Oscillator-field model of moving mirrors in quantum optomechanics

Abstract

We present a microphysics model for the kinematics and dynamics of optomechanics describing the coupling between an optical field, modeled here by a massless scalar field, and the internal and mechanical degrees of freedom of a movable mirror. Instead of implementing boundary conditions on the field, we introduce an internal degree of freedom and its dynamics to describe the mirror's reflectivity. Depending on parameter values, the internal degrees of freedom of the mirror in this model capture a range of its optical activities, from those exhibiting broadband reflective properties to those reflecting only in a narrow band. After establishing the model we show how appropriate parameter choices lead to other well-known optomechanical models, including those of Barton and Calogeracos [Ann. Phys. (NY) 238, 227 (1995)], Calogeracos and Barton, Ann. Phys. (NY) 238, 268 (1995), Law [Phys. Rev. A 51, 2537 (1995)], and Golestanian and Kardar [Phys. Rev. Lett. 78, 3421 (1997); Phys. Rev. A 58, 1713 (1998)]. As a simple illustrative application we derive classical radiation pressure cooling from this model. We then connect our microphysics model to the common descriptions of a moving mirror coupled to radiation pressure (e.g., with N x coupling, where N is the photon number and x is the mirror displacement), making explicit the underlying assumptions made in these phenomenological models. Our model is also applicable to the lesser explored case of small N , which existing models based on sideband approximations [Kimble et al., Phys. Rev. D 65, 022002 (2001)] have not addressed. Interestingly, we also find that slow-moving mirrors in our model can be described by the ubiquitous Brownian motion model of quantum open systems. The scope of applications of this model ranges from a full quantum-mechanical treatment of radiation pressure cooling and quantum entanglement between macroscopic mirrors to the back reaction of Hawking radiation on black-hole evaporation in a moving mirror analog.

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