Multi-mode cooling of a Bose-Einstein condensate with linear quantum feedback

• URL: http://arxiv.org/abs/2506.02377v1
• Date: Tue, 03 Jun 2025 02:26:48 GMT
• Title: Multi-mode cooling of a Bose-Einstein condensate with linear quantum feedback
• Authors: Zain Mehdi, Matthew L. Goh, Matthew J. Blacker, Joseph J. Hope, Stuart S. Szigeti,
• Abstract summary: We theoretically investigate measurement-based feedback control over the motional degrees of freedom of an oblate quasi-2D atomic Bose-Einstein condensate (BEC)<n>We develop a linear-quadratic-Gaussian (LQG) model that describes the multi-mode dynamics of the condensate's collective excitations under continuous measurement and control.<n>We present analytical results showing that collective excitations can be cooled to below single-phonon average occupation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We theoretically investigate measurement-based feedback control over the motional degrees of freedom of an oblate quasi-2D atomic Bose-Einstein condensate (BEC) subject to continuous density monitoring. We develop a linear-quadratic-Gaussian (LQG) model that describes the multi-mode dynamics of the condensate's collective excitations under continuous measurement and control. Crucially, the multi-mode cold-damping feedback control we consider uses a realistic state-estimation scheme that does not rely upon a particular model of the atomic dynamics. We present analytical results showing that collective excitations can be cooled to below single-phonon average occupation (ground-state cooling) across a broad parameter regime and identify the conditions under which the lowest steady-state phonon occupation is asymptotically achieved. Further, we develop multi-objective optimization methods that explore the trade-off between cooling speed and the final energy of the cloud and provide numerical simulations demonstrating the ground-state cooling of the lowest ten motional modes above the condensate ground state. Our investigation provides concrete guidance on the feedback control design and parameters needed to experimentally realize a feedback-cooled BEC.

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