Measurement resolution enhanced coherence for lattice fermions

TL;DR

This paper investigates how measurement resolution affects the coherence and entanglement in lattice fermions under weak measurement, revealing the existence of backaction-free subspaces that influence the steady states.

Contribution

It introduces the concept of backaction-free subspaces in many-body fermionic systems and analyzes their role in measurement-induced state evolution and steady states.

Findings

Decreasing measurement resolution alters the stochastic evolution rate.

Backaction-free subspaces determine the steady states of the system.

Moderate measurement resolution preserves non-trivial entanglement and coherence.

Abstract

Weak measurement enables the extraction of targeted information from a quantum system while minimizing decoherence due to measurement backaction. However, in many-body quantum systems backaction can have unexpected effects on wavefunction collapse. We theoretically study a minimal many-particle model consisting of weakly measured non-interacting fermions in a one dimensional lattice. Repeated measurement of on-site occupation number with single-site resolution stochastically drives the system toward a Fock state, regardless of the initial state. This need not be the case for measurements that do not, even in principle, have single-site spatial resolution. We numerically show for systems with up to 16 sites that decreasing the spatial resolution strongly affects both the rate of stochastic evolution for each quantum trajectory and the allowed final states. The full Hilbert space can be partitioned into backaction-free subspaces (BFSs) the elements of which are indistinguishable to these measurements. Repeated measurements will drive any initial state into a single BFS, leading to a steady state that is a fixed point of the measurement process. We exactly calculate the properties of these BFSs for systems up to 32 sites and find that even for moderate reductions in measurement resolution they yield non-trivial steady state entanglement and coherence.