. L. Zhou, "Mean-field dynamics of a Bose Josephson junction in an optical cavity," Phys. Rev. A 78, 043618 (2008).
[CrossRef]

Lukin, M. D.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

L. M. Duan, E. Demler, and M. D. Lukin, "Controlling spin exchange interactions of ultracold atoms in optical lattices," Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

Mandel, O.

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

Martin-Delgando, M. A.

J. J. Garcia-Ripoll, M. A. Martin-Delgando, and J. I. Cirac, "Implementation of spin Hamiltonians in optical lattices," Phys. Rev. Lett. 93, 250405 (2004).
[CrossRef]

Maschler, C.

C. Maschler and H. Ritsch, "Cold atom dynamics in a quantum optical lattice potential," Phys. Rev. Lett. 95, 260401 (2005).
[CrossRef]

Meshkov, N.

H. J. Lipkin, N. Meshkov, and A. J. Glick, "Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory," Nucl. Phys. A 62, 188-198 (1965).
[CrossRef]

Meystre, P.

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

Miburn, G. J.

G. J. Miburn, J. Corney, E. M. Wright, and D. F. Walls, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. A 55, 4318-4324 (1997).
[CrossRef]

Moore, M. G.

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

Morigi, G.

J. Larson, B. Damski, G. Morigi, and M. Lewenstein, "Mott-Insulator states of ultracold atoms in optical resonators," Phys. Rev. Lett. 100, 050401 (2008).
[CrossRef] [PubMed]

Morrison, S.

S. Morrison and A. S. Parkins, "Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model with proposed realization in optical cavity QED," Phys. Rev. Lett. 100, 040403 (2008).
[CrossRef] [PubMed]

Mosseri, R.

P. Ribeiro, J. Vidal, and R. Mosseri, "Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections," Phys. Rev. E 78, 021106 (2008).
[CrossRef]

P. Ribeiro, J. Vidal, and R. Mosseri, "Thermodynamical Limit of the Lipkin-Meshkov-Glick Model," Phys. Rev. Lett. 99, 050402 (2007).
[CrossRef] [PubMed]

Nightingale, M. P.

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Nijs, "Quantized Hall conductance in a two-dimensional periodic potential," Phys. Rev. Lett. 49, 405-408 (1982).
[CrossRef]

Nijs, M.

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Nijs, "Quantized Hall conductance in a two-dimensional periodic potential," Phys. Rev. Lett. 49, 405-408 (1982).
[CrossRef]

Orus, R.

R. Orus, S. Dusuel, and J. Vidal, "Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 101, 025701 (2008).
[CrossRef] [PubMed]

Osterloh, A.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, "Entanglement in many-body systems," Rev. Mod. Phys. 80, 517-576 (2008).
[CrossRef]

Parkins, A. S.

S. Morrison and A. S. Parkins, "Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model with proposed realization in optical cavity QED," Phys. Rev. Lett. 100, 040403 (2008).
[CrossRef] [PubMed]

Pfeuty, P.

R. Botet, R. Jullien, and P. Pfeuty, "Size scaling for infinitely coordinated systems," Phys. Rev. Lett. 49, 478-481 (1982).
[CrossRef]

Ribeiro, P.

P. Ribeiro, J. Vidal, and R. Mosseri, "Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections," Phys. Rev. E 78, 021106 (2008).
[CrossRef]

P. Ribeiro, J. Vidal, and R. Mosseri, "Thermodynamical Limit of the Lipkin-Meshkov-Glick Model," Phys. Rev. Lett. 99, 050402 (2007).
[CrossRef] [PubMed]

Ritsch, H.

C. Maschler and H. Ritsch, "Cold atom dynamics in a quantum optical lattice potential," Phys. Rev. Lett. 95, 260401 (2005).
[CrossRef]

Ritter, S.

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, "Cavity optomechanics with a Bose-Einstein condensate," Science 322, 235-238 (2008).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

Sanpera, A.

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

Sen, A

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

Sen, U

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

Sessoli, R.

W. Wernsdorfer and R. Sessoli, "Quantum phase interference and parity effects in magnetic molecular clusters" Science 284, 133-135 (1999).
[CrossRef] [PubMed]

Thouless, D. J.

