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

Abstract

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.

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

References in corpus (8)

• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Ultracold Few-Boson Systems in a Double-Well Trap
• Correlations in Ultracold Trapped Few-Boson Systems: Transition from Condensation to Fermionization
• Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket
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• Dark stationary matter-waves via parity-selective evaporation in a Tonks-Girardeau gas
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Cited by in corpus (11)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Quenching small quantum gases: Genesis of the orthogonality catastrophe
• Ground state properties of ultracold trapped bosons with an immersed ionic impurity
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
• Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions
• Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches
• Binding between two-component bosons in one dimension
• Transport, atom blockade and output coupling in a Tonks-Girardeau gas
• Hard-core Bose-Fermi mixture in one-dimensional split traps