Density-functional theory of two-component Bose gases in one-dimensional harmonic traps

Abstract

We investigate the ground-state properties of two-component Bose gases confined in one-dimensional harmonic traps in the scheme of density-functional theory. The density-functional calculations employ a Bethe-ansatz-based local-density approximation for the correlation energy, which accounts for the correlation effect properly in the full physical regime. For the binary Bose mixture with spin-independent interaction, the homogeneous reference system is exactly solvable by the Bethe-ansatz method. Within the local-density approximation, we determine the density distribution of each component and study its evolution from Bose distributions to Fermi-like distribution with the increase in interaction. For the binary mixture of Tonks-Girardeau gases with a tunable inter-species repulsion, with a generalized Bose-Fermi transformation we show that the Bose mixture can be mapped into a two-component Fermi gas, which corresponds to exact soluble Yang-Gaudin model for the homogeneous system. Based on the ground-state energy function of the Yang-Gaudin model, the ground-state density distributions are calculated for various inter-species interactions. It is shown that with the increase in inter-species interaction, the system exhibits composite-fermionization crossover.

8 pages, 5 figures

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• Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension
• Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
• Quenching small quantum gases: Genesis of the orthogonality catastrophe
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• Solvable Model of a Generic Trapped Mixture of Interacting Bosons: Reduced Density Matrices and Proof of Bose-Einstein Condensation
• State engineering of impurities in a lattice by coupling to a Bose gas
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• Interaction induced single impurity tunneling in a binary mixture of trapped ultracold bosons
• Thermodynamics, density profiles and correlation functions of the inhomogeneous one-dimensional spinor Bose gas
• Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap
• Solvable model of a generic driven mixture of trapped Bose-Einstein condensates and properties of a many-boson Floquet state at the limit of an infinite number of particles
• Gap solitons and Bloch waves of interacting bosons in one-dimensional optical lattices: From the weak to the strong interaction limits
• Interfaces between Bose-Einstein and Tonks-Girardeau atomic gases
• The properties of Tonk-Girardeau Gas at Finite Temperature and Comparison with Polarized Free Fermions
• Gradient corrections to the local density approximation in the one-dimensional Bose gas
• The weakening of fermionization of one dimensional spinor Bose gases induced by spin-exchange interaction
• Ground State Properties of Anti-Ferromagnetic Spinor Bose gases in One Dimension
• Gap solitons of a super-Tonks-Girardeau gas in a one-dimensional periodic potential
• Fragmentation of identical and distinguishable bosons' pairs and natural geminals of a trapped bosonic mixture