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arXiv:2007.07266 · Physical Review Research

Feedback induced magnetic phases in binary Bose-Einstein condensates

Hilary M. Hurst, Shangjie Guo, I. B. Spielman

Published Dec 7, 2020• 15 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevresearch.2.043325

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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.
Understanding and controlling many-body quantum systems in noisy environments is paramount to developing robust quantum technologies. An external environment can be thought of as a measurement reservoir which extracts information about the quantum system. Cold atoms are well suited to examine system-environment interaction via weak (i.e. minimally destructive) measurement techniques, wherein the measurement probe acts as the environment and also provides a noisy record of system dynamics. The measurement record can then be used in a feedback scheme, opening the door to real time control of quantum gases. In this talk I discuss our theoretical proposal to use weak measurement and feedback to engineer new phases in spin-1/2 Bose-Einstein condensates. We show that measurement and feedback alters the effective Hamiltonian governing system dynamics, thereby driving phase transitions reminiscent of a quantum quench for the closed system. We also develop a feedback cooling protocol which prevents runaway heating of the condensate due to measurement backaction. Our results show that measurement and feedback can alter condensate dynamics in a stable, controllable manner and provides a route toward Hamiltonian engineering in many-body systems. Finally, I will discuss ongoing experimental work to realize our proposal using Rb87.
We consider the theory of feedback control of a Bose-Einstein condensate (BEC) confined in a harmonic trap under a continuous measurement constructed via nondestructive imaging. A filtering theory approach is used to derive a stochastic master equation (SME) for the system from a general Hamiltonian based upon system-bath coupling. Numerical solutions for this SME in the limit of a single atom show that the final steady-state energy is dependent upon the measurement strength, the ratio of photon kinetic energy to atomic kinetic energy, and the feedback strength. Simulations indicate that for a weak measurement strength, feedback can be used to overcome heating introduced by the scattering of light, thereby allowing the atom to be driven toward the ground state.
Recent great progress in studying theoretical and especially experimental properties of BoseEinstein condensate (BEC) creates a new era in developing and designing principally novel types of quantum devices, including quantum sensors for measuring nonlinear interactions, external electrical and magnetic fields, and other physical characteristics with high sensitivity. Here we discuss the application of feedback control over a quantum sensor based on the Bose-Einstein condensate trapped in twodimensional ring potential. For a weakly interacting regime, the dynamics of such a system are modeled by three coupled complex differential master equations containing the parameter of interaction and the chemical potential parameter. The last one plays the role of control variable in sensing protocol for twobody interaction. The goal of control is to minimize the effects of the higher energy levels in BEC by driving their corresponding matrix density elements. The control algorithm is designed as Kolesnikov’s feedback forming an artificial target attractor in the dynamical system. We re-formulate Kolesnikov’s approach in the operator form to adapt it to quantum engineering processes. The control approach proposed here can be efficiently extended to different sensing protocols for detecting external magnetic fields, rotational components, and other physical characteristics of BEC interacting with the environment.
Recent great progress in studying theoretical and especially experimental properties of Bose Einstein condensate (BEC) creates a new era in developing and designing principally novel types of quantum devices, including quantum sensors for measuring nonlinear interactions, external electrical and magnetic fields, and other physical characteristics with high sensitivity. Here we discuss the application of feedback control over a quantum sensor based on the Bose-Einstein condensate trapped in two dimensional ring potential. For a weakly interacting regime, the dynamics of such a system are modeled by three coupled complex differential master equations containing the parameter of interaction and the chemical potential parameter. The last one plays the role of control variable in sensing protocol for two body interaction. The goal of control is to minimize the effects of the higher energy levels in BEC by driving their corresponding matrix density elements. The control algorithm is designed as Kolesnikov’s feedback forming an artificial target attractor in the dynamical system. We re-formulate Kolesnikov’s approach in the operator form to adapt it to quantum engineering processes. The control approach proposed here can be efficiently extended to different sensing protocols for detecting external magnetic fields, rotational components, and other physical characteristics of BEC interacting with the environment.
Weakly measuring many-body systems and allowing for feedback in real time can simultaneously create and measure new phenomena in quantum systems. We theoretically study the dynamics of a continuously measured two-component Bose-Einstein condensate (BEC) potentially containing a domain wall and focus on the tradeoff between usable information obtained from measurement and quantum backaction. Each weakly measured system yields a measurement record from which we extract real-time dynamics of the domain wall. We show that quantum backaction due to measurement causes two primary effects: domain-wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We propose a feedback protocol to dynamically create a stable domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.
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