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A scheme for detecting the atom-field coupling constant in the Dicke superradiation regime using hybrid cavity optomechanical systemYueming Wang, Bin Liu, Jinling Lian, and Jiuqing Liang »View Author Affiliations
Yueming Wang,1,2,*
Bin Liu,1
Jinling Lian,1
and Jiuqing Liang1
1Department of Physics, Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China 2State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, 030006, China *Corresponding author: wang_ym@sxu.edu.cn |
Optics Express, Vol. 20, Issue 9, pp. 10106-10114 (2012)
http://dx.doi.org/10.1364/OE.20.010106
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Abstract
We proposed a scheme for detecting the atom-field coupling constant in the Dicke superradiation regime based on a hybrid cavity optomechanical system assisted by an atomic gas. The critical behavior of the Dicke model was obtained analytically using the spin-coherent-state representation. Without regard to the dynamics of cavity field an analytical formula of one-to-one correspondence between movable mirror’s steady position and atom-field coupling constant for a given number of atoms is obtained. Thus the atom-field coupling constant can be probed by measuring the movable mirror’s steady position, which is another effect of the cavity optomechanics.
© 2012 OSA
OCIS Codes
(220.4880) Optical design and fabrication : Optomechanics
(270.0270) Quantum optics : Quantum optics
(270.6630) Quantum optics : Superradiance, superfluorescence
ToC Category:
Quantum Optics
History
Original Manuscript: February 10, 2012
Revised Manuscript: April 10, 2012
Manuscript Accepted: April 11, 2012
Published: April 18, 2012
Citation
Yueming Wang, Bin Liu, Jinling Lian, and Jiuqing Liang, "A scheme for detecting the atom-field coupling constant in the Dicke superradiation regime using hybrid cavity optomechanical system," Opt. Express 20, 10106-10114 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-10106
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- D. Teufe, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature475, 359–363 (2011). [CrossRef]
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- N. Lambert, C. Emary, and T. Brandes, “Entanglement and entropy in a spin-boson quantum phase transition,” Phys. Rev. A71, 053804 (2005). [CrossRef]
- C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett.90, 044101 (2003). [CrossRef] [PubMed]
- C. Emary and T. Brandes, “Chaos and the quantum phase transition in the Dicke model,” Phys. Rev. E67, 066203 (2003). [CrossRef]
- F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science322, 235–238 (2008). [CrossRef] [PubMed]
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- D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett.98, 030405 (2007). [CrossRef] [PubMed]
- J. P. Santos, F. L. Semião, and K. Furuya, “Probing the quantum phase transition in the Dicke model through mechanical vibrations,” Phys. Rev. A82, 063801 (2010). [CrossRef]
- K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, “Strong coupling of a mechanical oscillator and a single atom,” Phys. Rev. Lett.103, 063005 (2009). [CrossRef] [PubMed]
- C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A77, 050307 (2008). [CrossRef]
- D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett.98, 030405 (2007). [CrossRef] [PubMed]
- S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Cooling of a micromirror by radiation pressure,” Nature444, 67–70 (2006). [CrossRef] [PubMed]
- S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploiting radiation pressure,” Phys. Rev. Lett.88, 120401 (2002). [CrossRef] [PubMed]
- K. Børkje, A. Nunnenkamp, and S. M. Girvin, “Proposal for entangling remote micromechanical oscillators via optical measurements,” Phys. Rev. Lett.107, 123601 (2011). [CrossRef] [PubMed]
- F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett.99, 093902 (2007). [CrossRef] [PubMed]
- H. Ian, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Cavity optomechanical coupling assisted by an atomic gas,” Phys. Rev. A78, 013824 (2008). [CrossRef]
