Optomechanics with a Bose-Einstein condensate in a high-finesse cavity operating in the regime of resolved atomic recoil sidebands

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It is proposed to exploit the coupling of a Bose-Einstein condensate (BEC) of rubidium atoms to a longitudinal mode of an optical high finesse cavity for targeted manipulation of a mesoscopic collective oscillation of the BEC. The 50 mm long resonator with a finesse above half a million exhibits a photon life time of 27 µs, corresponding to a line width of 5.8 kHz, which amounts to only 1.5 times the recoil frequency of a rubidium atom. The extreme frequency selectivity of the cavity permits to selectively manipulate a single phonon mode of the BEC oscillating with approximately four times the recoil frequency. This mode, which involves the coherent oscillation of up to several 105 atoms, represents a mesoscopic mechanical quantum oscillator. For light detuned sufficiently far from atomic resonances, the only source of dissipation is damping of the intra-cavity field via loss of photons. Since this damping and the temporal evolution of the mesoscopic oscillator occur on the same time scale, the oscillator can be efficiently cooled in certain parameter ranges. The system thus represents a paradigm of the emerging field of cavity optomechanics, where the cooling of mesoscopic mechanical oscillators (as e.g. micron scale cantilevers or nano scale membranes) via coupling to high finesse cavities is explored. Preliminary theoretical considerations indicate that the system can give rise to observable entanglement between mesoscopic quantum states of the atomic motion and the cavity light field, which will be explored theoretically and experimentally.