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Bulletin of the American Physical Society

Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases in arbitrary trapping potentials

Y. Y. Atas, Dimitri M. Gangardt, Isabelle Bouchoule, Karen V. Kheruntsyan

Published Jun 8, 2017• 0 citations
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Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping, we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective ``dressing'' of the single-particle wave functions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing-mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential.
Ultracold quantum gases offer a fascinating playground for exploring and understanding the fundamentals of out-of-equilibrium behaviour of quantum matter. Experimental systems whose many-body dynamics can be described by exactly solvable models play a particularly important role. A paradigmatic example in this realm is the Tonks-Girardeau (TG) gas of impenetrable bosons. Here we investigate and predict a striking dynamical manifestation of the impenetrability--a collective many-body bounce effect. This effect, while being invisible in the evolution of the in-situ density profile of the gas, can be revealed through a nontrivial narrowing of its momentum distribution during breathing-mode oscillations. To demonstrate this, we develop an exact finite-temperature dynamical theory of a harmonically trapped TG gas, thus extending on previous zero-temperature results and opening the way to solving arbitrary dynamical protocols of the TG gas. We identify physical regimes for observing the many-body bounce effect and foresee it as a valuable probe for characterising the nonequilibrium dynamics of interacting quantum fluids.