- J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature478, 89–92 (2011). [CrossRef] [PubMed]
- D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett.98, 030405 (2007). [CrossRef] [PubMed]
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- S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploiting radiation pressure,” Phys. Rev. Lett.88, 120401 (2002). [CrossRef] [PubMed]
- K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, “Strong coupling of a mechanical oscillator and a single atom,” Phys. Rev. Lett.103, 063005 (2009). [CrossRef] [PubMed]
- M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. OConnell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature454, 310–314 (2008). [CrossRef] [PubMed]
- Y. K. Wang and F. T. Hioes, “Phase transition in the Dicke model of superradiance,” Phys. Rev. A7, 831–836 (1973). [CrossRef]
- M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. OConnell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature454, 310–314 (2008). [CrossRef] [PubMed]
- T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett.98, 150802 (2007). [CrossRef] [PubMed]
- D. Teufe, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature475, 359–363 (2011). [CrossRef]
- I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett.99, 093901 (2007). [CrossRef] [PubMed]
- T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett.98, 150802 (2007). [CrossRef] [PubMed]
- Q. Sun, X.-H. Hu, W. M. Liu, X. C. Xie, and A.-C. Ji, “Effect on cavity optomechanics of the interaction between a cavity field and a one-dimensional interacting bosonic gas,” Phys. Rev. A84, 023822 (2011). [CrossRef]
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- S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Cooling of a micromirror by radiation pressure,” Nature444, 67–70 (2006). [CrossRef] [PubMed]
- L. Zhou, Y. Han, J. Jing, and W. Zhang, “Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence,” Phys. Rev. A83, 052117 (2011). [CrossRef]
- L. Zhou, Y. Han, J. Jing, and W. Zhang, “Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence,” Phys. Rev. A83, 052117 (2011). [CrossRef]
- K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, “Strong coupling of a mechanical oscillator and a single atom,” Phys. Rev. Lett.103, 063005 (2009). [CrossRef] [PubMed]
- K. Hammerer, M. Aspelmeyer, E. S. Polzik, and P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett.102, 020501 (2009). [CrossRef] [PubMed]
- L. Tian and P. Zoller, “Coupled ion-nanomechanical systems,” Phys. Rev. Lett.93, 266403 (2004). [CrossRef]
- I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett.99, 093901 (2007). [CrossRef] [PubMed]
Ann. Phys. (Leipzig)
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Annals Phys.(N.Y.)
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J. Opt. B: Quantum Semiclass. Opt
- T. Corbitt and N. Mavalvala, “Quantum noise in gravitational-wave interferometers,” J. Opt. B: Quantum Semiclass. Opt6, S675–S683 (2004). [CrossRef]
Nature
- S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Cooling of a micromirror by radiation pressure,” Nature444, 67–70 (2006). [CrossRef] [PubMed]
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- D. Teufe, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature475, 359–363 (2011). [CrossRef]
- M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. OConnell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature454, 310–314 (2008). [CrossRef] [PubMed]
Opt. Express
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Phys. Rev.
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- R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93, 99–110 (1954). [CrossRef]
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Phys. Rev. A
- J. P. Santos, F. L. Semião, and K. Furuya, “Probing the quantum phase transition in the Dicke model through mechanical vibrations,” Phys. Rev. A82, 063801 (2010). [CrossRef]
