Qvarfort, S; Serafini, A; Xuereb, A; Braun, D; Rätzel, D; Bruschi, DE; (2020) Time-evolution of nonlinear optomechanical systems: Interplay of mechanical squeezing and non-Gaussianity. Journal of Physics A: Mathematical and Theoretical , 53 (7) , Article 075304. 10.1088/1751-8121/ab64d5.

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Abstract

We analytically solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical squeezing and optomechanical coupling. The solution is based on techniques which provide a new set of analytical tools to study the unitary evolution of optomechanical systems in full generality. 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 state. We find that the addition of a constant mechanical squeezing term generally decreases the overall non-Gaussian character of the state. For squeezing modulated at resonance, we recover the Mathieu equations, which we solve pertubatively. We find that the non-Gaussianity increases with both time and the squeezing parameter in this specific regime.

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