Abstract

We propose a ground state cooling scheme for an optomechanical resonator based on the system of one Λ-type three-level atom trapped in an optomechanical cavity. This cooling scheme works in a single-photon coupling, and strong atom-cavity coupling regimes. By investigating the cooling dynamics, we find that there is an EIT-like quantum coherent effect in this system which can suppress the undesired transitions for heating. Moreover, our study shows that the final average phonon number of the optomechanical resonator can be smaller than the one based on the sideband cooling. Furthermore, the ground state cooling of the resonator can still be achieved after thermal fluctuations included. In addition, in comparison with previous cooling methods, there are fewer limitations on the decay rates of both the cavity and the atom in this scheme. As a result, this scheme is very suitable to realize the ground cooling of an optomechanical resonator in the experiment.

© 2014 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2014 (8)

Y.-C. Liu, Y.-F. Shen, Q.-H. Gong, and Y.-F. Xiao, “Optimal limits of cavity optomechanical cooling in the strong-coupling regime,” Phys. Rev. A 89, 053821 (2014).
[Crossref]

S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity induced transparency,” Phys. Rev. A 89, 013402 (2014).
[Crossref]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
[Crossref]

S. Zhang, J. Q. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Ground-state cooling of a trapped ion by quantum interference pathways,” Phys. Rev. A 90, 043409 (2014).
[Crossref]

A. Carmele, B. Vogell, K. Stannigel, and P. Zoller, “Opto-nanomechanics strongly coupled to a Rydberg super-atom: coherent versus incoherent dynamics,” New J. Phys. 16, 063042 (2014).
[Crossref]

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90, 033838 (2014).
[Crossref]

A. Dantan, B. Nair, G. Pupillo, and C. Genes, “Hybrid cavity mechanics with doped systems,” Phys. Rev. A 90, 033820 (2014).
[Crossref]

Z. Yi, G. X. Li, S. P. Wu, and Y. P. Yang, “Ground-state cooling of an oscillator in a hybrid atom-optomechanical system,” Opt. Express 22, 20060–20075 (2014).
[Crossref] [PubMed]

2013 (4)

W. J. Gu and G. X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87, 025804 (2013).
[Crossref]

J. Q. Zhang, S. Zhang, J. H. Zou, L. Chen, W. Yang, Y. Li, and M. Feng, “Fast optical cooling of nanomechanical cantilever with the dynamical Zeeman effect,” Opt. Express 21, 29695–29710 (2013).
[Crossref]

Z. Yi, W. J. Gu, and G. X. Li, “Ground-state cooling for a trapped atom using cavity-induced double electromagnetically induced transparency,” Opt. Express 21, 3345–3463 (2013).
[Crossref]

C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Experimental demonstration of ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 5547–5550 (2013).
[Crossref]

2012 (10)

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A 85, 053420 (2012).
[Crossref]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Cooling in the single-photon strong-coupling regime of cavity optomechanics,” Phys. Rev. A 85, 051803(R) (2012).
[Crossref]

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys. 14, 023002 (2012).
[Crossref]

J. P. Zhu and G. X. Li, “Ground-state cooling of a nanomechanical resonator with a triple quantum dot via quantum interference,” Phys. Rev. A 86, 053828 (2012).
[Crossref]

D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
[Crossref]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

J. Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

2011 (5)

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84, 051801(R) (2011).
[Crossref]

J. Teufel, 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,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

H. T. Tan and G. X. Li, “Multicolor quadripartite entanglement from an optomechanical cavity,” Phys. Rev. A 84, 024301 (2011).
[Crossref]

P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107, 063601 (2011).
[Crossref] [PubMed]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett. 107, 063602 (2011).
[Crossref] [PubMed]

2010 (4)

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

K. Stannigel, P. Rabl, A. S. Sorensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
[Crossref]

2009 (5)

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. Xia and J. Evers, “Ground State Cooling of a Nanomechanical resonator in the nonresolved regime via quantum interference,” Phys. Rev. Lett. 103, 227203 (2009).
[Crossref]

