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- W4315706781 abstract "In 1D quantum gases, the momentum distribution (MD) of the atoms is a standard experimental observable, routinely measured in various experimental setups. The MD is sensitive to correlations, and it is notoriously hard to compute theoretically for large numbers of atoms $N$, which often prevents direct comparison with experimental data. Here we report significant progress on this problem for the 1D Tonks-Girardeau gas in the asymptotic limit of large $N$, at zero temperature and driven out of equilibrium by a quench of the confining potential. We find an exact formula for the time-dependent one-particle density matrix $langle hat{Psi}^dagger(x) hat{Psi}(x') rangle$ of the out-of-equilibrium TG gas in the $N rightarrow infty$ limit, valid on distances $|x-x'| $ much larger than the interparticle distance. By comparing with numerical results for $N=33$ atoms, we demonstrate that the new asymptotically exact formula can be used to compute the out-of-equilibrium MD with great accuracy for a wide range of momenta (except in the tails of the distribution at very large momenta). For a quench from a double-well potential to a single harmonic well,which mimics a `quantum Newton cradle' setup, our method predicts the periodic formation of peculiar, multiply peaked, momentum distributions. Our results open up new perspectives for precision out-of-equilibrium quantum many-body physics and confrontation between theory and experiments in 1D quantum gases." @default.
- W4315706781 created "2023-01-12" @default.
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- W4315706781 date "2023-01-10" @default.
- W4315706781 modified "2023-10-16" @default.
- W4315706781 title "One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: exact results at large $N$" @default.
- W4315706781 doi "https://doi.org/10.48550/arxiv.2301.04094" @default.
- W4315706781 hasPublicationYear "2023" @default.
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