### 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 language | English (US) |
---|---|

Pages (from-to) | 861-881 |

Number of pages | 21 |

Journal | Modern Physics Letters B |

Volume | 19 |

Issue number | 18 |

DOIs | |

State | Published - Aug 10 2005 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Condensed Matter Physics

### Cite this

*Modern Physics Letters B*,

*19*(18), 861-881. https://doi.org/10.1142/S0217984905008876

}

*Modern Physics Letters B*, vol. 19, no. 18, pp. 861-881. https://doi.org/10.1142/S0217984905008876

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

Research output: Contribution to journal › Short survey

TY - JOUR

T1 - Free expansion of impenetrable bosons on one-dimensional optical lattices

AU - Rigol, Marcos Antonio

AU - Muramatsu, Alejandro

PY - 2005/8/10

Y1 - 2005/8/10

N2 - 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.

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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U2 - 10.1142/S0217984905008876

DO - 10.1142/S0217984905008876

M3 - Short survey

VL - 19

SP - 861

EP - 881

JO - Modern Physics Letters B

JF - Modern Physics Letters B

SN - 0217-9849

IS - 18

ER -