Strongly interacting Bose-Fermi mixtures in one dimension

Abstract

We study one-dimensional strongly interacting Bose-Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the one-dimensional Bose-Fermi gas with equal boson-boson and boson-fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose-Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized noninteracting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose-Fermi configurations and are sensitive to the anisotropy of interactions.

11 pages, 3 figures, Version published in "Focus on Strongly Interacting Quantum Gases in One Dimension" (NJP, IOP) dedicated to Marvin D. Girardeau (1930-2015)

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• Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
• Impurity induced quantum chaos for an ultracold bosonic ensemble in a double-well
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry
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• Quantum Coherent States of Interacting Bose-Fermi Mixtures in One Dimension
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Bunching-antibunching crossover in harmonically trapped few-body Bose-Fermi mixtures
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• Local manipulation of quantum magnetism in 1D ultracold Fermi gases across narrow resonances
• Strongly Repulsive 1D Gases at Higher Branches: Spin-Charge Correlation and Coupled Spin-Chain Model