Snapshot-based characterization of particle currents and the Hall response in synthetic flux lattices

Quantum simulators are attracting great interest because they promise insight into the behavior of quantum many-body systems that are prohibitive for classical simulations. The generic output of quantum simulators are snapshots, obtained by means of projective measurements. These provide new information, such as full distribution functions, that goes beyond the more commonly evaluated expectation values of observables while adding shot-noise uncertainty to the latter. Hence, a central goal of theoretical efforts must be to predict these exact same quantities that can be measured in experiments. Here, we report on a snapshot-based study of particle currents in quantum lattice models with a conserved number of particles. It is shown how the full probability distribution of locally resolved particle currents can be obtained from suitable snapshot data. Moreover, we investigate the Hall response of interacting bosonic flux ladders, exploiting snapshots drawn from matrix-product states. Flux ladders are minimal lattice models, which enable microscopic studies of the Hall response in correlated quantum phases, and they are successfully realized in current quantum-gas experiments. Using a specific pattern of unitary two-site transformations, it is shown that the Hall polarization and the Hall voltage can be faithfully computed from a realistic number of snapshots obtained in experimentally feasible quench and finite-bias simulations.

Automated summary

Quantum simulators are gaining attention for their ability to reveal the behavior of quantum many-body systems that cannot be simulated classically. This study focuses on the behavior of particle currents in quantum lattice models with a conserved number of particles, and investigates the Hall response of interacting bosonic flux ladders. The results show that the full probability distribution of locally resolved particle currents can be obtained from suitable snapshot data, and the Hall polarization and Hall voltage can be accurately computed from experimentally feasible snapshots.