Quantum Optimal Control of Squeezing in Cavity Optomechanics. 

Abstract

Squeezing is a non-classical feature of quantum states that is a useful 
resource, for example in quantum sensing of mechanical forces. Here, we 
show how to use optimal control theory to maximize squeezing in an 
optomechanical setup with two external drives and determine how fast the 
mechanical mode can be squeezed. For the autonomous drives considered 
here, we find the inverse cavity decay to lower-bound the protocol 
duration. At and above this limit, we identify a family of protocols 
leveraging a two-stage control strategy, where the mechanical mode is 
cooled before it is squeezed. Identification of the control strategy 
allows for two important insights - to determine the factors that limit 
squeezing and to simplify the time-dependence of the external drives, 
making our protocol readily applicable in experiments.