Many-body Dynamics with Measurement-based Feedback

Despite significant progress in understanding measurement-induced phenomena, the effect of actively processing measurement outcomes and feeding them back into the system dynamics remains largely unexplored. Although measurement-based feedback is a well-established tool in quantum optics, it has not yet been systematically applied to monitored quantum many-body systems. Understanding how feedback modifies monitored many-body systems is essential both for uncovering new nonequilibrium phases and for realizing experimentally accessible routes to engineered dissipation, including non-local forms.

Here, we develop a framework for pulsed feedback based on homodyne measurements and apply it to monitored fermionic systems. For free fermions, we recover the known feedback-driven transition, validating the method, and additionally identify a control-induced transition that does not arise in purely measurement-driven dynamics. We further demonstrate how measurement and feedback can be used to enforce gauge protection in a Z₂ lattice gauge theory, thereby enabling stabilized simulation of constrained dynamics and illustrating the versatility of the approach for constrained many-body systems. Our results show that feedback enables the realization of effective dissipators that are difficult to realize using measurement or Hamiltonian engineering alone.

This study establishes measurement-based feedback as a promising tool for quantum simulation of many-body physics, offering a flexible and experimentally viable approach to stabilizing novel phases and enforcing dynamical constraints. Drawing on techniques from quantum optics and cavity quantum electrodynamics, the proposed schemes are naturally adaptable to emerging platforms, including Rydberg-atom tweezer arrays via ancilla-assisted measurements. As a result, feedback-controlled many-body dynamics are within reach of current or near-term experimental capabilities. In particular, the pulsed feedback protocols we propose are compatible with existing control hardware, making them directly relevant to ongoing experiments in atomic and photonic systems.