Weak measurement in tandem with real-time feedback control is a new route toward engineering novel non-equilibrium 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 new tool for quantum engineering in cold-atom systems.

1 aHurst, Hilary, M.1 aGuo, Shangjie1 aSpielman, I., B. uhttps://arxiv.org/abs/2007.0726601239nas a2200145 4500008004100000245006500041210006400106260001500170520080100185100001800986700001601004700001801020700001801038856003701056 2019 eng d00aBeyond Spontaneous Emission: Giant Atom Bounded in Continuum0 aBeyond Spontaneous Emission Giant Atom Bounded in Continuum c12/20/20193 aThe quantum coupling of individual superconducting qubits to microwave photons leads to remarkable experimental opportunities. Here we consider the phononic case where the qubit is coupled to an electromagnetic surface acoustic wave antenna that enables supersonic propagation of the qubit oscillations. This can be considered as a giant atom that is many phonon wavelengths long. We study an exactly solvable toy model that captures these effects, and find that this non-Markovian giant atom has a suppressed relaxation, as well as an effective vacuum coupling between a qubit excitation and a localized wave packet of sound, even in the absence of a cavity for the sound waves. Finally, we consider practical implementations of these ideas in current surface acoustic wave devices.

1 aGuo, Shangjie1 aWang, Yidan1 aPurdy, Thomas1 aTaylor, Jacob uhttps://arxiv.org/abs/1912.09980