## Electromagnetically induced transparency and slow light in two-mode optomechanics |

Optics Express, Vol. 21, Issue 10, pp. 12165-12173 (2013)

http://dx.doi.org/10.1364/OE.21.012165

Acrobat PDF (980 KB)

### Abstract

We theoretically demonstrate the mechanically mediated electromagnetically induced transparency in a two-mode cavity optomechanical system, where two cavity modes are coupled to a common mechanical resonator. When the two cavity modes are driven on their respective red sidebands by two pump beams, a transparency window appears in the probe transmission spectrum due to destructive interference. Under this situation the transmitted probe beam can be delayed as much as 4 *μ*s, which can be easily controlled by the power of the pump beams.

© 2013 OSA

## 1. Introduction

1. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express **15**,17172–17205 (2007) [CrossRef] [PubMed] .

4. M. Aspelmeyer, P. Meystre, and K. Schwab, “Quantum optomechanics,” Phys. Today **65**,29–35 (2012) [CrossRef] .

5. F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science **322**,235–238 (2008) [CrossRef] [PubMed] .

10. B. He, “Quantum optomechanics beyond linearization,” Phys. Rev. A **85**,063820 (2012) [CrossRef] .

11. J. D. 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 (London) **475**,359–363 (2011) [CrossRef] .

12. J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature (London) **478**,89–92 (2011) [CrossRef] .

13. J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, “Parametric normal-mode splitting in cavity optomechanics,” Phys. Rev. Lett. **101**,263602 (2008) [CrossRef] [PubMed] .

14. S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature (London) **460**,724–727 (2009) [CrossRef] .

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

19. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. **77**,633–673 (2005) [CrossRef] .

20. L.V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) **397**,594–598 (1999) [CrossRef] .

21. D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. **13**,023003 (2011) [CrossRef] .

22. K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. **66**,2593–2596 (1991) [CrossRef] [PubMed] .

23. M. C. Phillips, H. Wang, I. Rumyantsev, N. H. Kwong, R. Takayama, and R. Binder, “Electromagnetically Induced Transparency in Semiconductors via Biexciton Coherence,” Phys. Rev. Lett. **91**,183602 (2003) [CrossRef] [PubMed] .

24. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. **8**,758–762 (2009) [CrossRef] [PubMed] .

25. C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. **97**,247401 (2006) [CrossRef] .

17. A. H. Safavi-Naeini, T. P. Mayer 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**, 69–73 (2011) [CrossRef] .

26. X. Zhou, F. Hocke, A. Schliesser, A. Marx, H. Huebl, R. Gross, and T. J. Kippenberg, “Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics,” Nat. Phys. **9**,179–184 (2013) [CrossRef] .

27. F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature **480**, 351–354 (2011) [CrossRef] [PubMed] .

28. F. Hocke, X. Zhou, A. Schliesser, T. J. Kippenberg, H. Huebl, and R. Gross, “Electromechanically induced absorption in a circuit nano-electromechanical system,” New J. Phys. **14**,123037 (2012) [CrossRef] .

*et al.*[29

29. J. M. Dobrindt and T. J. Kippenberg, “Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer,” Phys. Rev. Lett. **104**,033901 (2010) [CrossRef] [PubMed] .

*et al.*[30

30. M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, “Enhanced quantum nonlinearities in a two-mode optomechanical system,” Phys. Rev. Lett. **109**,063601 (2012) [CrossRef] [PubMed] .

*et al.*[31

31. P. Kómár, S. D. Bennett, K. Stannigel, S. J. M. Habraken, P. Rabl, P. Zoller, and M. D. Lukin, “Single-photon n onlinearities in two-mode optomechanics,” Phys. Rev. A **87**,013839 (2013) [CrossRef] .

32. K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. **109**,013603 (2012) [CrossRef] [PubMed] .

29. J. M. Dobrindt and T. J. Kippenberg, “Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer,” Phys. Rev. Lett. **104**,033901 (2010) [CrossRef] [PubMed] .

30. M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, “Enhanced quantum nonlinearities in a two-mode optomechanical system,” Phys. Rev. Lett. **109**,063601 (2012) [CrossRef] [PubMed] .

31. P. Kómár, S. D. Bennett, K. Stannigel, S. J. M. Habraken, P. Rabl, P. Zoller, and M. D. Lukin, “Single-photon n onlinearities in two-mode optomechanics,” Phys. Rev. A **87**,013839 (2013) [CrossRef] .

*et al.*[34

34. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. **3**,1196 (2012) [CrossRef] .

*et al.*[35] have experimentally demonstrated coherent wavelength conversion of optical photons between two different optical wavelengths in optomechanical crystal nanocavity and silica resonator, respectively. In the present paper, we investigate the optical response of the two-mode optomechanical system in the simultaneous presence of two strong pump beams and a weak probe beam. When the two cavities are pumped on their red sidebands (i.e., one mechanical frequency,

*ω*, below cavity resonances,

_{m}*ω*

_{1}and

*ω*

_{2}), respectively, a transparency window appears in the probe transmission spectrum.

