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We analyze the optomechanics of an atomic Bose-Einstein condensateinteracting with the optical lattice inside a laser-pumped optical cavity andsubject to a uniform bias force such as gravity. An atomic wave packet in atilted lattice undergoes Bloch oscillations; in a cavity the backaction of theatoms on the light leads to a time-dependent modulation of the intracavitylattice at the Bloch frequency. When the Bloch frequency is on the order of thecavity damping rate we find transport of the atoms either up or down thelattice. The transport dynamics can be interpreted as a manifestation ofdynamical backaction-induced sideband damping/amplification of theoptomechanical Bloch oscillator. Depending on the sign of the pump-cavitydetuning, atoms are transported either with or against the bias forceaccompanied by an up- or down-conversion of the frequency of the pump laserlight. We also evaluate the prospects for using the optomechanical Blochoscillator to make continuous measurements of forces by reading out the Blochfrequency. In this context we establish the significant result that the opticalspring effect is absent and the Bloch frequency is not modified by thebackaction.

atoms

An optomechanical elevator: Transport of a Bloch oscillating  Bose-Einstein condensate up and down an optical lattice by cavity sideband  amplification and cooling