Abstract

A new type of collective nonlinear coupling is presented via the indirect interaction between an ultracold atomic ensemble and a nanomechanical oscillator. More intriguingly, its interaction strength is enhanced largely with a factor of the atomic number, and thus, reaches a strong coupling regime within current experimental parameters. For the large atomic number, this obtained nonlinear coupling describes the interaction between the phonon and a pair of quasiparticle. Physically, this pair of quasiparticle is excited from the ultracold atomic ensemble when a phonon is emitted and vice versa. Based on these collective excitations, the nonlinear optical processes with the χ(2) term are simulated successfully.

© 2010 OSA

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2010 (2)

J. Larson, “Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model,” Europhys. Lett. 90, 54001 (2010).
[CrossRef]

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041 (2010).
[CrossRef]

2009 (6)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550 (2009).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. A. Aspemeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[CrossRef] [PubMed]

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (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]

C. Genes, H. Ritsch, and D. Vitali, “Micromechanical oscillator ground-state cooling via resonant intracavity optical gain or absorption,” Phys. Rev. A 80, 061803 (2009).
[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]

2008 (6)

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nature Phys. 4, 555 (2008).
[CrossRef]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A 77, 050307 (2008).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172 (2008).
[CrossRef] [PubMed]

G. Chen, X. 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]

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, “Cavity-assisted backaction cooling of mechanical resonators,” N. J. Phys. 10, 095007 (2008).
[CrossRef]

2007 (2)

K. Jacobs, “Engineering quantum states of a nanoresonator via a simple auxiliary system,” Phys. Rev. Lett. 99, 117203 (2007).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

2006 (2)

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

2005 (1)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

1998 (1)

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

1984 (1)

G. S. Agarwal, “Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity,” Phys. Rev. Lett. 53, 1732 (1984).
[CrossRef]

1968 (1)

G. Chen, J.-Q. Liang, and S. Jia, “Interaction-induced Lipkin-Meshkov-Glick model in a Bose-Einstein condensate inside an optical cavity,” Opt. Express 17, 19682 (2009).

1950 (1)

H. Fröhlich, “Theory of the superconducting state. I. the ground state at the absolute zero of temperature,” Phys. Rev. 79, 845 (1950).
[CrossRef]

1946 (1)

E. M. Purcell, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37 (1946).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity,” Phys. Rev. Lett. 53, 1732 (1984).
[CrossRef]

Andrews, M. R.

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

Aspelmeyer, M.

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]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Aspemeyer, M. A.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. A. Aspemeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[CrossRef] [PubMed]

Bäuerle, D.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Blaser, F.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Böhm, H. R.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Bourdel, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Brennecke, F.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550 (2009).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550 (2009).
[CrossRef] [PubMed]

Chen, G.

G. Chen, X. 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, J.-Q. Liang, and S. Jia, “Interaction-induced Lipkin-Meshkov-Glick model in a Bose-Einstein condensate inside an optical cavity,” Opt. Express 17, 19682 (2009).

Dobrindt, J.

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, “Cavity-assisted backaction cooling of mechanical resonators,” N. J. Phys. 10, 095007 (2008).
[CrossRef]

Donner, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

Eichenfield, M.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550 (2009).
[CrossRef] [PubMed]

Esslinger, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

Fröhlich, H.

H. Fröhlich, “Theory of the superconducting state. I. the ground state at the absolute zero of temperature,” Phys. Rev. 79, 845 (1950).
[CrossRef]

Genes, C.

C. Genes, H. Ritsch, and D. Vitali, “Micromechanical oscillator ground-state cooling via resonant intracavity optical gain or absorption,” Phys. Rev. A 80, 061803 (2009).
[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. A 77, 050307 (2008).
[CrossRef]

Gigan, S.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Girvin, S. M.

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

Gröblacher, S.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. A. Aspemeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[CrossRef] [PubMed]

Hammerer, K.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041 (2010).
[CrossRef]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. A. Aspemeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (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]

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]

Harris, J. G. E.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

Hertzberg, J. B.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Inouye, S.

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

Jacobs, K.

K. Jacobs, “Engineering quantum states of a nanoresonator via a simple auxiliary system,” Phys. Rev. Lett. 99, 117203 (2007).
[CrossRef] [PubMed]

K. Jacobs and A. J. Landahl, Engineering giant nonlinearities in quantum nanosystems, Phys. Rev. Lett.103, 067201 (2009).
[CrossRef] [PubMed]

Jayich, A. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

Jia, S.

