Feedback cooled Bose-Einstein condensation: near and far from equilibrium

Continuously measured interacting quantum systems almost invariably heat, causing loss of quantum coherence. We study Bose-Einstein condensates (BECs) subject to repeated weak measurement of the atomic density and describe several protocols for generating a feedback signal designed to remove excitations created by measurement backaction. We use a stochastic Gross-Pitaevskii equation to model the system dynamics and develop feedback protocols that effectively cool both 1D and 2D BECs. Furthermore, we use this protocol to quench-cool 1D BECs from non-condensed highly excited states and find that they rapidly condense into a far from equilibrium state. We observe that these quench-cooled condensed states can have non-zero integer winding numbers described by quantized supercurrents.