Gaussian tomography for cold-atom simulators

TL;DR

This paper introduces a practical method for cold-atom quantum simulators to measure off-diagonal charge correlations, enabling more detailed quantum state analysis without complex local control.

Contribution

The authors propose a novel, experiment-friendly scheme to measure charge-off-diagonal correlations using non-interacting dynamics and standard measurements, requiring minimal control and resources.

Findings

Efficient estimation of local currents with less than 4000 samples.

Simultaneous measurement of all non-local correlations in 70-site systems.

Protocol is implementable on existing platforms, enabling advanced quantum measurements.

Abstract

A limitation of analog quantum simulators based on cold atoms in optical lattices is that readout is typically limited to observables diagonal in the charge basis, i.e., densities and density correlation functions. To overcome this limitation, we propose experiment-friendly schemes to measure charge-off-diagonal correlations (such as currents). Our protocols use non-interacting dynamics for random times followed by standard quantum gas microscope measurements to effectively measure in random bases. The main requirement of our scheme is the ability to turn off interactions, which can be done in many atomic species using Feshbach resonances. Importantly, our scheme requires no local control and otherwise also exhibits modest requirements in terms of total evolution time and number of repetitions. We numerically demonstrate efficient estimation of bilinear correlation functions, requiring less than $4000$ samples to measure local currents to 5% error (system-size independent) and $\sim 10^4$ samples to simultaneously measure all non-local correlations in 70-site systems. Due to its simplicity, our protocol is implementable in existing platforms and thus paves the way to precision measurements beyond particle number measurements.