Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates

TL;DR

This paper investigates how incoherent electronic feedback control influences collective light scattering in Bose-Einstein condensates, revealing its effects on stability, quantum noise, and potential applications in quantum technologies.

Contribution

It introduces a feedback scheme for BEC light scattering, analyzing its impact on stability and quantum noise, and explores its potential for quantum control and measurement.

Findings

Feedback reduces the attraction basin of the uniform state.

Quantum fluctuations can destabilize the system with feedback.

No feedback-induced noise in quadratures, but added noise in mode quanta.

Abstract

It is well known that in the presence of a ring cavity the light scattering from a uniform atomic ensemble can become unstable resulting in the collective atomic recoil lasing. This is the result of a positive feedback due to the cavity. We propose to add an additional electronic feedback loop based on the photodetection of the scattered light. The advantage is a great flexibility in choosing the feedback algorithm, since manipulations with electric signals are very well developed. In this paper we address the application of such a feedback to atoms in the Bose-Einstein condensed state and explore the quantum noise due to the incoherent feedback action. We show that although the feedback based on the photodetection does not change the local stability of the initial uniform distribution with respect to small disturbances, it reduces the region of attraction of the uniform equilibrium. The feedback-induced nonlinearity enables quantum fluctuations to bring the system out of the stability region and cause an exponential growth even if the uniform state is globally stable without the feedback. Using numerical solution of the feedback master equation we show that there is no feedback-induced noise in the quadratures of the excited atomic and light modes. The feedback loop, however, introduces additional noise into the number of quanta of these modes. Importantly, the feedback opens an opportunity to position the modulated BEC inside a cavity as well as tune the phase of scattered light. This can find applications in precision measurements and quantum simulations.