Optomechanical trapping and cooling of partially transparent mirrors

We consider the radiative trapping and cooling of a partially transmitting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.}, arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially transmissive mirrors.