K. Qu and G. S. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2009).
[Crossref]

Z. R. Gong, H. Ian, Y. X. Liu, C. P. Sun, and F. Nori, “Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system,” Phys. Rev. A 80, 065801 (2009).
[Crossref]

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

2008 (2)

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101, 200503 (2008).
[Crossref] [PubMed]

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

2007 (1)

I. Wilso-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]

2006 (1)

L. F. Wei, Y. X. Liu, C. P. Sun, and F. Nori, “Probing tiny nanomechanical resonator: classical or quantum mechanical?” Phys. Rev. Lett. 97, 237201 (2006).
[Crossref]

2005 (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherentmedia,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state coolin-gin a high-finesse cavity,” Phys. Rev. A 72, 053408 (2005).
[Crossref]

2004 (1)

J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett. 68, 370–376 (2004).
[Crossref]

2000 (1)

G. Morigi, J. Eschner, and C. H. Keitel, “Ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 4458 (2000).
[Crossref] [PubMed]

1999 (1)

M. Tan. Sze, “A computational toolbox for quantum and atomic optics,” J. Opt. B 1, 424 (1999).
[Crossref]

1996 (1)

P. R. Rice and R. J. Brecha, “Cavity induced transparency,” Opt. Comm. 126, 230–235 (1996).
[Crossref]

1992 (1)

J. I. Cirac, R. Blatt, and P. Zoller, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A 46, 2668–2681 (1992).
[Crossref] [PubMed]

Agarwal, G. S.

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
[Crossref]

K. Qu and G. S. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2009).
[Crossref]

Allman, M. S.

J. Teufel, 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,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Alt, W.

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

Bariani, F.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90, 033838 (2014).
[Crossref]

Bienert, M.

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
[Crossref]

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys. 14, 023002 (2012).
[Crossref]

D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
[Crossref]

Blatt, R.

C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Experimental demonstration of ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 5547–5550 (2013).
[Crossref]

J. I. Cirac, R. Blatt, and P. Zoller, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A 46, 2668–2681 (1992).
[Crossref] [PubMed]

Børkje, K.

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Cooling in the single-photon strong-coupling regime of cavity optomechanics,” Phys. Rev. A 85, 051803(R) (2012).
[Crossref]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett. 107, 063602 (2011).
[Crossref] [PubMed]

Bowen, W. P.

S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Braginsky, V. B.

V. B. Braginsky and A. B. Manukin, Measurements of Weak Forces in Physics Experiments, D. H. Douglass, ed. (Chicago University, 1977).

Brecha, R. J.

P. R. Rice and R. J. Brecha, “Cavity induced transparency,” Opt. Comm. 126, 230–235 (1996).
[Crossref]

Breyer, D.

D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
[Crossref]

Buchmann, L. F.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90, 033838 (2014).
[Crossref]

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S. Zhang, J. Q. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Ground-state cooling of a trapped ion by quantum interference pathways,” Phys. Rev. A 90, 043409 (2014).
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K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherentmedia,” Rev. Mod. Phys. 77, 633–673 (2005).
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T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
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J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett. 68, 370–376 (2004).
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G. Morigi, J. Eschner, and C. H. Keitel, “Ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 4458 (2000).
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K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
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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).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
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A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
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J. Teufel, 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,” Nature 475, 359–363 (2011).
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C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Experimental demonstration of ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 5547–5550 (2013).
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J. Teufel, 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,” Nature 475, 359–363 (2011).
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Z. Yi, G. X. Li, S. P. Wu, and Y. P. Yang, “Ground-state cooling of an oscillator in a hybrid atom-optomechanical system,” Opt. Express 22, 20060–20075 (2014).
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Z. Yi, W. J. Gu, and G. X. Li, “Ground-state cooling for a trapped atom using cavity-induced double electromagnetically induced transparency,” Opt. Express 21, 3345–3463 (2013).
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J. Q. Zhang, S. Zhang, J. H. Zou, L. Chen, W. Yang, Y. Li, and M. Feng, “Fast optical cooling of nanomechanical cantilever with the dynamical Zeeman effect,” Opt. Express 21, 29695–29710 (2013).
[Crossref]

J. Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Y. Guo, K. Li, W. Nie, and Y. Li, “Electromagnetially-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” arXiv:1407.5202 (2014).

