Noise cancellation system for shaking optical lattice by controlling optical path.

We present a simple way to control the phase of an optical lattice by detecting the interference signal of two beams. The optical lattice is intentionally shaken by varying the relative phase of the beams. However, the lattice may also be shaken by unwanted variations of the relative optical path length, e.g., due to mirror vibrations. The purpose of the servo is to attenuate these unwanted variations while the intended shaking remains. We demonstrate that the servo changes the relative phase between beams and follows the intended shaking function with 99% accuracy. The bandwidth for the acceptable attenuation of unwanted shaking, -13 dB, is measured to 1.2 kHz to control the atomic Bloch state. The servo will be implemented to attenuate the unknown system vibrations for a shaken lattice and engineer the momentum state of atoms trapped in the lattice. This idea can also be applied to any time varying experiment.