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arXiv:1802.02010 · Few-Body Systems

Effects of Interaction Imbalance in a Strongly Repulsive One-Dimensional Bose Gas

R. E. Barfknecht, Angela Foerster, Nikolaj Thomas Zinner

Published Mar 5, 2018• 8 citations
arXivHTMLPDF
DOI
10.1007/s00601-018-1352-4

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The behavior of a one-dimensional isotropic Heisenberg antiferromagnet of arbitrary spin in a strong magnetic field is studied in terms of an equivalent Bose-gas problem. The cases of spin 1/2 and classical spins are described by different limits of the ``Bose gas with repulsion'' model. The square-root dependence of magnetization on field is obtained in both cases, but in the quantum case one should use a properly defined effective-interaction constant, while in the classical case the result may be obtaind with a ``bare'' interaction. We find in addition that the region of linear behavior of the magnetization for classical spins is also covered partially by the Bose-gas approximation.
The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform one-dimensional Bose gas with repulsive contact interactions at finite temperatures. Long-, medium-, and short-range effects are investigated. The results span the entire range of physical regimes from ideal gas to strongly interacting and from zero temperature to high temperature (Gross-Pitaevskii) and strongly interacting (Tonks-Girardeau) gases. We present perturbative analytic methods, available at strong and weak couplings, and first-principles numerical results using imaginary time simulations with the gauge-PPP representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching.
We use a semiclassical approximation to investigate density variations and dipole oscillations of an interacting three-component normal Fermi gas in a harmonic trap. We consider both attractive and repulsive interactions between different pairs of fermions and study the effect of population imbalance on densities. We find that the density profiles significantly deviate from those of non-interacting profiles and extremely sensitive to interactions and population imbalance. Unlike for a two-component Fermi system, we find density imbalance even for balanced populations. For some range of parameters, one component completely repels from the trap center giving rise a donut shape density profile. Further, we find that the in-phase dipole oscillation frequency is consistent with Kohn's theorem and other two dipole mode frequencies are strongly effected by the interactions and the number of atoms in the harmonic trap.