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Nijs, "Quantized Hall conductance in a two-dimensional periodic potential," Phys. Rev. Lett. 49, 405-408 (1982).
[CrossRef]

Trotzky, S.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

Unanyan, R. G.

R. G. Unanyan and M. Fleischhauer, "Decoherence-free generation of many-particle entanglement by adiabatic ground-state transitions," Phys. Rev. Lett. 90, 133601 (2003).
[CrossRef] [PubMed]

Vedral, V.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, "Entanglement in many-body systems," Rev. Mod. Phys. 80, 517-576 (2008).
[CrossRef]

Vidal, J.

R. Orus, S. Dusuel, and J. Vidal, "Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 101, 025701 (2008).
[CrossRef] [PubMed]

P. Ribeiro, J. Vidal, and R. Mosseri, "Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections," Phys. Rev. E 78, 021106 (2008).
[CrossRef]

P. Ribeiro, J. Vidal, and R. Mosseri, "Thermodynamical Limit of the Lipkin-Meshkov-Glick Model," Phys. Rev. Lett. 99, 050402 (2007).
[CrossRef] [PubMed]

S. Dusuel and J. Vidal, "Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model," Phys. Rev. B 71, 224420 (2005).
[CrossRef]

S. Dusuel and J. Vidal, "Finite-size scaling exponents of the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 93, 237204 (2004).
[CrossRef] [PubMed]

Walls, D. F.

G. J. Miburn, J. Corney, E. M. Wright, and D. F. Walls, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. A 55, 4318-4324 (1997).
[CrossRef]

Wang, X. G.

G. Chen, X. G. Wang, J. -Q. Liang, and Z. D. Wang, "Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity," Phys. Rev. A 78, 023634 (2008).
[CrossRef]

Wang, Z. D.

G. Chen, X. G. Wang, J. -Q. Liang, and Z. D. Wang, "Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity," Phys. Rev. A 78, 023634 (2008).
[CrossRef]

Wernsdorfer, W.

W. Wernsdorfer and R. Sessoli, "Quantum phase interference and parity effects in magnetic molecular clusters" Science 284, 133-135 (1999).
[CrossRef] [PubMed]

Widera, A.

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

Wright, E. M.

G. J. Miburn, J. Corney, E. M. Wright, and D. F. Walls, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. A 55, 4318-4324 (1997).
[CrossRef]

Zhang, J. M.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, "Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity," Phys. Rev. A 79, 033401 (2009).
[CrossRef]

J. M. Zhang, W. M. Liu, and D. L. Zhou, "Mean-field dynamics of a Bose Josephson junction in an optical cavity," Phys. Rev. A 78, 043618 (2008).
[CrossRef]

Zhang, W. M.

W. M. Zhang, D. H. Feng, and R. Gilmore, "Coherent states: theory and some applications," Rev. Mod. Phys. 62, 867-927 (1990).
[CrossRef]

Zhou, D. L.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, "Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity," Phys. Rev. A 79, 033401 (2009).
[CrossRef]

J. M. Zhang, W. M. Liu, and D. L. Zhou, "Mean-field dynamics of a Bose Josephson junction in an optical cavity," Phys. Rev. A 78, 043618 (2008).
[CrossRef]

Zobay, O.

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

Adv. Phys. (1)

M. Lewenstein, A. Sanpera, V , Ahufinger, B . Damski, A . Sen, and U . Sen, "Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond," Adv. Phys. 56, 243-379 (2007).
[CrossRef]

Ann. Phys. (1)

A. Kitaev,"Anyons in an exactly solved model and beyond" Ann. Phys. 321, 2-111 (2006).
[CrossRef]

Nature (1)

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. K¨ohl, and T Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268-271 (2007).
[CrossRef] [PubMed]

New J. Phys. (2)

J. Larson and M. Lewenstein, "Dilute gas of ultracold two-level atoms inside a cavity: generalized Dicke model," New J. Phys. 11, 063027 (2009).
[CrossRef]

