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Qvarfort, S Serafini, A Xuereb, A Braun, D Ratzel, D Bruschi, DE.
Original Title
Time-evolution of nonlinear optomechanical systems: interplay of mechanical squeezing and non-Gaussianity
Type
journal article in Web of Science
Language
English
Original Abstract
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.
Keywords
optomechanics; nonlinear optomechanics; quantum optomechanics; non-Gaussianity; squeezing
Authors
Qvarfort, S ; Serafini, A; Xuereb, A; Braun, D; Ratzel, D; Bruschi, DE.
Released
21. 2. 2020
Publisher
IOP PUBLISHING LTD
Location
BRISTOL
ISBN
1751-8113
Periodical
Journal of Physics A-Mathematical and Theoretical
Year of study
53
Number
7
State
United Kingdom of Great Britain and Northern Ireland
Pages from
075304-1
Pages to
075304-40
Pages count
40
URL
https://iopscience.iop.org/article/10.1088/1751-8121/ab64d5