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Frontiers of Physics

Unravelling-based (auto)control of back-action in atomic Bose–Einstein condensate

V. A. Tomilin, Leonid V. Il'ichov

Published Jan 24, 2024• 1 citation
Publisher

Abstract

We present a novel feedback control method for quantum systems. Feedback does not affect the controlled system itself. Instead, it controls the unravelling of the quantum channel of interaction between the system and its environment. This interaction can be represented as a history of events. If their informational content is changed, their back-action on the system is also modified. Feedback action is trigged by the events, thus granting the system the degree of control over its own state. The efficiency of the proposed scheme is demonstrated on the example of two-mode atomic Bose-Einstein condensate, with one of its modes subject to phase-contrast imaging in a Mach–Zehnder interferometer. The histories of photocounts in the output channels of the interferometer are used for feedback. Its capabilities of state engineering are studied for different settings of the feedback loop and different numbers of events in the recorded histories.

DOI
10.1007/s11467-023-1375-2

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We present a novel feedback control method for quantum systems. Feedback does not affect the controlled system itself. Instead, it controls the unravelling of the quantum channel of interaction between the system and its environment. This interaction can be represented as a history of events. If their informational content is changed, their back-action on the system is also modified. Feedback action is trigged by the events, thus granting the system the degree of control over its own state. The efficiency of the proposed scheme is demonstrated on the example of two-mode atomic Bose-Einstein condensate, with one of its modes subject to phase-contrast imaging in a Mach–Zehnder interferometer. The histories of photocounts in the output channels of the interferometer are used for feedback. Its capabilities of state engineering are studied for different settings of the feedback loop and different numbers of events in the recorded histories.
We propose a novel method for controlling quantum systems via feedback. Rather than modifying parameters of the controlled system, the feedback loop changes the way it interacts with environment (the unraveling of the quantum operation describing this interaction). As an example, a problem of controlling the state of two-mode atomic Bose–Einstein condensate, with one mode subject to interferometric phase-contrast imaging in the Mach–Zehnder interferometer is considered. Different unravelings of photodetection operation are implemented by varying the phase shift in the condensate-free arm of the interferometer. A master equation governing the evolution of the condensate is derived. Based on its steady-state solution, the Kullback–Leibler divergence between the atomic distributions with and without feedback is calculated. The results show that this divergence reaches maximum at non-trivial values of the parameters controlling unraveling.
Abstract We consider the problem of decoherence in a Bose – Einstein condensate (BEC) of noninteracting atoms during interferometric probing with a classical monochromatic external field. The condensate is located in one of the arms of the Mach – Zehnder interferometer, while part of the radiation from the interferometer output is fed back to the input, thereby closing the coherent feedback loop. A more general setting of the problem is also considered, in which the condensate is located in a system of interferometers ‘nested’ into each other, while part of the output radiation of each of them is also fed back to its input, closing the so-called multiloop feedback. The possibility of effective control of decoherence rates of various matrix elements is shown. The application of feedback of the proposed type to BEC in a double-well potential is investigated. It is found that this feedback allows efficient control of the distribution of atoms between the wells.
The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. A 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.
Cold atomic ensembles and spinor Bose-Einstein condensates are potential candidates for quantum memories as they have long coherence times and can be coherently controlled. Unlike most candidates for quantum memories, which are genuine or effective single-particle systems, in atomic ensembles the quantum information is stored as a spin coherent state involving a very large number of atoms. A typical task with such ensembles is to drive the state towards a particular quantum state. While such quantum control methods are well developed for qubit systems, it is a nontrivial task to extend quantum control methods to the many-particle case. The objective of this work is to deterministically steer an arbitrary state of the atomic ensemble into a desired spin coherent state. To this end, we design our control law using stochastic stability theory, the quantum filtering theorem, and phase contrast imaging. We apply our control laws to different axes and show that it is possible to manipulate the atoms into different target states.
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.
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.