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Z. R. Gong, H. Ian, Y. X. Liu, C. P. Sun, and F. Nori, “Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system,” Phys. Rev. A 80, 065801 (2009).
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L. F. Wei, Y. X. Liu, C. P. Sun, and F. Nori, “Probing tiny nanomechanical resonator: classical or quantum mechanical?” Phys. Rev. Lett. 97, 237201 (2006).
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Y.-C. Liu, Y.-F. Shen, Q.-H. Gong, and Y.-F. Xiao, “Optimal limits of cavity optomechanical cooling in the strong-coupling regime,” Phys. Rev. A 89, 053821 (2014).
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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).
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Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherentmedia,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

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).
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T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
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A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
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T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
[Crossref]

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F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90, 033838 (2014).
[Crossref]

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T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
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G. Morigi, J. Eschner, and C. H. Keitel, “Ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 4458 (2000).
[Crossref] [PubMed]

Mundt, A.

C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Experimental demonstration of ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 5547–5550 (2013).
[Crossref]

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A. Dantan, B. Nair, G. Pupillo, and C. Genes, “Hybrid cavity mechanics with doped systems,” Phys. Rev. A 90, 033820 (2014).
[Crossref]

Ni, K.-K.

K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
[Crossref] [PubMed]

Nie, W.

Y. Guo, K. Li, W. Nie, and Y. Li, “Electromagnetially-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” arXiv:1407.5202 (2014).

Nooshi, N.

I. Wilso-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]

Nori, F.

Z. R. Gong, H. Ian, Y. X. Liu, C. P. Sun, and F. Nori, “Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system,” Phys. Rev. A 80, 065801 (2009).
[Crossref]

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[Crossref]

Norte, R.

K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
[Crossref] [PubMed]

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A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Cooling in the single-photon strong-coupling regime of cavity optomechanics,” Phys. Rev. A 85, 051803(R) (2012).
[Crossref]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett. 107, 063602 (2011).
[Crossref] [PubMed]

Painter, O.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Passian, A.

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

Plenio, M. B.

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101, 200503 (2008).
[Crossref] [PubMed]

Prams, S.

S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Pupillo, G.

A. Dantan, B. Nair, G. Pupillo, and C. Genes, “Hybrid cavity mechanics with doped systems,” Phys. Rev. A 90, 033820 (2014).
[Crossref]

Qu, K.

K. Qu and G. S. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2009).
[Crossref]

Rabl, P.

P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107, 063601 (2011).
[Crossref] [PubMed]

K. Stannigel, P. Rabl, A. S. Sorensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Reimann, R.

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
[Crossref]

Rice, P. R.

P. R. Rice and R. J. Brecha, “Cavity induced transparency,” Opt. Comm. 126, 230–235 (1996).
[Crossref]

Ritsch, H.

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84, 051801(R) (2011).
[Crossref]

Rivière, R.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

Roos, C. F.

C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Experimental demonstration of ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 5547–5550 (2013).
[Crossref]

Rubinsztein-Dunlop, H.

S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Schliesser, A.

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

Schmidt-Kaler, F.

C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Experimental demonstration of ground state laser cooling with electromagnetically induced transparency,” Phys. Rev. Lett. 85, 5547–5550 (2013).
[Crossref]

Shekhawat, G.

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

Shen, Y.-F.

Y.-C. Liu, Y.-F. Shen, Q.-H. Gong, and Y.-F. Xiao, “Optimal limits of cavity optomechanical cooling in the strong-coupling regime,” Phys. Rev. A 89, 053821 (2014).
[Crossref]

Simmonds, R. W.

J. Teufel, 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,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Singh, S.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90, 033838 (2014).
[Crossref]

Sirois, A. J.

