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Physical Review A

Tonks-Girardeau gas in an optical lattice: Effects of a local potential (6 pages)

Alberto G. Rojo, Han Fu

Published Jan 1, 2006• 0 citations
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Tonks-Girardeau gas in an optical lattice: Effects of a local potential

Hao Fu, Alberto G. Rojo

The physics of a Tonks-Girardeau gas confined in an optical lattice in the presence of a local potential is studied. In order to evaluate the single-particle density matrix (SPDM) of the many-body ground state, the Wigner-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the ``Bose-Einstein condensate''(BEC) state. We find that the BEC-state density at the position of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Girardeau gas is discussed.

arXiv:cond-mat/0602163•Physical Review A•Jul 21, 2006•6 citations

Ultracold Atoms in One-Dimensional Optical Lattices Approaching the Tonks-Girardeau Regime

Lode Pollet, S. Rombouts, P. J. H. Denteneer

Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.

arXiv:cond-mat/0408596•Physical Review Letters•Nov 15, 2004•38 citations
The physics of a Tonks-Girardeau gas confined in an optical lattice in the presence of a local potential is studied. In order to evaluate the single-particle density matrix (SPDM) of the many-body ground state, the Wigner-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the ``Bose-Einstein condensate''(BEC) state. We find that the BEC-state density at the position of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Girardeau gas is discussed.
Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.