## 2. Model and theory

*a*

_{1},

*a*

_{2}, and

*Q*which is defined as

*Q*=

*b*

^{†}+

*b*and introducing the corresponding damping and noise terms [36

36. 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] .

*a*

_{in,1}and

*a*

_{in,2}are the input vacuum noise operators with zero mean value,

*ξ*is the Brownian stochastic force with zero mean value [36

36. 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] .

_{1}= Δ

_{1}−

*g*

_{1}

*Q*and Δ′

_{s}_{2}= Δ

_{2}−

*g*

_{2}

*Q*are the effective cavity detunings including radiation pressure effects. We can rewrite each Heisenberg operator of Eqs. (2)–(4) as the sum of its steady-state mean value and a small fluctuation with zero mean value, Inserting these equations into the Langevin equations Eqs. (2)–(4) and assuming |

_{s}*a*

_{s,1}| ≫ 1 and |

*a*

_{s,2}| ≫ 1, one can safely neglect the nonlinear terms

*δa*

_{1}

*δQ*, and

*δa*

_{2}

*δQ*. Since the drives are weak, but classical coherent fields, we will identify all operators with their expectation values, and drop the quantum and thermal noise terms [16

16. 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] .

*δa*

_{1}〉 =

*a*

_{1+}

*e*

^{−iδt}+

*a*

_{1−}

*e*, 〈

^{iδt}*δa*

_{2}〉 =

*a*

_{2+}

*e*

^{−iδt}+

*a*

_{2−}

*e*, and 〈

^{iδt}*δQ*〉 =

*Q*

_{+}

*e*

^{−iδt}+

*Q*

_{−}

*e*. Upon substituting the above ansatz into Eqs. (7)–(9), we derive the following solution where and

^{iδt}*n*= |

_{k}*a*|

_{s,k}^{2}. Here

*n*, approximately equal to the number of pump photons in each cavity, is determined by the following coupled equations

_{k}*a*(

_{out}*t*) is the output field operator. Considering the output field of the left cavity, we have The transmission of the probe field, defined by the ratio of the output and input field amplitudes at the probe frequency, is then given by The rapid phase dispersion

*ϕ*= arg[

*t*(

*ω*)] of the transmitted probe laser beam leads to a group delay

_{p}*τ*expressed as Note that, if

_{g}*E*= 0 and

_{R}*g*

_{2}= 0, the Eqs (10)–(16) lead to the well-known results for the single mode cavity optomechanical system, where electromagnetically induced transparency and slow light effect have been observed experimentally [16

16. 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] .

17. A. H. Safavi-Naeini, T. P. Mayer 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**, 69–73 (2011) [CrossRef] .

## 3. Results and discussion

34. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. **3**,1196 (2012) [CrossRef] .

*ω*

_{1}= 2

*π*× 205.3 THz,

*ω*

_{2}= 2

*π*× 194.1 THz,

*κ*

_{1}= 2

*π*× 520 MHz,

*κ*

_{2}= 1.73 GHz,

*κ*

_{e,1}= 0.2

*κ*

_{1},

*κ*

_{e,2}= 0.42

*κ*

_{2},

*g*

_{1}= 2

*π*× 960 kHz,

*g*

_{2}= 2

*π*× 430 kHz,

*ω*= 2

_{m}*π*× 4 GHz,

*Q*= 87 × 10

_{m}^{3}, where

*Q*is the quality factor of the nanomechanical resonator, and the damping rate

_{m}*γ*is given by

_{m}*ω*>

_{m}*κ*

_{1}and

*ω*>

_{m}*κ*

_{2}, therefore the system operates in the resolved-sideband regime also termed good-cavity limit which is a prerequisite for the ground state cooling of a mechanical resonator [39

39. 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] .

_{1}= Δ

_{2}=

*ω*), a weak probe beam is then swept across the left cavity mode. The resulting transmission spectra of the probe beam as a function of the probe-cavity detuning Δ

_{m}*=*

_{p}*ω*−

_{p}*ω*

_{1}are plotted in Fig. 2, where

*P*= 0, 0.1, 1 and 10

_{L}*μ*W, respectively, while the power of the right pump beam

*P*is kept equal to 0.1

_{R}*μ*W. When

*P*= 0

_{L}*μ*W, there is a transmission dip in the center of the probe transmission spectrum, as shown in Fig. 2(a). However, as

*P*= 0.1

_{L}*μ*W, the broad cavity resonance splits into two dips and a narrow transparency window appears when the probe beam is resonant with the cavity frequency. As the left pump power increases, and hence effective coupling strength

16. 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] .

34. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. **3**,1196 (2012) [CrossRef] .

39. 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] .