J. Teufel, 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,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Sorensen, A. S.

K. Stannigel, P. Rabl, A. S. Sorensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Stannigel, K.

A. Carmele, B. Vogell, K. Stannigel, and P. Zoller, “Opto-nanomechanics strongly coupled to a Rydberg super-atom: coherent versus incoherent dynamics,” New J. Phys. 16, 063042 (2014).
[Crossref]

K. Stannigel, P. Rabl, A. S. Sorensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Sun, C. P.

Z. R. Gong, H. Ian, Y. X. Liu, C. P. Sun, and F. Nori, “Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system,” Phys. Rev. A 80, 065801 (2009).
[Crossref]

L. F. Wei, Y. X. Liu, C. P. Sun, and F. Nori, “Probing tiny nanomechanical resonator: classical or quantum mechanical?” Phys. Rev. Lett. 97, 237201 (2006).
[Crossref]

Swaim, J. D.

S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Szorkovszky, A.

S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Tan, H. T.

H. T. Tan and G. X. Li, “Multicolor quadripartite entanglement from an optomechanical cavity,” Phys. Rev. A 84, 024301 (2011).
[Crossref]

Tan. Sze, M.

M. Tan. Sze, “A computational toolbox for quantum and atomic optics,” J. Opt. B 1, 424 (1999).
[Crossref]

Tetard, L.

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

Teufel, J.

J. Teufel, 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,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Thundat, T.

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

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]

van Ooijen, E. D.

S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Vengalattore, M.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90, 033838 (2014).
[Crossref]

Venmar, K. T.

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

Vogell, B.

A. Carmele, B. Vogell, K. Stannigel, and P. Zoller, “Opto-nanomechanics strongly coupled to a Rydberg super-atom: coherent versus incoherent dynamics,” New J. Phys. 16, 063042 (2014).
[Crossref]

Voy, B. H.

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

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]

Wei, L. F.

L. F. Wei, Y. X. Liu, C. P. Sun, and F. Nori, “Probing tiny nanomechanical resonator: classical or quantum mechanical?” Phys. Rev. Lett. 97, 237201 (2006).
[Crossref]

Weis, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

Whittaker, J. D.

J. Teufel, 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,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Wilson, D. J.

K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
[Crossref] [PubMed]

Wilso-Rae, I.

I. Wilso-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]

Wu, C. W.

S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity induced transparency,” Phys. Rev. A 89, 013402 (2014).
[Crossref]

S. Zhang, J. Q. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Ground-state cooling of a trapped ion by quantum interference pathways,” Phys. Rev. A 90, 043409 (2014).
[Crossref]

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A 85, 053420 (2012).
[Crossref]

Wu, S. P.

Wu, W.

S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity induced transparency,” Phys. Rev. A 89, 013402 (2014).
[Crossref]

S. Zhang, J. Q. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Ground-state cooling of a trapped ion by quantum interference pathways,” Phys. Rev. A 90, 043409 (2014).
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Xia, K.

K. Xia and J. Evers, “Ground State Cooling of a Nanomechanical resonator in the nonresolved regime via quantum interference,” Phys. Rev. Lett. 103, 227203 (2009).
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Xiao, Y.-F.

Y.-C. Liu, Y.-F. Shen, Q.-H. Gong, and Y.-F. Xiao, “Optimal limits of cavity optomechanical cooling in the strong-coupling regime,” Phys. Rev. A 89, 053821 (2014).
[Crossref]

Xu, Y.

J. Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Yang, W.

Yang, Y. P.

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]

Yi, Z.

Z. Yi, G. X. Li, S. P. Wu, and Y. P. Yang, “Ground-state cooling of an oscillator in a hybrid atom-optomechanical system,” Opt. Express 22, 20060–20075 (2014).
[Crossref] [PubMed]

Z. Yi, W. J. Gu, and G. X. Li, “Ground-state cooling for a trapped atom using cavity-induced double electromagnetically induced transparency,” Opt. Express 21, 3345–3463 (2013).
[Crossref]

Yoon, S.

