Introduction

The interaction between a movable mirror and the radiation field of an optical cavity has recently been the subject of extensive theoretical and experimental investigations. This field known as cavity opto-mechanics has played a vital role in the conceptual exploration of the boundaries between classical and quantum mechanical systems. These opto-mechanical systems couple the mechanical motion to an optical field directly via radiation pressure buildup in a cavity. The coupling of mechanical and optical degrees of freedomvia radiation pressure has been a subject of early research in the context of laser cooling[1, 2, 3] and gravitational-wave detectors[4]. The recent improvements in nanofabrication techniques suggest that in the near future, these devices will reach the regime in which their sensitivitywill be limited by the ultimate quantumlimits set by the Heisenberg principle. The importance of the limits imposed by quantum mechanics on the resonator motion was first pointed out by Braginsky and coworkers[5] in the completely different context of massive resonators employed in the detection of gravitational waves[6]. However, in recent years, the quest for the experimental demonstration of genuine quantum states of macroscopic mechanical resonators has spread well beyond the gravitational wave physics community and has attracted wide interest.

Recently, there has been a great surge of interest in the application of radiation forces to manipulate the center-of-mass motion of mechanical oscillators covering a huge range of scales from macroscopic mirrors in the laser interferometer gravitational wave observatory (LIGO) project[7, 8] to nano-mechanical cantilevers[9, 10, 11, 12], membranes[13] and Bose−Einstein condensates[14, 15, 16, 17]. The central accomplishment of the field of cavity opto-mechanics is the investigation of radiation pressure force which allows one to manipulate the motional state of micromechanical oscillators. In particular, it has become possible to substantially cool the thermal excitation of a single mechanical mode, down to a few tens of remaining phonons[18]. With these developments, micro- and nano-mechanical resonators now represent an important model system with the prospect of demonstrating quantum effects on a macroscopic scale.

The quantum optical properties of a mirror coupled via radiation pressure to a cavity field show interesting similarities to an intracavity Kerr-like interaction[19, 20]. Recently, in the context of classical investigations of non-linear regimes, the dynamical instability of a driven cavity having a movable mirror has been investigated[21].