Squeezing of mechanical motion via qubit-assisted control

We propose a feedback control mechanism for the squeezing of the phononic mode of a mechanical oscillator. We show how, under appropriate working conditions, a simple adiabatic approach is able to induce mechanical squeezing. We then go beyond the limitations of such a working point and demonstrate the stationary squeezing induced by using repeated measurements and reinitialization of the state of a two-level system ancilla coupled to the oscillator. Our nonadaptive feedback loop offers interesting possibilities for quantum state engineering and steering in open-system scenarios.