Time-evolution of nonlinear optomechanical systems: interplay of mechanical squeezing and non-Gaussianity

journal article in Web of Science

English

We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the non-Gaussian state and its closest Gaussian reference state. We find that the addition of a constant mechanical squeezing term to the standard optomechanical Hamiltonian generally decreases the overall non-Gaussian character of the state. For sinusoidally modulated squeezing, the two second-order differential equations mentioned above take the form of the Mathieu equation. We derive perturbative solutions for a small squeezing amplitude at parametric resonance and show that they correspond to the rotating-wave approximation at times larger than the scale set by the mechanical frequency. We find that the non-Gaussianity of the state increases with both time and the squeezing parameter in this specific regime.

optomechanics; nonlinear optomechanics; quantum optomechanics; non-Gaussianity; squeezing

Qvarfort, S ; Serafini, A; Xuereb, A; Braun, D; Ratzel, D; Bruschi, DE.

21. 2. 2020

IOP PUBLISHING LTD

BRISTOL

1751-8113

Journal of Physics A-Mathematical and Theoretical

53

7

United Kingdom of Great Britain and Northern Ireland

075304-1

075304-40

40

https://iopscience.iop.org/article/10.1088/1751-8121/ab64d5