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

提出利用铷原子的玻色-爱因斯坦凝聚体（BEC）与光学高精细腔的纵向模式的耦合来有针对性地操纵BEC的介观集体振荡。50 mm长的谐振腔，精密度在50万以上，光子寿命为27µs，对应的线宽为5.8 kHz，仅相当于铷原子反冲频率的1.5倍。腔的极端频率选择性允许有选择地操纵BEC的单声子模式，振荡大约四倍的反冲频率。这种模式涉及到多达105个原子的相干振荡，代表了介观力学量子振荡器。对于离原子共振足够远的失谐光，耗散的唯一来源是通过光子的损失来衰减腔内场。由于这种阻尼和介观振子的时间演化发生在同一时间尺度上，因此可以在一定的参数范围内有效地冷却振子。因此，该系统代表了新兴的腔光力学领域的一个范例，其中介观机械振荡器（例如微米尺度悬臂或纳米尺度膜）通过耦合到高精细腔的冷却进行了探索。初步的理论考虑表明，该系统可以在原子运动的介观量子态和腔光场之间产生可观察到的纠缠，这将在理论和实验上进行探索。

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.