Abstract
Weak measurement in tandem with real-time feedback control is a new route toward engineering novel nonequilibrium quantum matter. Here we develop a theoretical toolbox for quantum feedback control of multicomponent Bose-Einstein condensates (BECs) using backaction-limited weak measurements in conjunction with spatially resolved feedback. Feedback in the form of a single-particle potential can introduce effective interactions that enter into the stochastic equation governing system dynamics. The effective interactions are tunable and can be made analogous to Feshbach resonances-spin independent and spin dependent-but without changing atomic scattering parameters. Feedback cooling prevents runaway heating due to measurement backaction and we present an analytical model to explain its effectiveness. We showcase our toolbox by studying a two-component BEC using a stochastic mean-field theory, where feedback induces a phase transition between easy-axis ferromagnet and spin-disordered paramagnet phases. We present the steady-state phase diagram as a function of intrinsic and effective spin-dependent interaction strengths. Our result demonstrates that closed-loop quantum control of Bose-Einstein condensates is a powerful tool for quantum engineering in cold-atom systems.
Highlights
Quantum gas experiments have exquisite control over the low-energy Hamiltonian governing system dynamics, providing demonstrated opportunities to study interacting many-body quantum systems with great precision
We develop a theory of weak measurement and classical feedback in weakly interacting quantum systems framed in the context of quantum control theory [28]
Using our general formalism, we investigate the steady-state phases of a two-component Bose-Einstein condensates (BECs) subject to weak measurement and classical feedback via a spin-dependent applied potential, enabling both density- and spin-dependent feedback protocols
Summary
Quantum gas experiments have exquisite control over the low-energy Hamiltonian governing system dynamics, providing demonstrated opportunities to study interacting many-body quantum systems with great precision. Using our general formalism, we investigate the steady-state phases of a two-component BEC subject to weak measurement and classical feedback via a spin-dependent applied potential, enabling both density- and spin-dependent feedback protocols. Local feedback can result in spin-dependent effective interaction terms in the stochastic equation governing condensate dynamics. Depending on the interplay of intrinsic and effective (i.e., feedback induced) spin-dependent interactions, the condensate steady-state phase is either an easy-axis ferromagnet or spin-disordered paramagnet. Our result opens the door to engineering dynamical and/or spatially dependent effective interactions in quantum gases via closed-loop feedback control. The paper is structured as follows: In Sec. II, we present our main formal results, including the stochastic equation describing condensate dynamics, and introduce a toy model illustrating the salient features of the control protocol.
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