Steady-state entanglement of interacting masses in free space through optimal feedback control

We develop a feedback strategy based on optimal quantum feedback control for Gaussian systems to maximise the likelihood of steady-state entanglement detection between two directly interacting masses. We employ linear quadratic Gaussian (LQG) control to engineer the phase space dynamics of the two masses and propose Einstein-Podolsky-Rosen (EPR)-type variance minimisation constraints for the feedback to facilitate unconditional entanglement generation. This scheme allows for stationary entanglement in parameter regimes where strategies based on total energy minimisation ($cooling$) would fail. This feedback strategy, applied to the system of two masses driven out-of-thermal equilibrium [arXiv:2408.06251] enables unconditional entanglement generation under realistic experimental conditions.