Quantum theory of mirror-mediated atom cooling

We have recently suggested that a polarisable particle may be cooled by its interaction with a monochromatic laser beam if the transmitted beam is reflected back onto the particle by a mirror. The interference of the incoming beam with the reflected beam, which carries a phase imprinted by the particle at an earlier time, leads to a non-conservative potential and to frictional cooling. This simple scheme poses some challenging problems for accurate modelling. On one hand, cooling relies on the back-action of the particle-light interaction on the light itself and therefore the electromagnetic field must be treated dynamically, in contrast to standard free-space laser cooling methods. On the other hand, the system is intrinsically non-Markovian and thus cannot be described by the interaction of the particle with a single or a few discrete quantised modes coupled to a thermal reservoir, as in the case of cavity-mediated cooling [1]. Instead, a mathematical description must either keep track of the system at earlier times or, equivalently by Fourier transform, contain a continuous set of quantised modes [2]. In this talk, I will present a quantum mechanical model following this latter approach. Friction and momentum diffusion can be derived analytically to lowest order in the atom-light coupling strength. This allows us to predict cooling times and steady-state temperatures as a function of system parameters. Finally, we use corresponding semiclassical Monte-Carlo simulations [3] to corroborate these results and to access certain parameter regimes outside the validity of the analytical model