G. Chen and J. -Q. Liang, "Unconventional quantum phase transition in the finite-size Lipkin-Meshkov-Glick model," New J. Phys. 8, 297 (2006).
[CrossRef]

Nucl. Phys. A (1)

H. J. Lipkin, N. Meshkov, and A. J. Glick, "Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory," Nucl. Phys. A 62, 188-198 (1965).
[CrossRef]

Phys. Rev. A (5)

J. M. Zhang, W. M. Liu, and D. L. Zhou, "Mean-field dynamics of a Bose Josephson junction in an optical cavity," Phys. Rev. A 78, 043618 (2008).
[CrossRef]

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, "Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity," Phys. Rev. A 79, 033401 (2009).
[CrossRef]

G. Chen, X. G. Wang, J. -Q. Liang, and Z. D. Wang, "Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity," Phys. Rev. A 78, 023634 (2008).
[CrossRef]

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

G. J. Miburn, J. Corney, E. M. Wright, and D. F. Walls, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. A 55, 4318-4324 (1997).
[CrossRef]

Phys. Rev. B (2)

R. Botet and R. Jullien, "Large-size critical behavior of infinitely coordinated systems," Phys. Rev. B 28, 3955-3967 (1983).
[CrossRef]

S. Dusuel and J. Vidal, "Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model," Phys. Rev. B 71, 224420 (2005).
[CrossRef]

Phys. Rev. E (1)

P. Ribeiro, J. Vidal, and R. Mosseri, "Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections," Phys. Rev. E 78, 021106 (2008).
[CrossRef]

Phys. Rev. Lett. (13)

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Nijs, "Quantized Hall conductance in a two-dimensional periodic potential," Phys. Rev. Lett. 49, 405-408 (1982).
[CrossRef]

P. Ribeiro, J. Vidal, and R. Mosseri, "Thermodynamical Limit of the Lipkin-Meshkov-Glick Model," Phys. Rev. Lett. 99, 050402 (2007).
[CrossRef] [PubMed]

S. Dusuel and J. Vidal, "Finite-size scaling exponents of the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 93, 237204 (2004).
[CrossRef] [PubMed]

R. Botet, R. Jullien, and P. Pfeuty, "Size scaling for infinitely coordinated systems," Phys. Rev. Lett. 49, 478-481 (1982).
[CrossRef]

L. M. Duan, E. Demler, and M. D. Lukin, "Controlling spin exchange interactions of ultracold atoms in optical lattices," Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

J. J. Garcia-Ripoll, M. A. Martin-Delgando, and J. I. Cirac, "Implementation of spin Hamiltonians in optical lattices," Phys. Rev. Lett. 93, 250405 (2004).
[CrossRef]

R. G. Unanyan and M. Fleischhauer, "Decoherence-free generation of many-particle entanglement by adiabatic ground-state transitions," Phys. Rev. Lett. 90, 133601 (2003).
[CrossRef] [PubMed]

S. Morrison and A. S. Parkins, "Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model with proposed realization in optical cavity QED," Phys. Rev. Lett. 100, 040403 (2008).
[CrossRef] [PubMed]

A. Widera, O. Mandel, M. Greiner, S. Kreim, T W. Hansch, and I. Bloch, "Entanglement interferometry for precision measurement of atomic scattering properties," Phys. Rev. Lett. 92, 160406 (2004).
[CrossRef] [PubMed]

A. Widera, S. Trotzky, P. Cheinet, S. Foling, F. Gerbier, Immanuel Bloch, V. Gritsev, M. D. Lukin, and E . Demler, "Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases," Phys. Rev. Lett. 100, 140401 (2008).
[CrossRef] [PubMed]

C. Maschler and H. Ritsch, "Cold atom dynamics in a quantum optical lattice potential," Phys. Rev. Lett. 95, 260401 (2005).
[CrossRef]

J. Larson, B. Damski, G. Morigi, and M. Lewenstein, "Mott-Insulator states of ultracold atoms in optical resonators," Phys. Rev. Lett. 100, 050401 (2008).
[CrossRef] [PubMed]

R. Orus, S. Dusuel, and J. Vidal, "Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model," Phys. Rev. Lett. 101, 025701 (2008).
[CrossRef] [PubMed]

