Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases

Abstract

We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The eigenfunctions are constructed from the wave functions of non-interacting spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave functions of distinguishable spins. We show that the spinor bosons behave like a compound of non-interacting spinless fermions and non-interacting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigenstates depends on the symmetry of the spin function. Furthermore, we discuss the splitting of the ground state multiplet in the regime of large but finite repulsion.

Revised to discuss large but finite interactions

References in corpus (8)

• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Ultracold Few-Boson Systems in a Double-Well Trap
• Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Correlations in Ultracold Trapped Few-Boson Systems: Transition from Condensation to Fermionization
• Ferromagnetic behaviour in the strongly interacting two-component Bose gas
• Ground-state properties of hard core bosons in one-dimensional harmonic traps
• Ramsey interferometry with a two-level Tonks-Girardeau gas

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