Feedback-stabilized dynamical steady states in the Bose-Hubbard model

TL;DR

This paper explores how continuous measurement and classical feedback can stabilize and control quantum states in the Bose-Hubbard model, revealing new dynamical steady states and phase transitions.

Contribution

It introduces a comprehensive analysis of feedback control in the Bose-Hubbard model across classical, quantum, and numerical regimes, highlighting feedback-induced phase transitions and state preparation methods.

Findings

Exact equations of motion for large-atom systems with feedback

Quantum fluctuations influence feedback effectiveness in small systems

Feedback can induce symmetry-breaking phase transitions in Hubbard chains

Abstract

The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three perspectives. First, we consider a double-well system in the classical large-atom-number limit, deriving the exact equations of motion in the presence of feedback. Second, we consider the same system in the limit of small atom number, revealing the effect that quantum fluctuations have on the feedback scheme. Finally, we explore the behavior of modest sized Hubbard chains using exact numerics, demonstrating the near-deterministic preparation of number states, a tradeoff between local and non-local feedback for state preparation, and evidence of a feedback-driven symmetry-breaking phase transition.