Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas

Abstract

Using exact Bethe ansatz (BA) solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated through exact results of the excitation spectrum, the effective mass, binding energy and kinetic energy. Furthermore, a clear distinction between the polaron and molecule is conceived by the probability distribution, single particle reduced density matrix and density-density correlations, which are calculated directly from the Bethe ansatz wave function. Such a polaron-molecule crossover presents a universal nature of an impurity immersed into a fermionic medium with an attraction in one dimension.

arXiv comment11 pages, 7 figures

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• Universal many-body response of heavy impurities coupled to a Fermi sea
• Repulsive Fermi Polarons and Their Induced Interactions in Binary Mixtures of Ultracold Atoms
• In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas
• Hartree-Fock treatment of Fermi polarons using the Lee-Low-Pine transformation
• Medium-induced bosonic clusters in a Bose-Fermi mixture: Towards simulating cluster formations in neutron-rich matter
• Highly polarized one-dimensional Fermi gases near a narrow $p-$wave resonance