Quantum Weak Measurement Back-action Control On A Strongly Interacting BEC

The choice of weak measurement phase can affect the energy dynamics of a nonlinear quantum system. We report on progress towards controlling the measurement back-action on a strongly interacting Bose Einstein condensate (BEC) continuously monitored under phase-contrast imaging setup. We have derived the master equation using the fixed number state approximation. These have been reduced to a coupled set of differential equations of motions under Gaussian Approximation for the BEC. We use measurement phase dependent back-action in these equations for feed-back control. We discuss potential applications and experimental realizations.