  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.
