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arXiv:2209.04400 · Communications Physics

Quantum back-action limits in dispersively measured Bose-Einstein condensates

Emine Altuntaş, Ian B. Spielman

Published Apr 8, 2023• 7 citations
arXivHTMLPDF

Abstract

Abstract A fundamental tenet of quantum mechanics is that measurements change a system’s wavefunction to that most consistent with the measurement outcome, even if no observer is present. Weak measurements produce only limited information about the system, and as a result only minimally change the system’s state. Here, we theoretically and experimentally characterize quantum back-action in atomic Bose-Einstein condensates interacting with a far-from resonant laser beam. We theoretically describe this process using a quantum trajectories approach where the environment measures the scattered light and present a measurement model based on an ideal photodetection mechanism. We experimentally quantify the resulting wavefunction change in terms of the contrast of a Ramsey interferometer and control parasitic effects associated with the measurement process. The observed back-action is in good agreement with our measurement model; this result is a necessary precursor for achieving true quantum back-action limited measurements of quantum gases.

DOI
10.1038/s42005-023-01181-5

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In this paper, we investigate theoretically the back-action evading measurement of the collective mode of an interacting atomic Bose–Einstein condensate (BEC) trapped in an optical cavity that is driven coherently by a pump laser with a modulated amplitude. It is shown that, for a specified kind of amplitude modulation of the driving laser, one can measure a generalized quadrature of the collective mode of the BEC indirectly through the output cavity field with a negligible back-action noise in the good-cavity limit. Nevertheless, the on-resonance added noise of measurement is suppressed below the standard quantum limit (SQL), even in the bad cavity limit. Moreover, the measurement precision can be controlled through the s -wave scattering frequency of atomic collisions.
We investigate a non-destructive homodyne measurement of atomic condensates using off-resonant optical laser beam that interacts with atomic Bose-Einstein condensate (BEC). The interaction between laser beam and the atomic BEC creates entangled states of atom and light that are destroyed in a homodyne detection of light. The destruction of the entangled states causes back-action on the atomic states. We derive expression for the measurement operator on the atomic states due to the photon measurement. We characterize the back-action by calculating quantities such as the Q-function and observe the variation of the measured state with the strength of the light-BEC interaction.
We develop a classical theoretical description for nonlinear many-body dynamics that incorporates the back-action of a continuous measurement process. The classical approach is compared with the exact quantum solution in an example with an atomic Bose–Einstein condensate in a double-well potential where the atom numbers in both potential wells are monitored by light scattering. In the classical description, the back-action of the measurements appears as diffusion of the relative phase of the condensates on each side of the trap. When the measurements are frequent enough to resolve the system dynamics, the system behaves classically. This happens even deep in the quantum regime, and demonstrates how classical physics emerges from quantum mechanics as a result of measurement back-action.
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.