## Macroscopic mechanical oscillators at the quantum limit through optomechanical cooling

JOSA B, Vol. 20, Issue 5, pp. 1054-1065 (2003)

http://dx.doi.org/10.1364/JOSAB.20.001054

Acrobat PDF (227 KB)

### Abstract

We discuss ways in which the optomechanical coupling provided by radiation pressure can be used to cool macroscopic collective degrees of freedom such as the vibrational modes of movable mirrors. Cooling is achieved with a phase-sensitive feedback loop that effectively overdamps a mirror’s motion without increasing the thermal noise. The feedback that results can bring macroscopic objects down to the quantum limit. In particular, it is possible to achieve squeezing and entanglement.

© 2003 Optical Society of America

**OCIS Codes**

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

**Citation**

David Vitali, Stefano Mancini, Luciano Ribichini, and Paolo Tombesi, "Macroscopic mechanical oscillators at the quantum limit through optomechanical cooling," J. Opt. Soc. Am. B **20**, 1054-1065 (2003)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-20-5-1054

Sort: Year | Journal | Reset

### References

- S. Mancini, D. Vitali, and P. Tombesi, “Optomechanical cooling of a macroscopic oscillatory by homodyne feedback,” Phys. Rev. Lett. 80, 688–691 (1998).
- P. F. Cohadon, A. Heidmann, and M. Pinard, “Cooling of a mirror by radiation pressure,” Phys. Rev. Lett. 83, 3174–3177 (1999).
- M. Pinard, P. F. Cohadon, T. Briant, and A. Heidmann, “Full mechanical characterization of a cold damped mirror,” Phys. Rev. A 63, 013808/1–12 (2000).
- T. Briant, P. F. Cohadon, M. Pinard, and A. Heidmann, “Optical phase-space reconstruction of mirror motion at the attometer level,” Eur. Phys. J. D 22, 131–140 (2003).
- S. van der Meer, “Stochastic cooling and the accumulation of antiprotons,” Rev. Mod. Phys. 57, 689–697 (1985).
- D. Vitali, S. Mancini, and P. Tombesi, “Optomechanical scheme for the detection of weak impulsive forces,” Phys. Rev. A 64, 051401/1–4 (2001).
- D. Vitali, S. Mancini, L. Ribichini, and P. Tombesi, “Mirror quiescence and high-sensitivity position measurements with feedback,” Phys. Rev. A 65, 063803/1–19 (2002).
- M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
- R. C. Ritter and G. T. Gillies, “Classical limit of mechanical thermal noise reduction by feedback,” Phys. Rev. A 31, 995–1000 (1985), and references therein.
- J.-M. Courty, A. Heidmann, and M. Pinard, “Quantum limits of cold damping with optomechanical coupling,” Eur. Phys. J. D 17, 399–408 (2001).
- M. P. Blencowe and M. N. Wybourne, “Quantum squeezing of mechanical motion for micron-sized cantilevers,” Physica B 280, 555–556 (2000).
- A. N. Cleland and M. L. Roukes, “A nanometre-scale mechanical electrometer,” Nature 392, 160–162 (1998).
- A. D. Armour, M. P. Blencowe, and K. C. Schwab, “Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box,” Phys. Rev. Lett. 88, 148301/1–4 (2002).
- H. M. Wiseman, “Quantum theory of continuous feedback,” Phys. Rev. A 49, 2133–2150 (1994).
- V. Giovannetti, P. Tombesi, and D. Vitali, “Non-Markovian quantum feedback from homodyne measurements: the effect of a nonzero feedback delay time,” Phys. Rev. A 60, 1549–1561 (1999).
- C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45, 75–79 (1980).
- R. Loudon, “Quantum limit on the Michelson interferometer used for gravitational-wave detection,” Phys. Rev. Lett. 47, 815–818 (1981).
- C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
- P. Samphire, R. Loudon, and M. Babiker, “Quantum theory of radiation-pressure fluctuations on a mirror,” Phys. Rev. A 51, 2726–2737 (1995).
- J. Mertz, O. Marti, and J. Mlynek, “Regulation of a microcantilever response by force feedback,” Appl. Phys. Lett. 62, 2344–2346 (1993).
- T. D. Stowe, K. Yasamura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett. 71, 288–290 (1997).
- G. J. Milburn, K. Jacobs, and D. F. Walls, “Quantum-limited measurements with the atomic force microscope,” Phys. Rev. A 50, 5256–5263 (1994).
- M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D 7, 107–116 (1999).
- C. K. Law, “Interaction between a moving mirror and radiation pressure: a Hamiltonian formulation,” Phys. Rev. A 51, 2537–2541 (1995).
- A. F. Pace, M. J. Collett, and D. F. Walls, “Quantum limits in interferometric detection of gravitational radiation,” Phys. Rev. A 47, 3173–3189 (1993).
- K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, “Quantum-nondemolition measurement of photon number using radiation pressure,” Phys. Rev. A 49, 1961–1966 (1994).
- S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49, 4055–4065 (1994).
- K. Jacobs, I. Tittonen, H. M. Wiseman, and S. Schiller, “Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion,” Phys. Rev. A 60, 538–548 (1999).
- Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, “High-sensitivity optical measurement of mechanical Brownian motion,” Europhys. Lett. 47, 545–551 (1999).
- I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. Müller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, “Interferometric measurements of the position of a macroscopic body: towards observation of quantum limits,” Phys. Rev. A 59, 1038–1044 (1999).
- C. W. Gardiner, Quantum Noise (Springer-Verlag, Berlin, 1991).
- V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63, 023812/1–8 (2001).
- H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of the damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984).
- F. Haake and R. Reibold, “Strong damping and low-temperature anomalies for the harmonic oscillator,” Phys. Rev. A 32, 2462–2475 (1985).
- H. M. Wiseman and G. J. Milburn, “Quantum theory of field-quadrature measurements,” Phys. Rev. A 47, 642–662 (1993).
- F. Grassia, J. M. Courty, S. Reynaud, and P. Touboul, “Quantum theory of fluctuations in a cold damped accelerometer,” Eur. Phys. J. D 8, 101–110 (2000).
- R. Folman, J. Schmiedmayer, H. Ritsch, and D. Vitali, “On the observation of decoherence with a movable mirror,” Eur. Phys. J. D 13, 93–107 (2001).
- H. P. Yuen, “Contractive states and the standard quantum limit for monitoring free-mass positions,” Phys. Rev. Lett. 51, 719–722 (1983).
- M. Ozawa, “Measurement breaking the standard quantum limit for free-mass position,” Phys. Rev. Lett. 60, 385–388 (1988).
- S. M. Tan, “Confirming entanglement in continuous variable quantum teleportation,” Phys. Rev. A 60, 2752–2758 (1999).
- L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
- R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
- S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploiting radiation pressure,” Phys. Rev. Lett. 88, 120401/1–4 (2002).
- M. D. Reid, “The Einstein–Podolsky–Rosen paradox and entanglement. 1. Signatures of EPR correlations for continuous variables,” arXiv.org e-Print archive, URL http://arXiv.org/abs/quant-ph/0112038.
- S. Mancini, D. Vitali, V. Giovannetti, and P. Tombesi, “Stationary entanglement between macroscopic mechanical oscillators,” arXiv.org e-Print archive, URL http://arXiv.org/abs/quant-ph/0209014.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.