# In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas

## TL;DR

This paper explores how a one-dimensional Fermi gas with two bosonic impurities can form in-medium bound states due to induced attractive interactions, with exact and effective models analyzing various interaction regimes.

## Contribution

It introduces an exactly solvable model for impurity interactions in a 1D Fermi gas and develops an effective model to study non-integrable cases with unequal masses or potentials.

## Key findings

- Attractive impurity interactions lead to in-medium bound states.
- Repulsive interactions do not produce bound states.
- Effective models agree with exact solutions for certain parameters.

## Abstract

We investigate the ground-state energy of a one-dimensional Fermi gas with two bosonic impurities. We consider spinless fermions with no fermion-fermion interactions. The fermion-impurity and impurity-impurity interactions are modelled with Dirac delta functions. First, we study the case where impurity and fermions have equal masses, and the impurity-impurity two-body interaction is identical to the fermion-impurity interaction, such that the system is solvable with the Bethe ansatz. For attractive interactions, we find that the energy of the impurity-impurity subsystem is below the energy of the bound state that exists without the Fermi gas. We interpret this as a manifestation of attractive boson-boson interactions induced by the fermionic medium, and refer to the impurity-impurity subsystem as an in-medium bound state. For repulsive interactions, we find no in-medium bound states. Second, we construct an effective model to describe these interactions, and compare its predictions to the exact solution. We use this effective model to study non-integrable systems with unequal masses and/or potentials. We discuss parameter regimes for which impurity-impurity attraction induced by the Fermi gas can lead to the formation of in-medium bound states made of bosons that repel each other in the absence of the Fermi gas.