Mechanical cooling and squeezing using optimal control

A mechanical system can be optimally controlled through continuous measurements of its position followed by feedback. We revisit the complete formalism for predicting the performance of such as system without invoking the standard rotating wave approximations and the adiabatic approximation. Using this formalism we deduce both the conditional and unconditional state of a mechanical oscillator using the optimal control and feedback that leads to mechanical cooling and mechanical squeezing. We find large discrepancies between the exact solutions and the approximate solutions stressing the importance of using the complete model. We also highlight the importance of distinguishing between the conditional and unconditional state by demonstrating that these two cannot coincide in a typical control scheme, even with infinite feedback strength.