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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 Liang^{1}
^{1}Department of Physics, Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China ^{2}State 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]
- F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science322, 235–238 (2008). [CrossRef] [PubMed]
- 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, “Chaos and the quantum phase transition in the Dicke model,” Phys. Rev. E67, 066203 (2003). [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]
- 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]
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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]
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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. 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]
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- 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]
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- 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]
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- 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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- 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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- 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)
- P. Lebedew, “Experimental examination of light pressure,” Ann. Phys. (Leipzig)6, 433–458 (1901).
Annals Phys.(N.Y.)
- 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]
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]
- 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]
- 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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- E. F. Nichols and G. F. Hull, “A preliminary communication on the pressure of heat and light radiation,” Phys. Rev.13, 307 (1901).
Phys. Rev. A
- C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A77, 050307 (2008). [CrossRef]
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- M. Ludwig, K. Hammerer, and F. Marquardt, “Entanglement of mechanical oscillators coupled to a nonequilibrium environment,” Phys. Rev. A82, 012333 (2010). [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]
- 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]
- 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]
- 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]
- N. Lambert, C. Emary, and T. Brandes, “Entanglement and entropy in a spin-boson quantum phase transition,” Phys. Rev. A71, 053804 (2005). [CrossRef]
- 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]
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- 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]
Phys. Rev. E
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Phys. Rev. Lett.
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- 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]
- 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]
- 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]
- 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]
- 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]
- 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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