Cavity optomechanics with a trapped, interacting Bose-Einstein condensate

The dispersive interaction of a Bose-Einstein condensate with a single mode of a high-finesse optical cavity realizes the radiation pressure coupling Hamiltonian. In this system the role of the mechanical oscillator is played by a single condensate excitation mode that is selected by the cavity mode function. We study the effect of atomic s-wave collisions and show that it merely renormalizes parameters of the usual optomechanical interaction. Moreover, we show that even in the case of strong harmonic confinement—which invalidates the use of Bloch states—a single excitation mode of the Bose-Einstein condensate couples significantly to the light field, that is the simplified picture of a single “mechanical” oscillator mode remains valid.