Interferometric probe for the zeros of the many-body wavefunction

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.