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- G. D. Chiara, M. Paternostro, and G. M. Palma, “Entanglement detection in hybrid optomechanical systems,” Phys. Rev. A83, 052324–052329 (2011). [CrossRef]
- G. Chen, J. Li, and J.-Q. Liang, “Critical property of the geometric phase in the Dicke model,” Phys. Rev. A74, 054101 (2006). [CrossRef]
- Q. Sun, X.-H. Hu, W. M. Liu, X. C. Xie, and A.-C. Ji, “Effect on cavity optomechanics of the interaction between a cavity field and a one-dimensional interacting bosonic gas,” Phys. Rev. A84, 023822 (2011). [CrossRef]
- Q. Sun, X.-H. Hu, A.-C. Ji, and W. M. Liu, “Dynamics of a degenerate Fermi gas in a one-dimensional optical lattice coupled to a cavity,” Phys. Rev. A83, 043606 (2011). [CrossRef]
- F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A75, 013804 (2007). [CrossRef]
- S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Phys. Rev. A81, 042311 (2010). [CrossRef]
- C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A77, 050307 (2008). [CrossRef]
- L. Zhou, Y. Han, J. Jing, and W. Zhang, “Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence,” Phys. Rev. A83, 052117 (2011). [CrossRef]
- M. Ludwig, K. Hammerer, and F. Marquardt, “Entanglement of mechanical oscillators coupled to a nonequilibrium environment,” Phys. Rev. A82, 012333 (2010). [CrossRef]
- S. K. Steinke, S. Singh, M. E. Tasgin, P. Meystre, K. C. Schwab, and M. Vengalattore, “Quantum-measurement backaction from a Bose-Einstein condensate coupled to a mechanical oscillator,” Phys. Rev. A84, 023841 (2011). [CrossRef]
- H. Ian, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Cavity optomechanical coupling assisted by an atomic gas,” Phys. Rev. A78, 013824 (2008). [CrossRef]
- Y. Chang and C. P. Sun, “Analog of the electromagnetically-induced-transparency effect for two nanomechanical or micromechanical resonators coupled to a spin ensemble,” Phys. Rev. A83, 053834 (2011). [CrossRef]
- Y. K. Wang and F. T. Hioes, “Phase transition in the Dicke model of superradiance,” Phys. Rev. A7, 831–836 (1973). [CrossRef]
- F. T. Hioes, “Phase transitions in some generalized Dicke models of superradiance,” Phys. Rev. A8, 1440–1445 (1973). [CrossRef]
- A. B. Bhattacherjee, “Cavity quantum optomechanics of ultracold atoms in an optical lattice: normal-mode splitting,” Phys. Rev. A80, 043607 (2009). [CrossRef]
- S. Bose, K. Jacobs, and P. L. Knight, “Preparation of nonclassical states in cavities with a moving mirror,” Phys. Rev. A56, 4175 (1997). [CrossRef]
Phys. Rev. E
- C. Emary and T. Brandes, “Chaos and the quantum phase transition in the Dicke model,” Phys. Rev. E67, 066203 (2003). [CrossRef]
Phys. Rev. Lett.
- E. K. Irish, “Generalized rotating-wave approximation for arbitrarily large coupling,” Phys. Rev. Lett.99, 173601 (2007). [CrossRef] [PubMed]
- W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards quantum superpositions of a mirror,” Phys. Rev. Lett.91, 130401 (2003). [CrossRef] [PubMed]
- F. Khalili, S. Danilishin, H. Miao, H. Müller-Ebhardt, H. Yang, and Y. Chen, “Preparing a mechanical oscillator in non-Gaussian quantum states,” Phys. Rev. Lett.105, 070403 (2010). [CrossRef] [PubMed]
- D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett.98, 030405 (2007). [CrossRef] [PubMed]
- D. Hunger, S. Camerer, T. W. Hänsch, D. König, J. P. Kotthaus, J. Reichel, and P. Treutlein, “Resonant coupling of a Bose-Einstein condensate to a micromechanical oscillator,” Phys. Rev. Lett.104, 143002 (2010). [CrossRef] [PubMed]
- C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett.90, 044101 (2003). [CrossRef] [PubMed]
- K. Hammerer, M. Aspelmeyer, E. S. Polzik, and P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett.102, 020501 (2009). [CrossRef] [PubMed]
- K. Børkje, A. Nunnenkamp, and S. M. Girvin, “Proposal for entangling remote micromechanical oscillators via optical measurements,” Phys. Rev. Lett.107, 123601 (2011). [CrossRef] [PubMed]
- S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploiting radiation pressure,” Phys. Rev. Lett.88, 120401 (2002). [CrossRef] [PubMed]
