Unveiling hidden structure of many-body wavefunctions of integrable systems via sudden expansion experiments

TL;DR

This paper links the theoretical rapidities in integrable quantum systems to experimental measurements in sudden expansion experiments with ultracold gases, showing how initial rapidity distributions predict expansion velocities.

Contribution

It establishes a direct connection between Bethe-ansatz rapidities and observable expansion velocities in ultracold quantum gas experiments, validated through numerical comparisons.

Findings

Expansion velocity can be predicted from rapidity distributions.

Bethe-ansatz solutions approximate Bose-Hubbard dynamics.

Results bridge theoretical rapidities with experimental observables.

Abstract

In the theory of Bethe-ansatz integrable quantum systems, rapidities play an important role as they are used to specify many-body states, apart from phases. The physical interpretation of rapidities going back to Sutherland is that they are the asymptotic momenta after letting a quantum gas expand into a larger volume making it dilute and noninteracting. We exploit this picture to make a direct connection to quantities that are accessible in sudden-expansion experiments with ultracold quantum gases. By a direct comparison of Bethe-ansatz and time-dependent density matrix renormalization group results, we demonstrate that the expansion velocity of a one-dimensional Fermi-Hubbard model can be predicted from knowing the distribution of occupied rapidities defined by the initial state. Curiously, an approximate Bethe-ansatz solution works well also for the Bose-Hubbard model.