Protocols for a many-body phase microscope: From coherences and d-wave superconductivity to Green's functions

TL;DR

This paper introduces a method using Fourier-space manipulation in matter-wave microscopes to directly measure complex many-body correlations, phases, and order parameters in quantum lattice systems, expanding the capabilities of quantum gas microscopy.

Contribution

It proposes a novel approach to access off-diagonal correlators and phase information in quantum many-body states using matter-wave microscopy, enabling direct measurement of exotic order parameters.

Findings

Demonstrates measurement of d-wave superconducting order parameter

Shows how to access non-equal time Green's functions and spectral functions

Enables detection of hidden order in fractional Chern insulators

Abstract

Quantum gas microscopes probe quantum many-body lattice states via projective measurements in the occupation basis, enabling access to various density and spin correlations. Phase information, however, cannot be directly obtained in these setups. Recent experiments went beyond this by measuring local current operators and local phase fluctuations. Here we propose how Fourier-space manipulation in a matter-wave microscope allows access to various long-range off-diagonal correlators in experimentally realistic settings, realizing a many-body phase microscope. We demonstrate in particular how the fermionic d-wave superconducting order parameter in arbitrary Hubbard-type models, the non-equal time Green's function yielding the spectral function, or the hidden order of composite bosons in a fractional Chern insulator can be directly measured. Our results show the great potential of matter-wave microscopy for accessing exotic correlators including phases and coherences and characterizing intriguing quantum many-body states.