Phase-space microscopes for quantum gases: Measuring conjugate variables and momentum-weighted densities

TL;DR

This paper introduces phase-space measurement protocols for quantum gases using quantum gas microscopes, enabling joint position-momentum measurements and momentum density analysis with high spatial resolution.

Contribution

The authors develop concrete protocols to extend quantum gas microscopes for phase-space measurements, distinguishing between joint and averaged measurement modes.

Findings

Joint position-momentum measurement in quantum gases demonstrated.

High spatial resolution of momentum density averages achieved.

Protocols applicable to diverse physical settings.

Abstract

Quantum gas microscopes offer unprecedented insights into quantum many-body states of cold atomic gases. Here we introduce concrete protocols for extending quantum gas microscopes to measure in phase space, by mapping momentum onto auxiliary degrees of freedom and using positive operator-valued measures. We distinguish between two distinct operational modes. In the Husimi-Q phase space microscope, position and momentum are jointly measured; in this mode the fundamental quantum noise appears in the position measurement. Conversely, the averaged-mode phase space microscope extracts the spatial dependence of averages of the momentum density (and its moments); these averages can be retrieved with arbitrary spatial resolution. We illustrate the utility of these techniques in diverse physical settings.