- L. Tian and P. Zoller, “Coupled ion-nanomechanical systems,” Phys. Rev. Lett.93, 266403 (2004). [CrossRef]
- K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, “Strong coupling of a mechanical oscillator and a single atom,” Phys. Rev. Lett.103, 063005 (2009). [CrossRef] [PubMed]
- P. Treutlein, D. Hunger, S. Camerer, T. W. Hänsch, and J. Reichel, “Bose-Einstein condensate coupled to a nanomechanical resonator on an atom chip,” Phys. Rev. Lett.99, 140403 (2007). [CrossRef] [PubMed]
- T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett.98, 150802 (2007). [CrossRef] [PubMed]
- P. F. Cohadon, A. Heidmann, and M. Pinard, “Cooling of a mirror by radiation pressure,” Phys. Rev. Lett.833174 (1999). [CrossRef]
- F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett.99, 093902 (2007). [CrossRef] [PubMed]
- I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett.99, 093901 (2007). [CrossRef] [PubMed]
Physics Today
- K. C. Schwab and M. L. Roukes, “Putting mechanics into quantum mechanics,” Physics Today58, 36–42 (2005). [CrossRef]
Science
- T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321, 1172–1176 (2008). [CrossRef] [PubMed]
- F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science322, 235–238 (2008). [CrossRef] [PubMed]
2011, Chan, Nature
- J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature478, 89–92 (2011). [CrossRef] [PubMed]
- D. Teufe, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature475, 359–363 (2011). [CrossRef]
- L. Zhou, Y. Han, J. Jing, and W. Zhang, “Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence,” Phys. Rev. A83, 052117 (2011). [CrossRef]
- K. Børkje, A. Nunnenkamp, and S. M. Girvin, “Proposal for entangling remote micromechanical oscillators via optical measurements,” Phys. Rev. Lett.107, 123601 (2011). [CrossRef] [PubMed]
- S. K. Steinke, S. Singh, M. E. Tasgin, P. Meystre, K. C. Schwab, and M. Vengalattore, “Quantum-measurement backaction from a Bose-Einstein condensate coupled to a mechanical oscillator,” Phys. Rev. A84, 023841 (2011). [CrossRef]
- Y. Chang and C. P. Sun, “Analog of the electromagnetically-induced-transparency effect for two nanomechanical or micromechanical resonators coupled to a spin ensemble,” Phys. Rev. A83, 053834 (2011). [CrossRef]
- Q. Sun, X.-H. Hu, W. M. Liu, X. C. Xie, and A.-C. Ji, “Effect on cavity optomechanics of the interaction between a cavity field and a one-dimensional interacting bosonic gas,” Phys. Rev. A84, 023822 (2011). [CrossRef]
- Q. Sun, X.-H. Hu, A.-C. Ji, and W. M. Liu, “Dynamics of a degenerate Fermi gas in a one-dimensional optical lattice coupled to a cavity,” Phys. Rev. A83, 043606 (2011). [CrossRef]
- G. D. Chiara, M. Paternostro, and G. M. Palma, “Entanglement detection in hybrid optomechanical systems,” Phys. Rev. A83, 052324–052329 (2011). [CrossRef]
- J. P. Santos, F. L. Semião, and K. Furuya, “Probing the quantum phase transition in the Dicke model through mechanical vibrations,” Phys. Rev. A82, 063801 (2010). [CrossRef]
- S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states,” Phys. Rev. A81, 042311 (2010). [CrossRef]
- D. Hunger, S. Camerer, T. W. Hänsch, D. König, J. P. Kotthaus, J. Reichel, and P. Treutlein, “Resonant coupling of a Bose-Einstein condensate to a micromechanical oscillator,” Phys. Rev. Lett.104, 143002 (2010). [CrossRef] [PubMed]
- M. Ludwig, K. Hammerer, and F. Marquardt, “Entanglement of mechanical oscillators coupled to a nonequilibrium environment,” Phys. Rev. A82, 012333 (2010). [CrossRef]
- F. Khalili, S. Danilishin, H. Miao, H. Müller-Ebhardt, H. Yang, and Y. Chen, “Preparing a mechanical oscillator in non-Gaussian quantum states,” Phys. Rev. Lett.105, 070403 (2010). [CrossRef] [PubMed]
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- A. B. Bhattacherjee, “Cavity quantum optomechanics of ultracold atoms in an optical lattice: normal-mode splitting,” Phys. Rev. A80, 043607 (2009). [CrossRef]
- K. Hammerer, M. Aspelmeyer, E. S. Polzik, and P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett.102, 020501 (2009). [CrossRef] [PubMed]