G. Chen, J.-Q. Liang, and S. Jia, “Interaction-induced Lipkin-Meshkov-Glick model in a Bose-Einstein condensate inside an optical cavity,” Opt. Express 17, 19682 (2009).

Ketterle, W.

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

Kimble, H. J.

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]

H. J. Kimble in Cavity Quantum Electrodynamics, edited by P. Berman (Academic, New York, 1994).

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172 (2008).
[CrossRef] [PubMed]

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, “Cavity-assisted backaction cooling of mechanical resonators,” N. J. Phys. 10, 095007 (2008).
[CrossRef]

Köhl, M.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

Landahl, A. J.

K. Jacobs and A. J. Landahl, Engineering giant nonlinearities in quantum nanosystems, Phys. Rev. Lett.103, 067201 (2009).
[CrossRef] [PubMed]

Langer, G.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Larson, J.

J. Larson, “Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model,” Europhys. Lett. 90, 54001 (2010).
[CrossRef]

Lehnert, K. W.

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nature Phys. 4, 555 (2008).
[CrossRef]

Liang, J.-Q.

G. Chen, X. 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, J.-Q. Liang, and S. Jia, “Interaction-induced Lipkin-Meshkov-Glick model in a Bose-Einstein condensate inside an optical cavity,” Opt. Express 17, 19682 (2009).

Ludwig, M.

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]

Marquardt, F.

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]

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

Miesner, H.-J.

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

Mizel, A.

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[CrossRef]

Nooshi, N.

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, “Cavity-assisted backaction cooling of mechanical resonators,” N. J. Phys. 10, 095007 (2008).
[CrossRef]

Painter, O.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550 (2009).
[CrossRef] [PubMed]

Paternostro, M.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Polzik, E. S.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041 (2010).
[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]

Purcell, E. M.

E. M. Purcell, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37 (1946).
[CrossRef]

Regal, C. A.

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nature Phys. 4, 555 (2008).
[CrossRef]

Ritsch, H.

C. Genes, H. Ritsch, and D. Vitali, “Micromechanical oscillator ground-state cooling via resonant intracavity optical gain or absorption,” Phys. Rev. A 80, 061803 (2009).
[CrossRef]

Ritter, S.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

Schwab, K. C.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).

Sørensen, A. S.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041 (2010).
[CrossRef]

Stamper-Kurn, D. M.

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

Stenger, J.

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

Teufel, J. D.

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nature Phys. 4, 555 (2008).
[CrossRef]

Thompson, J. D.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

Tombesi, P.

C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A 77, 050307 (2008).
[CrossRef]

Treutlein, P.

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]

Vahala, K. J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550 (2009).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172 (2008).
[CrossRef] [PubMed]

van Loock, P.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Vanner, M. R.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. A. Aspemeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[CrossRef] [PubMed]

Vitali, D.

C. Genes, H. Ritsch, and D. Vitali, “Micromechanical oscillator ground-state cooling via resonant intracavity optical gain or absorption,” Phys. Rev. A 80, 061803 (2009).
[CrossRef]

C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A 77, 050307 (2008).
[CrossRef]

Wallquist, M.

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]

Wang, X.

G. Chen, X. 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. 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]

Wilson-Rae, I.

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, “Cavity-assisted backaction cooling of mechanical resonators,” N. J. Phys. 10, 095007 (2008).
[CrossRef]

Ye, J.

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]

Zeilinger, A.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

Zhou, X.

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[CrossRef]

Zoller, P.

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]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).

Zwerger, W.

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, “Cavity-assisted backaction cooling of mechanical resonators,” N. J. Phys. 10, 095007 (2008).
[CrossRef]

Zwickl, B. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

Europhys. Lett. (1)

J. Larson, “Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model,” Europhys. Lett. 90, 54001 (2010).
[CrossRef]

N. J. Phys. (1)

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, “Cavity-assisted backaction cooling of mechanical resonators,” N. J. Phys. 10, 095007 (2008).
[CrossRef]

Nature (6)

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268 (2007).
[CrossRef] [PubMed]

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151 (1998).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67 (2006).
[CrossRef] [PubMed]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72 (2008).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550 (2009).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. A. Aspemeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009).
[CrossRef] [PubMed]

Nature Phys. (1)

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nature Phys. 4, 555 (2008).
[CrossRef]

Opt. Express (1)

G. Chen, J.-Q. Liang, and S. Jia, “Interaction-induced Lipkin-Meshkov-Glick model in a Bose-Einstein condensate inside an optical cavity,” Opt. Express 17, 19682 (2009).

