Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas

TL;DR

This study numerically explores how fermionic impurities form bound states and polarons in a one-dimensional Bose gas, revealing spin-dependent pairing behaviors and effective mass changes through advanced DMRG calculations.

Contribution

It provides new insights into impurity pairing and polaron formation in 1D Bose gases, highlighting spin-dependent effects and the role of interaction strength.

Findings

Bipolarons form for opposite spins at any impurity-bath coupling.

Binding energy approaches that of a single polaron in strong coupling.

Bipolarons only emerge beyond a critical interaction strength for same spins.

Abstract

We investigate numerically the problem of few (one, two) noninteracting spin$-1/2$ fermions in a shallow harmonic trap coupled via contact repulsive interactions to a uniform one-dimensional bath of lattice bosons, described by the Bose-Hubbard model. Through extensive density-matrix renormalization group calculations, we extract the binding energy and the effective mass of quasiparticles, including dressed impurities (polarons) and their two-body bound states (bipolarons), emerging from the effective non-local Casimir interaction between the impurities. We show that the mixture exhibits rather different pairing behaviors depending on the singlet \textit{vs}.~triplet spin state configurations of the two fermions. For opposite spin states, bipolarons are found for any finite value of the impurity-bath coupling. In particular, in the strong coupling regime their binding energy reduces to that of a single polaron, provided the boson-boson repulsion is not too weak. For equal spin states, we show that bipolarons emerge only beyond a critical strength of the Bose-Fermi interaction and their effective mass grows rapidly approaching the strong coupling regime.