- H. Ian, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Cavity optomechanical coupling assisted by an atomic gas,” Phys. Rev. A78, 013824 (2008). [CrossRef]
- F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science322, 235–238 (2008). [CrossRef] [PubMed]
- C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A77, 050307 (2008). [CrossRef]
- T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321, 1172–1176 (2008). [CrossRef] [PubMed]
- M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. OConnell, H. Wang, J. M. Martinis, and A. N. Cleland, “Generation of Fock states in a superconducting quantum circuit,” Nature454, 310–314 (2008). [CrossRef] [PubMed]
- F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A75, 013804 (2007). [CrossRef]
- E. K. Irish, “Generalized rotating-wave approximation for arbitrarily large coupling,” Phys. Rev. Lett.99, 173601 (2007). [CrossRef] [PubMed]
- F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett.99, 093902 (2007). [CrossRef] [PubMed]
- I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett.99, 093901 (2007). [CrossRef] [PubMed]
- T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett.98, 150802 (2007). [CrossRef] [PubMed]
- D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett.98, 030405 (2007). [CrossRef] [PubMed]
- P. Treutlein, D. Hunger, S. Camerer, T. W. Hänsch, and J. Reichel, “Bose-Einstein condensate coupled to a nanomechanical resonator on an atom chip,” Phys. Rev. Lett.99, 140403 (2007). [CrossRef] [PubMed]
- S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Cooling of a micromirror by radiation pressure,” Nature444, 67–70 (2006). [CrossRef] [PubMed]
- G. Chen, J. Li, and J.-Q. Liang, “Critical property of the geometric phase in the Dicke model,” Phys. Rev. A74, 054101 (2006). [CrossRef]
- N. Lambert, C. Emary, and T. Brandes, “Entanglement and entropy in a spin-boson quantum phase transition,” Phys. Rev. A71, 053804 (2005). [CrossRef]
- K. C. Schwab and M. L. Roukes, “Putting mechanics into quantum mechanics,” Physics Today58, 36–42 (2005). [CrossRef]
- T. Corbitt and N. Mavalvala, “Quantum noise in gravitational-wave interferometers,” J. Opt. B: Quantum Semiclass. Opt6, S675–S683 (2004). [CrossRef]
- L. Tian and P. Zoller, “Coupled ion-nanomechanical systems,” Phys. Rev. Lett.93, 266403 (2004). [CrossRef]
- W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards quantum superpositions of a mirror,” Phys. Rev. Lett.91, 130401 (2003). [CrossRef] [PubMed]
- C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett.90, 044101 (2003). [CrossRef] [PubMed]
- C. Emary and T. Brandes, “Chaos and the quantum phase transition in the Dicke model,” Phys. Rev. E67, 066203 (2003). [CrossRef]
- S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploiting radiation pressure,” Phys. Rev. Lett.88, 120401 (2002). [CrossRef] [PubMed]
- P. F. Cohadon, A. Heidmann, and M. Pinard, “Cooling of a mirror by radiation pressure,” Phys. Rev. Lett.833174 (1999). [CrossRef]
- S. Bose, K. Jacobs, and P. L. Knight, “Preparation of nonclassical states in cavities with a moving mirror,” Phys. Rev. A56, 4175 (1997). [CrossRef]
- K. Hepp and E. H. Lieb, “On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model,” Annals Phys.(N.Y.)76, 360–404 (1973). [CrossRef]
- Y. K. Wang and F. T. Hioes, “Phase transition in the Dicke model of superradiance,” Phys. Rev. A7, 831–836 (1973). [CrossRef]
- F. T. Hioes, “Phase transitions in some generalized Dicke models of superradiance,” Phys. Rev. A8, 1440–1445 (1973). [CrossRef]
- R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93, 99–110 (1954). [CrossRef]
- T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev.58, 1098–1113 (1940). [CrossRef]
- P. Lebedew, “Experimental examination of light pressure,” Ann. Phys. (Leipzig)6, 433–458 (1901).
- E. F. Nichols and G. F. Hull, “A preliminary communication on the pressure of heat and light radiation,” Phys. Rev.13, 307 (1901).
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