## Controllable optomechanically induced transparency and ponderomotive squeezing in an optomechanical system assisted by an atomic ensemble |

Optics Express, Vol. 22, Issue 15, pp. 17979-17989 (2014)

http://dx.doi.org/10.1364/OE.22.017979

Acrobat PDF (871 KB)

### Abstract

We propose a system for realizing controllable optomechanically induced transparency (OMIT) and ponderomotive squeezing. In this system, an atomic ensemble driven by an external optical field couples with the cavity field in a typical optomechanical cavity. When the cavity is driven by a coupling laser and a probe laser, we can produce a switch for the probe field and adjust the width of the transparency window flexibly by manipulating the coupling strength between the atomic ensemble and the external optical field. We also investigate the ponderomotive squeezing properties of the transmitted field by analyzing its spectrum. Interestingly, the coupling strength between the atomic ensemble and the cavity field plays an important role in controlling the squeezing properties and the squeezing spectrum presents distinct features at red-detuned and blue-detuned frequencies by adjusting the coupling strength.

© 2014 Optical Society of America

## 1. Introduction

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

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

4. A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London) **472**, 69 (2011). [CrossRef]

5. Devrim Tarhan, Sumei Huang, Ö zgür, and E. Müstecaplioğlu, “Superluminal and ultraslow light propagation in optomechanical systems,” Phys. Rev. A **87**, 013824 (2013). [CrossRef]

6. Bin Chen, Cheng Jiang, and Ka-Di Zhu, “Slow light in a cavity optomechanical system with a Bose-Einstein condensate,” Phys. Rev. A **83**, 055803 (2011). [CrossRef]

7. A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics **3**, 706 (2009). [CrossRef]

9. E. Verhagen, S. Delalise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) **482**, 63 (2012). [CrossRef]

6. Bin Chen, Cheng Jiang, and Ka-Di Zhu, “Slow light in a cavity optomechanical system with a Bose-Einstein condensate,” Phys. Rev. A **83**, 055803 (2011). [CrossRef]

5. Devrim Tarhan, Sumei Huang, Ö zgür, and E. Müstecaplioğlu, “Superluminal and ultraslow light propagation in optomechanical systems,” Phys. Rev. A **87**, 013824 (2013). [CrossRef]

10. G. S. Agarwal and S. Huang, “Optomechanical systems as single-photon routers,” Phys. Rev. A **85**, 021801(R) (2012). [CrossRef]

11. C. Jiang, B. Chen, and K.-D. Zhu, “Demonstration of a single-photon router with a cavity electromechanical system,” J. Appl. Phys. **112**, 033113 (2012). [CrossRef]

12. S. Shahidani, M. H. Naderi, and M. Soltanolkotabi, “Control and manipulation of electromagnetically induced transparency in a nonlinear optomechanical system with two movable mirrors,” Phys. Rev. A **88**, 053813 (2013). [CrossRef]

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

14. F. Marquardt and S. M. Girvin, “Trend: optomechanics,” Physics **2**, 40 (2009). [CrossRef]

15. 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]

17. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A **77**, 033804 (2008). [CrossRef]

18. L. Tian and H. L. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A **82**, 053806 (2010). [CrossRef]

20. T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature (London) **495**, 210–214 (2013). [CrossRef]

21. 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]

22. 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]

23. A A Clerk, F Marquardt, and K Jacobs, “Back-action evasion and squeezing of a mechanical resonator using a cavity detector,” New J. Phys. **10**, 095010 (2008). [CrossRef]

25. C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A **49**, 1337 (1994). [CrossRef] [PubMed]

26. N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, “Nonclassical excitation for atoms in a squeezed vacuum,” Phys. Rev. Lett. **75**, 3426 (1995). [CrossRef] [PubMed]

27. E. Alebachew and K. Fessah, “Interaction of a two-level atom with squeezed light,” Opt. Commun. **271**, 154 (2007). [CrossRef]

25. C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A **49**, 1337 (1994). [CrossRef] [PubMed]

28. S. Mancini and P. Tombesi, “Quantum noise reduction by radiation yressure,” Phys. Rev. A **49**, 4055 (1994). [CrossRef] [PubMed]

29. D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature (London) **448**, 476 (2012). [CrossRef]

## 2. Model and theory

*ω*, and the cavity mode of frequency

_{c}*ω*

_{0}is driven simultaneously by a strong classical external field of frequency

*ω*and a weak probe field of frequency

_{c}*ω*. The model Hamiltonian reads

_{p}*c*(

*c*

^{†}) is the annihilation (creation) operator of the cavity field. The second term is the free Hamiltonian of the atom ensemble. The third and fourth terms are the interaction Hamiltonian describing the coupling between the atom ensemble and the cavity field and that between the atom ensemble and the external driving field, respectively.

