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.
Highlights
Equilibrium is a concept central to many-body physics, both classical and quantum
We focus instead on many-body quantum systems maintained in the dynamical steady state—a kind of generalized equilibrium—stabilized by the interplay of unitary dynamics, minimally destructive quantum measurement, and classical feedback [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]
This sense is it possible to identify and explore systems maintained in low-entropy steady states associated with exotic effective Hamiltonians with highly nonlocal or N-body interactions? Optical pumping [50] and laser cooling [51]— both described by the physics of open quantum systems—are iconic examples where large ensembles of atoms enter lowentropy steady states well described by single-atom physics with little correlation between atoms
Summary
The bosonic field operator b†j describes the addition of a photon into mode j associated with lattice site j (here we focus on an idealized case with mode functions associated one-to-one with lattice sites), g captures the strength of the system-reservoir coupling, and the reservoir modes bj are each in the coherent state |α prior to interacting with the system. This operator describes rotations in the Xj-Pj quadrature plane for each reservoir mode, in proportion to the local number of atoms. We consider the continuous limit of many such weak measurements, taking the time between subsequent measurements to be tm and applying measurements with a strength associated with a measurement time tm
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