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

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