Control of an atom laser using feedback

TL;DR

This paper introduces a feedback control method for Bose-Einstein condensates modeled by the Gross-Pitaevskii equation, enabling energy reduction and dynamic control, especially when nonlinear interactions are tunable.

Contribution

It presents a generalized feedback scheme for controlling condensates, including nonlinear controls via Feshbach resonance, with demonstrated effectiveness in harmonic traps.

Findings

Feedback reduces condensate energy while maintaining dynamics.

Control efficiency improves with tunable nonlinear interactions.

The scheme accommodates nonlinear control mechanisms.

Abstract

A generalised method of using feedback to control Bose-Einstein condensates is introduced. The condensates are modelled by the Gross-Pitaevskii equation, so only semiclassical fluctations can be suppressed, and back-action from the measurement is ignored. We show that for any available control, a feedback scheme can be found to reduce the energy while the appropriate moment is still dynamic. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of non-linear controls. If the non-linear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency.