Ground State Properties of a Tonks-Girardeau Gas in a Split Trap

Details Ground State Properties of a Tonks-Girardeau Gas in a Split Trap Ground State Properties of a Tonks-Girardeau Gas in a Split Trap

2008-03-06

arxiv.org/abs/0803.0846v4

Phys. Rev. A 77, 063601 (2008)

Physics

Condensed Matter

Other Condensed Matter

7 pages, 10 figures.New Fig. 8 added and text reference to figure in Sec IV C. New reference [15] added

Scientific paper

10.1103/PhysRevA.77.063601

We determine the exact many-body properties of a bosonic Tonks-Girardeau gas confined in a harmonic potential with a tunable $\delta$-function barrier at the trap center. This is done by calculating the reduced single particle density matrix, the pair-distribution function, and momentum distribution of the gas as a function of barrier strength and particle number. With increasing barrier height we find that the ground state occupation in a diagonal basis diverges from the $\sqrt N$ behavior that is expected for the case of a simple harmonic trap. In fact, the scaling of the occupation number depends on whether one has an even or odd number of particles. Since this quantity is a measure of the coherence of our sample we show how the odd-even effect manifests itself in both the momentum distribution of the Bose gas and interference fringe visibility during free temporal evolution.

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