*ith*atom in the atomic ensemble. The number of atoms in the atomic ensemble is

*N*, and we assume that all the atoms have the same excited (ground) state |

*e*〉 (|

*g*〉), so they have the same transition frequency

*ω*. The atomic ensemble is arranged in a thin layer whose size in the direction of the cavity axis is much smaller than the wavelength of the cavity field, thus all the atoms have the same coupling strength

_{a}*G*with the cavity field [34

34. C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. **91**, 147903 (2003). [CrossRef] [PubMed]

*ω*and effective mass

_{m}*m*. The sixth term is the interaction Hamiltonian describing the radiation pressure interaction between the cavity mode and the mechanical resonator, where

*g*is the optomechanical coupling rate between the mechanical mode and cavity mode. The last two terms describe the interaction of the cavity field with the coupling field and that of the cavity field with the probe field, with the amplitude

*κ*is the decay rate of the cavity field, and

*P*and

_{c}*P*are the laser powers. We have also assumed that no direct interaction exists between the atoms and the mirror, the indirect interaction between them solely relies on the cavity field.

_{p}*ω*, we can consider the atomic ensemble in the cavity as a whole to be a Hopfield dielectric [35

_{a}35. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. **112**, 1555 (1958). [CrossRef]

34. C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. **91**, 147903 (2003). [CrossRef] [PubMed]

*N*, the above operators satisfy the standard bosonic commutation relations Then we have The Hamiltonian (1) can be rewritten in terms of the atomic collective operators

*A*(

*A*

^{†}) as

*G*and

_{A}*χ*that the coupling coefficients are enhanced by

*H*

_{0}=

*h̄ω*(

_{c}*c*

^{†}

*c*+

*A*

^{†}

*A*), the interaction Hamiltonian is given in the form as where Δ

*=*

_{c}*ω*

_{0}−

*ω*, Δ

_{c}*=*

_{a}*ω*−

_{a}*ω*and

_{c}*δ*=

*ω*−

_{p}*ω*are the detunings.

_{c}## 4. Ponderomotive squeezing

29. D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature (London) **448**, 476 (2012). [CrossRef]

28. S. Mancini and P. Tombesi, “Quantum noise reduction by radiation yressure,” Phys. Rev. A **49**, 4055 (1994). [CrossRef] [PubMed]

41. M. J. Collett and D. F. Walls, “Squeezing spectra for nonlinear optical systems,” Phys. Rev. A **32**, 2887 (1985). [CrossRef] [PubMed]

*S*(

_{θ}*ω*) < 1. Then we rewrite Eq. (24) to be where 〈

*δc*(

*ω*)

*δc*(

*ω′*)〉 =

*δ*(

*ω*+

*ω′*)

*B*and other terms are defined in a similar way. As the phase angle

_{cc}*θ*is an adjustable parameter, we choose appropriate

*θ*by solving

*dS*(

_{θ}*ω*)/

*dθ*= 0, then we obtain here, we choose the negative value to optimize the degree of squeezing. So Eq. (25) can be rewritten as For calculating in frequency domain, we define the Fourier transform for an operator

*u*(

*u*=

*δc*,

*δA*,

*δp*,

*c*,

_{in}*A*and

_{in}*ξ*) as which lead to the following nonzero correlation functions in the frequency domain [36, 37

37. V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A **63**, 023812 (2001). [CrossRef]

*Z*= (

*δc*,

*δc*

^{†},

*δA*,

*δA*

^{†},

*δp*,

*δq*)

*,*

^{T}_{1}=

*κ*−

*i*(

*ω*− Δ), Λ

_{2}=

*κ*−

*i*(

*ω*+ Δ), Θ

_{1}=

*γ*−

_{a}*i*(

*ω*− Δ

*), and Θ*

_{a}_{2}=

*γ*−

_{a}*i*(

*ω*+ Δ

*). By solving Eq. (32), we obtain where By using the results above and the input-output relation, we can obtain*

_{a}*B*

_{c†c}and

*B*in the expression of squeezing spectrum (27), Now we focus on the dependence of the degree of squeezing on the coupling strength between the cavity field and the atomic ensemble. The parameters are:

_{cc}*χ*= 0,

*P*= 5

_{c}*mW*and other parameters are the same as in Fig. 2. The parameters we choose meet the stability conditions which can be obtained by the Routh-Hurwitz criterion [42

42. E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A **35**, 5288 (1987). [CrossRef] [PubMed]

*G*= 0.08

_{A}*κ*, the degree of squeezing increases at the blue-detuned frequency while it decreases at the red-detuned frequency, but they both present the property of squeezing, as shown in Fig. 3(b). In Fig. 3(c), if we increase the coupling strength

*G*to 0.1

_{A}*κ*, the degree of squeezing at the blue-detuned frequency is increased further, yet the frequency at the red-detuned presents nearly no squeezing. But we cannot increase the degree of squeezing to the perfect squeezing corresponding to

*S*(

_{opt}*ω*) = 0, and we can find it in Fig. 3(d), in which the degree of squeezing decreases rather than increases with the coupling strength increasing to 0.8

*κ*. This can be understood by considering the effective cavity decay rate

*G*, the decay will predominate the process. We have also made a numerical calculation about the effects of a larger coupling strength

_{A}*G*on the properties of squeezing, and found that there were no squeezing just as the case in which the optomechanical coupling

_{A}*λ*= 0. Thus this provides us a good methods for controlling the degree of squeezing and finding the optimal squeezing.

## 5. Conclusion

## Acknowledgments

## References and links

1. | G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A |

2. | S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science |

3. | J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature (London) |

4. | A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London) |

5. | Devrim Tarhan, Sumei Huang, Ö zgür, and E. Müstecaplioğlu, “Superluminal and ultraslow light propagation in optomechanical systems,” Phys. Rev. A |

6. | Bin Chen, Cheng Jiang, and Ka-Di Zhu, “Slow light in a cavity optomechanical system with a Bose-Einstein condensate,” Phys. Rev. A |

7. | A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics |

8. | Victor Fiore, Yong Yang, Mark C. Kuzyk, Russell Barbour, Lin Tian, and Hailin Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. |

9. | E. Verhagen, S. Delalise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) |

10. | G. S. Agarwal and S. Huang, “Optomechanical systems as single-photon routers,” Phys. Rev. A |

11. | C. Jiang, B. Chen, and K.-D. Zhu, “Demonstration of a single-photon router with a cavity electromechanical system,” J. Appl. Phys. |

12. | S. Shahidani, M. H. Naderi, and M. Soltanolkotabi, “Control and manipulation of electromagnetically induced transparency in a nonlinear optomechanical system with two movable mirrors,” Phys. Rev. A |

13. | T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science |

14. | F. Marquardt and S. M. Girvin, “Trend: optomechanics,” Physics |

15. | 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. |

16. | M. Bhattacharya and P. Meystre, “Trapping and cooling a mirror to its quantum mechanical ground state,” Phys. Rev. Lett. |

17. | C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A |

18. | L. Tian and H. L. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A |

19. | Y. D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett. |

20. | T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature (London) |

21. | 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. |

22. | M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. |

23. | A A Clerk, F Marquardt, and K Jacobs, “Back-action evasion and squeezing of a mechanical resonator using a cavity detector,” New J. Phys. |

24. | Jie-Qiao Liao and C. K. Law, “Parametric generation of quadrature squeezing of mirrors in cavity optomechanics,” Phys. Rev. A |

25. | C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A |

26. | N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, “Nonclassical excitation for atoms in a squeezed vacuum,” Phys. Rev. Lett. |

27. | E. Alebachew and K. Fessah, “Interaction of a two-level atom with squeezed light,” Opt. Commun. |

28. | S. Mancini and P. Tombesi, “Quantum noise reduction by radiation yressure,” Phys. Rev. A |

29. | D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature (London) |

30. | A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature (London) |

31. | T. P. Purdy, P.-L. Yu, R.W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X , |

32. | D. Meiser and P. Meystre, “Coupled dynamics of atoms and radiation-pressure-driven interferometers,” Phys. Rev. A |

33. | K. Hammerer, K. Stannigel, C. Genes, and P. Zoller, “Optical lattices with micromechanical mirrors,” Phys. Rev. A |

34. | C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. |

35. | J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. |

36. | C. W. Gardiner and P. Zoller, |

37. | V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A |

38. | S. Gröblacher, K. Hammerer, M. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature (London) |

39. | C. Genes, D. Vitali, and P. Tombesi, “Emergence of atom-light-mirror entanglement inside an optical cavity,” Phys. Rev. A |