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
[Crossref]

Zhang, J. Q.

S. Zhang, J. Q. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Ground-state cooling of a trapped ion by quantum interference pathways,” Phys. Rev. A 90, 043409 (2014).
[Crossref]

J. Q. Zhang, S. Zhang, J. H. Zou, L. Chen, W. Yang, Y. Li, and M. Feng, “Fast optical cooling of nanomechanical cantilever with the dynamical Zeeman effect,” Opt. Express 21, 29695–29710 (2013).
[Crossref]

J. Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Zhang, S.

S. Zhang, J. Q. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Ground-state cooling of a trapped ion by quantum interference pathways,” Phys. Rev. A 90, 043409 (2014).
[Crossref]

S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity induced transparency,” Phys. Rev. A 89, 013402 (2014).
[Crossref]

J. Q. Zhang, S. Zhang, J. H. Zou, L. Chen, W. Yang, Y. Li, and M. Feng, “Fast optical cooling of nanomechanical cantilever with the dynamical Zeeman effect,” Opt. Express 21, 29695–29710 (2013).
[Crossref]

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A 85, 053420 (2012).
[Crossref]

Zhu, J. P.

J. P. Zhu and G. X. Li, “Ground-state cooling of a nanomechanical resonator with a triple quantum dot via quantum interference,” Phys. Rev. A 86, 053828 (2012).
[Crossref]

Zippilli, S.

S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state coolin-gin a high-finesse cavity,” Phys. Rev. A 72, 053408 (2005).
[Crossref]

Zoller, P.

A. Carmele, B. Vogell, K. Stannigel, and P. Zoller, “Opto-nanomechanics strongly coupled to a Rydberg super-atom: coherent versus incoherent dynamics,” New J. Phys. 16, 063042 (2014).
[Crossref]

K. Stannigel, P. Rabl, A. S. Sorensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (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]

J. I. Cirac, R. Blatt, and P. Zoller, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A 46, 2668–2681 (1992).
[Crossref] [PubMed]

Zou, J. H.

Zwerger, W.

I. Wilso-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]

Europhys. Lett. (1)

J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett. 68, 370–376 (2004).
[Crossref]

J. Opt. B (1)

M. Tan. Sze, “A computational toolbox for quantum and atomic optics,” J. Opt. B 1, 424 (1999).
[Crossref]

Nat. Nanotechnol. (1)

L. Tetard, A. Passian, K. T. Venmar, R. M. Lynch, B. H. Voy, G. Shekhawat, V. P. Dravid, and T. Thundat, “Imaging nanoparticles in cells by nanomechanical holography,” Nat. Nanotechnol. 3, 501–505 (2008).
[Crossref] [PubMed]

Nature (1)

J. Teufel, 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,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

New J. Phys. (2)

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys. 14, 023002 (2012).
[Crossref]

A. Carmele, B. Vogell, K. Stannigel, and P. Zoller, “Opto-nanomechanics strongly coupled to a Rydberg super-atom: coherent versus incoherent dynamics,” New J. Phys. 16, 063042 (2014).
[Crossref]

Opt. Comm. (1)

P. R. Rice and R. J. Brecha, “Cavity induced transparency,” Opt. Comm. 126, 230–235 (1996).
[Crossref]

Opt. Express (3)

Phys. Rev. A (20)

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
[Crossref]

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90, 033838 (2014).
[Crossref]

A. Dantan, B. Nair, G. Pupillo, and C. Genes, “Hybrid cavity mechanics with doped systems,” Phys. Rev. A 90, 033820 (2014).
[Crossref]

D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
[Crossref]

J. I. Cirac, R. Blatt, and P. Zoller, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A 46, 2668–2681 (1992).
[Crossref] [PubMed]

S. Zhang, J. Q. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Ground-state cooling of a trapped ion by quantum interference pathways,” Phys. Rev. A 90, 043409 (2014).
[Crossref]

J. P. Zhu and G. X. Li, “Ground-state cooling of a nanomechanical resonator with a triple quantum dot via quantum interference,” Phys. Rev. A 86, 053828 (2012).
[Crossref]

