Abstract
Squeezed state in harmonic systems can be generated through a variety of techniques, including varying the oscillator frequency or using nonlinear two-photon Raman interaction. We focus on these two techniques to drive an initial thermal state into a final squeezed thermal state with controlled squeezing parameters – amplitude and phase – in arbitrary time. The protocols are designed through reverse engineering for both unitary and open dynamics. Control of the dissipation is achieved using stochastic processes, readily implementable via, e.g., continuous quantum measurements. Importantly, this allows controlling the state entropy and can be used for fast thermalization. The developed protocols are thus suited to generate squeezed thermal states at controlled temperature in arbitrary time.
Highlights
Squeezing is a paradigmatic quantum effect that allows reducing fluctuations of one variable beneath the standard quantum limit
We focus on its dynamics to design control protocols generating a squeezed thermal state at arbitrary final temperature βf−1 and target parameters {rf, φf } at the end of the control protocol, tf
Starting from the general evolution for a squeezed thermal, we first clarified how squeezing without phase control can be achieved in arbitrary time by modulating the trap-frequency of a harmonic oscillator and as such, relates to known Shortcuts to Adiabaticity (STA) techniques
Summary
Renewed interest in squeezing has come with progress in quantum optomechanics [20,21,22,23,24]. While much progress has been achieved for increasing the squeezing parameter, the protocols have so far been restricted to unitary dynamics and do not allow for the control of entropy We here lift this limitation and provide protocols to generate squeezed thermal states at controlled temperature in a fixed time. We focus on two different methods, already known as useful to generate squeezing, that we extend to open setups: (i) squeezing from nonadiabatic driving of the oscillator frequency—how is the trap control frequency modified by the dissipative dynamics; (ii) squeezing through the use of twophoton Raman interaction In both cases, knowledge of the analytical dynamics allows finding the control processes through reverse engineering.
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