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

TL;DR

This paper uses exact Bethe ansatz solutions to demonstrate a continuous crossover from polaron to molecule states for a spin-down fermion in a one-dimensional spin-up Fermi sea, revealing universal impurity behavior.

Contribution

It provides the first exact analysis of the polaron-molecule crossover in a 1D Fermi gas using Bethe ansatz, detailing spectral and correlation properties.

Findings

Demonstrates a continuous polaron-molecule crossover with exact spectra

Calculates effective mass, binding energy, and kinetic energy across regimes

Distinguishes polaron and molecule states via density correlations

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.