W. J. Gu and G. X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87, 025804 (2013).
[Crossref]

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84, 051801(R) (2011).
[Crossref]

S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity induced transparency,” Phys. Rev. A 89, 013402 (2014).
[Crossref]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “Electromagnetically-induced-transparency control of single-atom motion in an optical cavity,” Phys. Rev. A 89, 033404 (2014).
[Crossref]

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A 85, 053420 (2012).
[Crossref]

S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state coolin-gin a high-finesse cavity,” Phys. Rev. A 72, 053408 (2005).
[Crossref]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Cooling in the single-photon strong-coupling regime of cavity optomechanics,” Phys. Rev. A 85, 051803(R) (2012).
[Crossref]

Y.-C. Liu, Y.-F. Shen, Q.-H. Gong, and Y.-F. Xiao, “Optimal limits of cavity optomechanical cooling in the strong-coupling regime,” Phys. Rev. A 89, 053821 (2014).
[Crossref]

Z. R. Gong, H. Ian, Y. X. Liu, C. P. Sun, and F. Nori, “Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system,” Phys. Rev. A 80, 065801 (2009).
[Crossref]

J. Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

H. T. Tan and G. X. Li, “Multicolor quadripartite entanglement from an optomechanical cavity,” Phys. Rev. A 84, 024301 (2011).
[Crossref]

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
[Crossref]

K. Qu and G. S. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2009).
[Crossref]

Phys. Rev. Lett. (14)

P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107, 063601 (2011).
[Crossref] [PubMed]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett. 107, 063602 (2011).
[Crossref] [PubMed]

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101, 200503 (2008).
[Crossref] [PubMed]

L. F. Wei, Y. X. Liu, C. P. Sun, and F. Nori, “Probing tiny nanomechanical resonator: classical or quantum mechanical?” Phys. Rev. Lett. 97, 237201 (2006).
[Crossref]

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[Crossref]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
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Physics (1)

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[Crossref]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherentmedia,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Science (1)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

Other (3)

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C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom–Photon Interactions: Basic Processes and Applications (Wiley, 1998).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

(a) The model of the MR cooling. A Λ-type atom is fixed in an optomechanical cavity, and the MR is coupled to the cavity via the radiative pressure. A pump laser is applied to inject photons into the cavity, and the Λ-type atom is coupled to the cavity mode and a laser field. The dissipations of the whole system include the atomic spontaneous emission, the cavity decay and the MR dissipating to the thermal bath. The dynamics of the whole system can be described by the master equation (5). (b) The energy levels and the corresponding transitions in the atom. This atom takes one excited state |e〉 and two ground states |g〉 and |r〉. The states |e〉 and |g〉 couples to the cavity field, and the one|e〉 ↔ |r〉 is driven by an external laser. The detunings are defined by Eq. (3).

Fig. 2
Fig. 2

The schematic illustration of the cooling and heating processes. Suppose the system is initially in the state |g〉|n〉, it would be excited to state |1〉|n〉 by the pump laser, and then it will evolve to the state |1〉|n ± 1〉 via the interaction V1. After that, with the assistance of the internal scattering process, the whole system will decay to the state |g〉|n±1〉 via the (a) cavity decay or the (b) atomic dissipation.

Fig. 3
Fig. 3

(a) The EIT-like interference in the dressed state representation. The external light field dresses two states |e〉 and |r〉 into two dressed states |D1〉 and |D2〉. Then the coupling between |1〉 and |e〉 can be effectively treated as two transition channels |1〉 ↔ |D1〉 and |1〉 ↔ |D2〉. There is a EIT-like structure among the states {|D2〉, |g〉, |1〉}, which include two transitions |g〉 ↔ |1〉 and |D2〉 ↔ |1〉 and their corresponding detunings −δP and −δPE D 2 . When tune the two detunings to the same, i.e. E D 2 = 0, the EIT-like effect will arise, and therefore the two transitions are suppressed. (b) The schematic illustration for the suppression mechanism of the heating transitions. A heating transition starts from internal steady state |g〉|n〉. Then the system is excited to |1〉|n〉, and heated to |1〉|n + 1〉 via the interaction V1. It can be suppressed by the transition |D2〉|n + 1〉 ↔ |1〉|n + 1〉 due to the EIT-like effect. When the two detunings are the same, the EIT-like dark resonance will prohibit the two paths.

