Interferometric probe for the zeros of the many-body wavefunction

TL;DR

This paper proposes an interferometric method to directly probe the zeros of the many-body wavefunction in ultra-cold atomic systems, revealing fundamental geometric features related to particle statistics and interactions.

Contribution

It introduces a heterodyne interferometric technique to visualize nodal surfaces of the many-body wavefunction, including symmetry and interaction-induced features.

Findings

Nodal surfaces manifest as discontinuities in interference fringes.

Spin degrees of freedom produce distinct interference pattern signatures.

The method applies to correlated quantum systems and aids quantum simulation.

Abstract

The nodal surfaces of the many-body wavefunction are fundamental geometric features that encode critical information regarding particle statistics and their interaction. Directly probing these structures, particularly in correlated quantum systems, remains a significant experimental challenge. Here, we provide rigorous results on the structure of the many-body wavefunction and propose to use an interferometric technique to probe its zeros in ultra-cold atomic systems. Specifically, we refer to the so-called heterodyne interferometric reconstruction of the phase of the many-body wavefunction. We prove that the sought nodal surfaces show up as specific discontinuities in the interference fringes. Following Leggett, both `symmetry-dictated' nodal surfaces, due to particle statistics, and `non-symmetry dictated' nodal surfaces emerging from interaction effects, can be probed. We demonstrate how the spin degrees of freedom, effectively modifying the structure of the nodal surfaces of the many-body wavefunction, leave distinct fingerprints in the resulting interference pattern. Our work addresses important features of the structure of the many-body wavefunction that are broadly relevant for quantum science ranging from conceptual aspects to computational questions of extended systems and quantum simulation.