Mechanical cooling and squeezing using optimal control

Abstract

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 a system without invoking the standard rotating-wave approximation and the adiabatic approximation. Using this formalism, we deduce both the conditional and unconditional states 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 states by demonstrating that these two cannot coincide in a typical control scheme, even with infinite feedback strength.

Analysis of spin-squeezing generation in cavity-coupled atomic ensembles with continuous measurements

“…Measurement protocols based on continuous monitoring [27] have been extensively studied for quantum state engineering purposes [28,29], leading to the outstanding experimental results observed in [30][31][32] for the cooling of a quantum mechanical oscillator towards its quantum ground state. In particular much theoretical effort has been devoted to the exploitation of this kind of protocols for the generation of metrologically useful quantum states, such as squeezed states of quantum harmonic oscillators or of SSSs for atomic ensembles [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. The physical intuition behind these protocols is the following: by continuously monitoring a particular observable of the quantum system, for example a spin operator for an atomic ensemble, the variance of such operators will decrease reaching eventually values below the so-called standard quantum limit, fixed by the fluctuations of the corresponding coherent (classical) states.…”