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

Journal article

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 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.

Authors: Mehdi, Z; Goh, ML; Blacker, MJ; Hope, JJ; Szigeti, SS

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Quantum Science and Technology
• Volume: 10
• Issue: 4
• Article number: 045059
• Publication date: 2025-10-10
• Acceptance date: 2025-09-23
• DOI: 10.1088/2058-9565/ae0a7c
• EISSN: 2058-9565
• Language: English
• Keywords: quantum control; Bose–Einstein condensate; quantum feedback