Measurement resolution enhanced coherence of lattice fermions

Weak measurement enables the extraction of targeted information from a quantum system while minimizing measurement backaction. However, in many-body quantum systems, backaction from weak measurements can have novel effects on the system evolution. We theoretically study continuously measured non-interacting fermions on a lattice, starting in a ground-state Fermi sea. Repeated measurement of on-site occupation number, with single-site resolution, stochastically drives the system from the completely delocalized Fermi sea toward a Fock state. However, this is not the case for measurements that do not, even in principle, have single-site spatial resolution. We numerically investigate systems of varying sizes and show 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, the elements of which are indistinguishable to these measurements. Repeated measurements will drive any initial state into a single backaction-free subspace, leading to a steady state that is a fixed point of the measurement process. The existence of non-trivial backaction-free subspaces, i.e. high dimensional backaction-free subspaces, indicates that measurements with varying spatial resolution can be a tool for stabilizing non-trivial entanglement and coherence in many-particle systems.