Scattering theory of cooling and heating in optomechanical systems

Abstract

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

“…As in our previous work [9], this interaction is accounted for by the multiplication of the various transfer matrices of the elements making up the system; this model is, in principle, applicable to systems of arbitrary complexity.…”

“…To this end, we denote the two polarization basis vectors by µ and ν, whereby the standard circular polarization basis is equivalent to setting µ = σ + and ν = σ − . Starting from the transfer matrix model explored in [9] and using the definitions in figure 1, we replace each of the field modes by a corresponding Jones vector, similar to the model used in [11]. Thus, for example,…”

“…A general recipe for transforming the formulae for the field mode amplitudes, as given in [9], can be summarized by means of the two replacements…”

“…We work to lowest order in ζ 0 and make use of the above relationships to find the net force acting on the atom [9,15]:…”

“…We recently [9] explored a new scattering theory that deals with the interaction of light and matter in a unified form applicable to microscopic and macroscopic systems. In that work we only considered the two-level atom model and showed, in particular, how our model can explain such mechanisms as standard optical molasses and mirror-mediated cooling [10].…”