Free expansion of impenetrable bosons on one-dimensional optical lattices

TL;DR

This paper reviews exact results on the free expansion of impenetrable bosons in one-dimensional lattices, highlighting how initial states influence the momentum distribution, coherence, and emergence of quasicondensates, with implications for understanding quantum many-body dynamics.

Contribution

It provides a comprehensive review of exact solutions for out-of-equilibrium dynamics of impenetrable bosons, emphasizing the role of initial states and introducing entropy measures to distinguish regimes.

Findings

Bosons in superfluid states quickly mimic fermionic momentum distributions.

Mott insulator initial states lead to finite-momentum quasicondensates during expansion.

Shannon entropy in momentum space differentiates regimes and reveals crossover behavior.

Abstract

We review recent exact results for the free expansion of impenetrable bosons on one-dimensional lattices, after switching off a confining potential. When the system is initially in a superfluid state, far from the regime in which the Mott-insulator appears in the middle of the trap, the momentum distribution of the expanding bosons rapidly approaches the momentum distribution of noninteracting fermions. Remarkably, no loss in coherence is observed in the system as reflected by a large occupation of the lowest eigenstate of the one-particle density matrix. In the opposite limit, when the initial system is a pure Mott insulator with one particle per lattice site, the expansion leads to the emergence of quasicondensates at finite momentum. In this case, one-particle correlations like the ones shown to be universal in the equilibrium case develop in the system. We show that the out-of-equilibrium behavior of the Shannon information entropy in momentum space, and its contrast with the one of noninteracting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.