*δ*=

*ω*−

_{p}*ω*between the pump beam and the probe beam. If this driving force is close to the mechanical resonance frequency

_{L}*ω*, the vibrational mode is excited coherently, resulting in Stokes and anti-Stokes scattering of light from the strong pump field. If the cavity is driven on its red sideband, the highly off-resonant Stokes scattering is suppressed and only the anti-Stokes scattering builds up within the cavity. However, when the probe beam is resonant with the cavity, destructive interference with the anti-Stokes field suppresses its build-up and hence a transparency window appears in the probe transmission spectrum. These processes are captured by the linearized Langevin Eqs. (7)–(9). In the resolved sideband regime (

_{m}*κ*

_{1},

*κ*

_{2}<

*ω*), when the pump beam detuning Δ′

_{m}_{1}= Δ′

_{2}≈

*ω*, the lower sideband can be neglected, i.e.,

_{m}*a*

_{1−}≈ 0 and

*a*

_{2−}≈ 0 [16

**330**, 1520–1523 (2010) [CrossRef] [PubMed] .

*x*(=

*δ*−

*ω*) represents the detuning of the probe frequency to the cavity frequency. When

_{m}*g*

_{2}= 0, Eq. (17) leads to the result for the single cavity [16

**330**, 1520–1523 (2010) [CrossRef] [PubMed] .

19. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. **77**,633–673 (2005) [CrossRef] .

_{1}= Δ′

_{2}=

*ω*.

_{m}## 4. Conclusion

*μ*s of the transmitted probe beam.

## Acknowledgments

## References and links

1. | T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express |

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

3. | F. Marquardt and S. M. Girvin, “Optomechanics,” Physics |

4. | M. Aspelmeyer, P. Meystre, and K. Schwab, “Quantum optomechanics,” Phys. Today |

5. | F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science |

6. | P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. |

7. | A. Nunnenkamp, K. Borkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett. |

8. | 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) |

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

10. | B. He, “Quantum optomechanics beyond linearization,” Phys. Rev. A |

11. | J. D. 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 (London) |

12. | J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature (London) |

13. | J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, “Parametric normal-mode splitting in cavity optomechanics,” Phys. Rev. Lett. |

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

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

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

17. | A. H. Safavi-Naeini, T. P. Mayer 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) |

18. | M. Karuza, C. Biancofiore, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, “Optomechanically induced transparency in a room temperature membrane-in-the-middle setup,” arXiv:1209.1352 (2012). |

19. | M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. |

20. | L.V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) |

21. | D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. |

22. | K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. |

23. | M. C. Phillips, H. Wang, I. Rumyantsev, N. H. Kwong, R. Takayama, and R. Binder, “Electromagnetically Induced Transparency in Semiconductors via Biexciton Coherence,” Phys. Rev. Lett. |

24. | N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. |

25. | C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. |

26. | X. Zhou, F. Hocke, A. Schliesser, A. Marx, H. Huebl, R. Gross, and T. J. Kippenberg, “Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics,” Nat. Phys. |

27. | F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature |

28. | F. Hocke, X. Zhou, A. Schliesser, T. J. Kippenberg, H. Huebl, and R. Gross, “Electromechanically induced absorption in a circuit nano-electromechanical system,” New J. Phys. |

29. | J. M. Dobrindt and T. J. Kippenberg, “Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer,” Phys. Rev. Lett. |

30. | M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, “Enhanced quantum nonlinearities in a two-mode optomechanical system,” Phys. Rev. Lett. |

31. | P. Kómár, S. D. Bennett, K. Stannigel, S. J. M. Habraken, P. Rabl, P. Zoller, and M. D. Lukin, “Single-photon n onlinearities in two-mode optomechanics,” Phys. Rev. A |

32. | K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. |

33. | K. Qu and G. S. Agarwal, “Optical memories and transduction of fields in double cavity optomechanical systems,” arXiv:1210.4067 (2012). |

34. | J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. |

35. | C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” arXiv:1205.2360 (2012). |

36. | 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 |

37. | R. W. Boyd, |

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

39. | 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. |

**OCIS Codes**

(270.1670) Quantum optics : Coherent optical effects

(140.3945) Lasers and laser optics : Microcavities

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 25, 2013

Revised Manuscript: April 17, 2013

Manuscript Accepted: April 25, 2013

Published: May 10, 2013

**Citation**

Cheng Jiang, Hongxiang Liu, Yuanshun Cui, Xiaowei Li, Guibin Chen, and Bin Chen, "Electromagnetically induced transparency and slow light in two-mode optomechanics," Opt. Express **21**, 12165-12173 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12165

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### References

- T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express15,17172–17205 (2007). [CrossRef] [PubMed]
- T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science321,1172–1176 (2008). [CrossRef] [PubMed]
- F. Marquardt and S. M. Girvin, “Optomechanics,” Physics2,40 (2009). [CrossRef]
- M. Aspelmeyer, P. Meystre, and K. Schwab, “Quantum optomechanics,” Phys. Today65,29–35 (2012). [CrossRef]
- F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science322,235–238 (2008). [CrossRef] [PubMed]
- P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett.107,063601 (2011). [CrossRef] [PubMed]
- A. Nunnenkamp, K. Borkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett.107,063602 (2011). [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, 204–208 (2011). [CrossRef]
- E. Verhagen, S. Delglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London)482,63–67 (2012). [CrossRef]
- B. He, “Quantum optomechanics beyond linearization,” Phys. Rev. A85,063820 (2012). [CrossRef]
- J. D. 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 (London)475,359–363 (2011). [CrossRef]
- J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature (London)478,89–92 (2011). [CrossRef]
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