Phys. Rev. (2)

E. M. Purcell, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37 (1946).
[CrossRef]

H. Fröhlich, “Theory of the superconducting state. I. the ground state at the absolute zero of temperature,” Phys. Rev. 79, 845 (1950).
[CrossRef]

Phys. Rev. A (3)

G. Chen, X. 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]

C. Genes, H. Ritsch, and D. Vitali, “Micromechanical oscillator ground-state cooling via resonant intracavity optical gain or absorption,” Phys. Rev. A 80, 061803 (2009).
[CrossRef]

C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A 77, 050307 (2008).
[CrossRef]

Phys. Rev. Lett. (5)

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. 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]

X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett. 97, 267201 (2006).
[CrossRef]

K. Jacobs, “Engineering quantum states of a nanoresonator via a simple auxiliary system,” Phys. Rev. Lett. 99, 117203 (2007).
[CrossRef] [PubMed]

G. S. Agarwal, “Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity,” Phys. Rev. Lett. 53, 1732 (1984).
[CrossRef]

Physics (1)

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

Rev. Mod. Phys. (2)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041 (2010).
[CrossRef]

Science (1)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172 (2008).
[CrossRef] [PubMed]

Other (3)

K. Jacobs and A. J. Landahl, Engineering giant nonlinearities in quantum nanosystems, Phys. Rev. Lett.103, 067201 (2009).
[CrossRef] [PubMed]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).

H. J. Kimble in Cavity Quantum Electrodynamics, edited by P. Berman (Academic, New York, 1994).

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Figures (1)

Fig. 1
Fig. 1

(Color online) Schematic diagram for our proposed triple hybrid system with the ultracold atoms, photon and phonon. When the mirror oscillates, the wavelength of the photon will be affected, and correspondingly, the interaction strength between the ultracold atoms and the photon will be changed.

Equations (22)

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

H CO = ω a a + ω M b b ξ a a ( b + b ) ,
H T = H CO + g ( a S + a S + ) + ω 0 S z qS z 2 ,
S + = i = 1 N c i , 2 c i , 1 , S = i = 1 N c i , 1 c i , 2 , S z = 1 2 i = 1 N ( c i , 2 c i , 2 c i , 1 c i , 1 )
g = μ ɛ sin k x 0
ω 0 = ω 2 ω 1 + 1 2 ( N 1 ) ( η 2 η 1 ) + ω 12
q = 1 2 [ ( η 1 + η 2 ) 2 χ 1 , 2 ] ,
H d ph ( t ) = Ω p [ a exp ( i ω p t ) + a exp ( i ω p t ) ]
H d at ( t ) = Ω a [ S + exp ( i ω a t ) + S exp ( i ω a t ) ] ,
H ˜ ( t ) = H T + H d p h ( t ) + H d at ( t ) .
H ˜ R = Δ p a a + ω M b b ξ a a ( b + b ) + Δ a S z + g ( a S + a S + ) + Ω p ( a + a ) + 2 Ω a S x q S z 2 ,
H R = ω M b b + λ 0 ( S 2 S z 2 ) ( b + b ) + Δ a S z + Ω S x v S z 2 ,
H = ω M b b λ ( J + 2 b + J 2 b ) + Ω J z
ρ t = i [ H , ρ ] κ b ( b b ρ 2 b ρ b + ρ b b ) .
{ | ψ + = cos θ | N 2 + 2 , 0 + sin θ | N 2 , 1 | ψ = sin θ | N 2 + 2 , 0 + cos θ | N 2 , 1
Im [ χ ( ϖ ) ] = Γ cos 2 θ π { Γ 2 + [ ϖ 2 Ω δ / 2 d ] 2 } + Γ + sin 2 θ π { Γ + 2 + [ ϖ 2 Ω δ / 2 + d ] 2 } ,
ϖ 2 Ω ± 2 N λ .
J + = N d , J = N d , J z = ( d d N 2 ) .
H CM = ω M b b N λ [ ( d ) 2 b + d 2 b ] + Ω d d
H int = N λ λ b [ ( d ) 2 exp ( i φ ) + d 2 exp ( i φ ) ] ,
{ d ( t ) = d ( 0 ) cosh ( u ) i d ( 0 ) sinh ( u ) exp ( i φ ) d ( t ) = d ( 0 ) cosh ( u ) + i d ( 0 ) sinh ( u ) exp ( i φ ) ,
{ X 1 = 1 2 ( d + d ) J x N X 2 = 1 2 i ( d d ) J y N
{ ( Δ X 1 ) t 2 = 1 4 exp ( 2 u ) ( Δ X 2 ) t 2 = 1 4 exp ( 2 u )

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