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

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.

10 pages, 8 figures

References in corpus (19)

• Many body localization and thermalization in quantum statistical mechanics
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Experimental Observation of a Generalized Gibbs Ensemble
• Observation of the supersolid stripe phase in spin-orbit coupled Bose-Einstein condensates
• A Straightforward Introduction to Continuous Quantum Measurement
• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Nonreciprocal Photon Transmission and Amplification via Reservoir Engineering
• Spectral signatures of many-body localization with interacting photons
• Generalized Thermalization in an Integrable Lattice System
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Atom-light crystallization of BECs in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration
• Mean field theory and fluctuation spectrum of a pumped, decaying Bose-Fermi system across the quantum condensation transition
• Non-reciprocal quantum interactions and devices via autonomous feed-forward
• Driven-dissipative Ising Model: An exact field-theoretical analysis
• Time-delayed feedback control of the Dicke-Hepp-Lieb superradiant quantum phase transition
• Tuning the universality class of phase transitions by feedback: Open quantum systems beyond dissipation

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• Feedback cooled Bose-Einstein condensation: near and far from equilibrium
• Quantum Back-action Limits in Dispersively Measured Bose-Einstein Condensates
• Weak-Measurement-Induced Heating in Bose-Einstein Condensates
• Preparing Quantum States by Measurement-feedback Control with Bayesian Optimization
• Feedback cooling of fermionic atoms in optical lattices