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

TL;DR

This paper presents a theoretical framework for measurement-based feedback control of a Bose-Einstein condensate's motional modes, demonstrating the possibility of ground-state cooling of multiple collective excitations through realistic control schemes.

Contribution

It introduces a linear-quadratic-Gaussian model for multi-mode BEC control that does not depend on specific atomic dynamics models, enabling practical feedback cooling strategies.

Findings

Collective excitations can be cooled below single-phonon levels.

Ground-state cooling of the lowest ten motional modes is achievable.

Optimal control parameters are identified for effective cooling.

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.