Fig. 4
Fig. 4

The analytical results of (a) log10 nss (b) log10 (W/ωm) as a function of the detunings Δ g and Δ g − Δ r (in units of ωm). The solid lines correspond to the condition (31), while the dashed lines correspond to the condition (25). The other parameters are γ = κ = ωm, λ = 0.1ωm, δP = −2ωm, g = 7ωm, ωP = 0.8ωm, Ω r = 5ωm.

Fig. 5
Fig. 5

The analytically predicted final mean phonon number log10 nss as a function of the environment temperature T and the quality of the MR. The parameters are ωm = 2π × 1MHz, γ = κ = ωm, λ = 0.1ωm, δP = −2ωm, g = 7ωm, ωP = 0.8ωm, Ω r = 5ωm, Δ g = −20ωm, Δ r is chosen under the condition (25).

Fig. 6
Fig. 6

Numerical simulations of cooling dynamics. The parameters are ωm = 2π × 1MHz, γ = κ = ωm, λ = 0.1ωm, δP = −2ωm, g = 7ωm, ωP = 0.8ωm, Ω r = 5ωm, Δ g = −20ωm, Δ r is chosen under the condition (25). The blue line denotes the case of γm = 0 and the dashed line is the corresponding analytical prediction. The red line denotes the case of γm = 10Hz, T = 20mK.

Equations (45)

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H = H 0 + H I .
H 0 = δ P a a + ω m b b δ g | e e | + δ P | g g | + ( Δ r δ g ) | r r | ,
δ P = ω P ω c , Δ r = ω L ( ω e ω r ) , δ g = ω c ( ω e ω g ) .
H I = Ω P ( a + a ) + g ( a | e g | + a | g e | ) + Ω r ( | e r | + | r e | ) + λ a a ( b + b ) ,
d d t ρ = i [ H , ρ ] + γ ρ + κ ρ + m ρ ,
γ ρ = j = g , r γ j ( 2 | j e | ρ | e j | | e e | ρ ρ | e e | ) ,
κ ρ = κ ( 2 a ρ a a a ρ ρ a a ) ,
m ρ = γ m ( n th + 1 ) ( 2 b ρ b b b ρ ρ b b ) + γ m n th ( 2 b ρ b b b ρ ρ b b ) ,
{ | g , 0 c , | g , 1 c , | e , 0 c , | r , 0 c } .
d d t ρ = i [ H , ρ ] + γ ρ + κ ρ + m ρ ,
H = H 0 + V 0 + V 1 , H 0 = δ P | 1 1 | + ω m b b Δ g | e e | + ( Δ r Δ g ) | r r | + Ω r ( | e r | + | r e | ) + g ( | e 1 | + | 1 e | ) , V 0 = Ω P ( | g 1 | + | 1 g | ) , V 1 = λ | 1 1 | ( b + b ) ;
κ ρ = κ [ 2 | g 1 | ρ | 1 g | | 1 1 | ρ ρ | 1 1 | ] .
Δ g = δ P + δ g = ω P ( ω e ω g ) .
d d t p n = ( n + 1 ) ( A + 2 ( n th + 1 ) γ m ) p n + 1 + n ( A + + 2 n th γ m ) p n 1 [ ( n + 1 ) ( A + + 2 n th γ m ) + n ( A + 2 ( n th + 1 ) γ m ) ] p n .
d d t n = ( A A + ) n + A + .
n = ( n 0 n s s ) e W t + n s s ,
W = A A + ,
n s s = A + A A + .
A ± = A ± κ + A ± γ ,
A ± κ = 2 κ 𝒮 | λ ( ω m + Δ g ) ( ω m + Δ g Δ r ) Ω r 2 + i γ ( ω m + Δ g Δ r ) f ( ω m ) | 2 ,
A ± γ = 2 γ 𝒮 | λ g ( ω m + Δ g Δ r ) f ( ω m ) | 2 ,
𝒮 = | Ω P Δ g ( Δ g Δ r ) Ω r 2 + i γ ( Δ g Δ r ) f ( 0 ) | 2 ,
f ( x ) = Ω r 2 ( x + δ P ) i κ Ω r 2 + ( x + Δ g Δ r ) [ g 2 + ( i κ + x + δ P ) ( i γ + x + Δ g ) ] .
C = g 2 κ γ 1 .
( ω m + Δ g ) ( ω m + Δ g Δ r ) Ω r 2 = 0 .
| D 1 = sin ϑ | r + cos ϑ | e , | D 2 = cos ϑ | r sin ϑ | e ,
ϑ = arctan Ω r 1 2 ( Δ r 2 4 + Ω r 2 Δ r ) .
E D 1 = 1 2 ( 2 Δ g + Δ r + Δ r 2 + 4 Ω r 2 ) , E D 2 = 1 2 ( 2 Δ g + Δ r Δ r 2 + 4 Δ r 2 ) ,
H 0 = δ P | 1 1 | + ω m b b + E D 1 | D 1 D 1 | + E D 2 | D 2 D 2 | + g ( cos ϑ | D 1 sin ϑ | D 2 ) 1 | + H . c .
δ P + ω m = δ P E D 2 ,
Re f ( ω m ) = 0 ,
Ω r 2 ( ω m + δ P ) + ( ω m + Δ g Δ r ) [ g 2 κ γ + ( ω m + δ P ) ( ω m + Δ g ) ] = 0 .
A + 2 λ 2 𝒮 γ [ ω m g ( ω m + Δ g Δ r ) ] 2 ~ 2 λ 2 𝒮 γ 1 g 2 ,
A 2 λ 2 𝒮 1 [ κ + γ g 2 ( ω m + δ P ) 2 ] .
n s s A + A = 1 C + γ 2 ( ω m + δ P ) 2 g 4 .
W = W + 2 γ m ; n s s = A + + 2 γ m n th W .
d d t p n = m = n ± 1 ( Γ m n p m Γ n m p n ) ,
Γ n n ± 1 = Γ n n ± 1 κ + Γ n n ± 1 γ ,
Γ n n ± 1 κ = 2 κ | 𝒯 n κ , ± | 2 , Γ n n ± 1 γ = 2 γ | 𝒯 n γ , ± | 2 .
𝒯 n κ , ± = ψ n ± 1 | W κ G ( E n ) V 1 G ( E n ) V 0 | ψ n , 𝒯 n γ , ± = ψ n ± 1 | W γ G ( E n ) V 1 G ( E n ) V 0 | ψ n ,
G ( z ) = 1 z H eff ,
𝒯 n κ , ± = n + δ ± Ω P Δ g ( Δ g Δ r ) Ω r 2 + i γ ( Δ g Δ r ) f ( 0 ) λ ( ω m + Δ g ) ( ω m + Δ g Δ r ) Ω r 2 + i γ ( ω m + Δ g Δ r ) f ( ω m ) , 𝒯 n γ , ± = n + δ ± Ω P Δ g ( Δ g Δ r ) Ω r 2 + i γ ( Δ g Δ r ) f ( 0 ) λ g ( ω m + Δ g Δ r ) f ( ω m ) ,
f ( x ) = Ω r 2 ( x + δ P ) i κ Ω r 2 + ( x + Δ g Δ r ) [ g 2 + ( i κ + x + δ P ) ( i γ + x + Δ g ) ] .
Γ n n ± 1 = ( n + δ ± ) A ± ;
Γ n n ± 1 κ = ( n + δ ± ) A ± κ , Γ n n ± 1 γ = ( n + δ ± ) A ± γ .

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