Free expansion of impenetrable bosons on one-dimensional optical lattices

Marcos Antonio Rigol, Alejandro Muramatsu

Research output: Contribution to journalShort survey

54 Citations (Scopus)

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 super-fluid 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 non-interacting 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 one of non-interacting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.

Original languageEnglish (US)
Pages (from-to)861-881
Number of pages21
JournalModern Physics Letters B
Volume19
Issue number18
DOIs
StatePublished - Aug 10 2005

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bosons
momentum
expansion
fermions
insulators
confining
occupation
crossovers
eigenvectors
traps
entropy
fluids

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

Cite this

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Free expansion of impenetrable bosons on one-dimensional optical lattices. / Rigol, Marcos Antonio; Muramatsu, Alejandro.

In: Modern Physics Letters B, Vol. 19, No. 18, 10.08.2005, p. 861-881.

Research output: Contribution to journalShort survey

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AB - 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 super-fluid 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 non-interacting 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 one of non-interacting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.

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