Continuous feedback on a quantum gas coupled to an optical cavity

TL;DR

This paper demonstrates a real-time feedback control system for a quantum gas in an optical cavity, stabilizing its photon number and enabling precise exploration of phase transitions.

Contribution

It introduces a continuous, micro-processor controlled feedback scheme to stabilize intra-cavity photon number in a quantum gas system, facilitating controlled studies of phase transitions.

Findings

Stabilized intra-cavity photon number between 0.17 and 27.6 for up to 4 seconds.

Enabled control of the system near criticality and deep in the self-organized phase.

Paved the way for feedback-driven many-body phase engineering.

Abstract

We present an active feedback scheme acting continuously on the state of a quantum gas dispersively coupled to a high-finesse optical cavity. The quantum gas is subject to a transverse pump laser field inducing a self-organization phase transition, where the gas acquires a density modulation and photons are scattered into the resonator. Photons leaking from the cavity allow for a real-time and non-destructive readout of the system. We stabilize the mean intra-cavity photon number through a micro-processor controlled feedback architecture acting on the intensity of the transverse pump field. The feedback scheme can keep the mean intra-cavity photon number $n_\text{ph}$ constant, in a range between $n_\text{ph}=0.17\pm 0.04$ and $n_\text{ph}=27.6\pm 0.5$, and for up to 4 s. Thus we can engage the stabilization in a regime where the system is very close to criticality as well as deep in the self-organized phase. The presented scheme allows us to approach the self-organization phase transition in a highly controlled manner and is a first step on the path towards the realization of many-body phases driven by tailored feedback mechanisms.