40. | Y. Han, J. Cheng, and L. Zhou, “Electromagnetically induced transparency in a cavity optomechanical system with an atomic medium,” J. Phys. B: At. Mol. Opt. Phys. |

41. | M. J. Collett and D. F. Walls, “Squeezing spectra for nonlinear optical systems,” Phys. Rev. A |

42. | E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A |

**OCIS Codes**

(270.1670) Quantum optics : Coherent optical effects

(270.6570) Quantum optics : Squeezed states

(140.3945) Lasers and laser optics : Microcavities

**ToC Category:**

Optoelectronics

**History**

Original Manuscript: May 12, 2014

Revised Manuscript: June 26, 2014

Manuscript Accepted: July 9, 2014

Published: July 17, 2014

**Citation**

Yin Xiao, Ya-Fei Yu, and Zhi-Ming Zhang, "Controllable optomechanically induced transparency and ponderomotive squeezing in an optomechanical system assisted by an atomic ensemble," Opt. Express **22**, 17979-17989 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-17979

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### References

- G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A81, 041803 (2010). [CrossRef]
- S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520 (2010). [CrossRef] [PubMed]
- J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature (London)471, 204 (2011). [CrossRef]
- A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69 (2011). [CrossRef]
- Devrim Tarhan, Sumei Huang, Ö zgür, and E. Müstecaplioğlu, “Superluminal and ultraslow light propagation in optomechanical systems,” Phys. Rev. A87, 013824 (2013). [CrossRef]
- Bin Chen, Cheng Jiang, and Ka-Di Zhu, “Slow light in a cavity optomechanical system with a Bose-Einstein condensate,” Phys. Rev. A83, 055803 (2011). [CrossRef]
- A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics3, 706 (2009). [CrossRef]
- Victor Fiore, Yong Yang, Mark C. Kuzyk, Russell Barbour, Lin Tian, and Hailin Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011). [CrossRef] [PubMed]
- E. Verhagen, S. Delalise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London)482, 63 (2012). [CrossRef]
- G. S. Agarwal and S. Huang, “Optomechanical systems as single-photon routers,” Phys. Rev. A85, 021801(R) (2012). [CrossRef]
- C. Jiang, B. Chen, and K.-D. Zhu, “Demonstration of a single-photon router with a cavity electromechanical system,” J. Appl. Phys.112, 033113 (2012). [CrossRef]
- S. Shahidani, M. H. Naderi, and M. Soltanolkotabi, “Control and manipulation of electromagnetically induced transparency in a nonlinear optomechanical system with two movable mirrors,” Phys. Rev. A88, 053813 (2013). [CrossRef]
- T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321, 1172 (2008). [CrossRef] [PubMed]
- F. Marquardt and S. M. Girvin, “Trend: optomechanics,” Physics2, 40 (2009). [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]
- M. Bhattacharya and P. Meystre, “Trapping and cooling a mirror to its quantum mechanical ground state,” Phys. Rev. Lett.99, 073601 (2007). [CrossRef] [PubMed]
- C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A77, 033804 (2008). [CrossRef]
- L. Tian and H. L. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A82, 053806 (2010). [CrossRef]
- Y. D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett.108, 153603 (2012). [CrossRef] [PubMed]
- T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature (London)495, 210–214 (2013). [CrossRef]
- D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett.98, 030405 (2007). [CrossRef] [PubMed]
- 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]
- A A Clerk, F Marquardt, and K Jacobs, “Back-action evasion and squeezing of a mechanical resonator using a cavity detector,” New J. Phys.10, 095010 (2008). [CrossRef]
- Jie-Qiao Liao and C. K. Law, “Parametric generation of quadrature squeezing of mirrors in cavity optomechanics,” Phys. Rev. A83, 033820 (2011). [CrossRef]
- C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A49, 1337 (1994). [CrossRef] [PubMed]
- N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, “Nonclassical excitation for atoms in a squeezed vacuum,” Phys. Rev. Lett.75, 3426 (1995). [CrossRef] [PubMed]
- E. Alebachew and K. Fessah, “Interaction of a two-level atom with squeezed light,” Opt. Commun.271, 154 (2007). [CrossRef]
- S. Mancini and P. Tombesi, “Quantum noise reduction by radiation yressure,” Phys. Rev. A49, 4055 (1994). [CrossRef] [PubMed]
- D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature (London)448, 476 (2012). [CrossRef]
- A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature (London)500, 185 (2013). [CrossRef]
- T. P. Purdy, P.-L. Yu, R.W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X, 3, 031012 (2013).
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