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.

💡 Research Summary

This paper addresses a fundamental challenge in quantum many-body physics: the direct detection of the nodal surfaces (zeros) of the many-body wavefunction. These high-dimensional geometric structures encode essential information about particle statistics and interactions but have remained largely inaccessible to experiment. The authors propose and rigorously analyze a novel interferometric technique to probe these nodal surfaces in ultra-cold atomic systems.

The core proposal leverages an existing experimental protocol based on self-heterodyne interferometry. In this setup, a ring-shaped quantum gas (the system of interest) and a disk-shaped condensate at the ring’s center (the phase reference) are trapped together. Upon simultaneous release and expansion, they interfere. The phase of the resulting interference fringes, ξ(x;t), is related to the phase of the ring’s many-body wavefunction.

The key theoretical insight is that the nodal surfaces of the wavefunction manifest as specific line discontinuities, termed “dislocations,” within these interference patterns. The authors prove this analytically for simple systems. For non-interacting spinless fermions on a ring, the anti-symmetry requirement forces the wavefunction to change sign when two particles exchange positions. This sign change corresponds to a π-phase jump in the argument of the conditional wavefunction Ψ(θ₁, {θ̃}), which, after the expansion and interference process, translates into a dislocation in the real-space interferogram. Bosonic wavefunctions, being symmetric, produce smooth interference patterns without such dislocations.

The study then extends to interacting systems, specifically a two-component (spin-1/2) Fermi-Hubbard model on a ring pierced by a magnetic flux. Using DMRG simulations and exact Bethe Ansatz solutions, the authors demonstrate how interactions and the resulting winding number (ℓ) modify the nodal structure. They show that the number of dislocations in the interferogram depends systematically on ℓ and the particle number parity.

A profound result is obtained in the limit of infinitely strong repulsion (U→∞). Here, the wavefunction factorizes into a charge part (described by spinless fermions) and a spin part (described by an XXX Heisenberg model). The spin amplitude ⟨α̅Q|λ̅⟩ can convert a node in the orbital wavefunction into a mere “cusp,” which appears as a smooth deformation rather than a sharp dislocation in the interference pattern. This reveals the distinct fingerprint of spin degrees of freedom on the many-body wavefunction’s geometry.

The work bridges a significant gap between theory and experiment. It provides a concrete, experimentally feasible path to observe not only the “symmetry-dictated” nodal surfaces mandated by particle statistics but also the “non-symmetry dictated” ones arising from interactions. This interferometric probe offers a new lens to study fundamental quantum many-body phenomena, validate quantum simulators, and explore the intricate geometry of quantum states relevant to condensed matter physics and quantum information science.