Proc. R. Soc. London A (1)

M. V. Berry, "Quantum phase factors accompanying adiabatic changes," Proc. R. Soc. London A 392, 45-57 (1984).
[CrossRef]

Rev. Mod. Phys. (2)

W. M. Zhang, D. H. Feng, and R. Gilmore, "Coherent states: theory and some applications," Rev. Mod. Phys. 62, 867-927 (1990).
[CrossRef]

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, "Entanglement in many-body systems," Rev. Mod. Phys. 80, 517-576 (2008).
[CrossRef]

Science (2)

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, "Cavity optomechanics with a Bose-Einstein condensate," Science 322, 235-238 (2008).
[CrossRef] [PubMed]

W. Wernsdorfer and R. Sessoli, "Quantum phase interference and parity effects in magnetic molecular clusters" Science 284, 133-135 (1999).
[CrossRef] [PubMed]

Other (2)

R. Lu, M. Zhang, J. L. Zhu, and L. You, "Effect of even and odd numbers of atoms in a condensate inside a double-well potential," Phys. Rev. A 78, 011605(R) (2008).
[CrossRef]

E. Fradkin, "Field Theories of Condensed Matter Systems," (MA: Addison-Wesley, Reading, 1992) Chap. 5.

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Figures (3)

Fig. 1.
Fig. 1.

(Color online) Schematic diagram for our considerations. The coherent dynamics of the ultracold atoms and the cavity field can be driven by both applying a pump laser along cavity axis and a classical driving laser.

Fig. 2.
Fig. 2.

(Color online) The energy gap of Hamiltonian (12) versus the effective Rabi frequency Ω. The parameters are given by q=0.1 Hz and N=20 with p=-10q (Red-solid line) and p=-12q (Blue-dashed line).

Fig. 3.
Fig. 3.

(Color online) The scaled ground-state Berry phase Γ/S and the ultracold atom population 〈Sz 〉/S versus the controllable interaction constant q.

Equations (21)

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

HLMG=νi<j(σxiσxj+γσyiσyi)hiσzi,
HLMG=2ν(Sx2+γSy2)2hSz,
H(t)=Hph+Hat+Hatph+Hpu+Hdr.
Hat=d3r[ω12Ψ2(r)Ψ2(r)+q1,2Ψ1(r)Ψ2(r)Ψ1(r)Ψ2(r)]
+ l=1,2 d3 r{Ψl(r)[22mR+Vl(r)]Ψl(r)+ql2Ψl(r)Ψl(r)Ψl(r)Ψl(r)} ,
Hatph=g˜d3rΨ1(r)Ψ2(r)(a+a)+H.c.
Hpu(t)=Ωp[aexp(iωpt)+aexp(iωpt)],
Hdr(t)=Ωd̃d3r[Ψ2(r)Ψ1(r)exp(iωdt)]+H . c . ,
H(t)=ωaa+l=1,2(ωlclcl+ω12c2c2+ηl2clclclcl)+χc1c1c2c2+λ2(c1c2+c2c1)(a+a)
+Ωd2[c2+c1exp(iωdt)+c1+cexp(iωdt)]+Ωp[aexp(iωpt)+aexp(iωpt)]
H(t)=ωaa+λ(Sa+S+a)+ω0SzqSz2+Ωd2[S+exp(iωdt)+Sexp(iωdt)]
+Ωp[aexp(iωpt)+aexp(iωpt)],
H=Δpaa+λ(Sa+S+a)+ΔaSzqSz2+ΩdSx+Ωp(a+a),
HL=pSx2qSz2+ΔaSz+ΩSx
HL1=pSx2qSz2+ΩSx.
HL2=p Sx2 q Sz2
E(θ,φ)=pS2sin2θcos2φqS2cos2θ ,
cosθ={0,q<p1,q>p.
SWZ=θ(0),φ(0)θ(τ),φ(τ)iS(1cosθ)φ˙dτ.
ΓS=π (1cosθ)={π,q<p0,q>p .
SzS=cosθ={0,q<p1,q>p.

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