Hard-core Bose-Fermi mixture in one-dimensional split traps

TL;DR

This paper investigates a strongly interacting 1D Bose-Fermi mixture in split traps, analyzing how barrier strength and particle number parity influence its quantum properties, revealing notable correlations across the split.

Contribution

It introduces a generalized Bose-Fermi mapping to compute the reduced density matrix and momentum distribution in split traps, highlighting effects of barrier strength and particle parity.

Findings

Secondary peaks in momentum distribution indicate strong correlations.

Barrier strength significantly affects particle distribution.

Parity of particle number influences the system's quantum correlations.

Abstract

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a hard wall trap or a harmonic oscillator trap with a tunable $\delta$-function barrier at the trap center. The mixture consists of 1D Bose gas with repulsive interactions and of 1D noninteracting spin-aligned Fermi gas, both species interacting through hard-core interactions. Using a generalized Bose-Fermi mapping, we calculated the reduced single-particle density matrix and the momentum distribution of the gas as a function of barrier strength and the parity of particle number. The secondary peaks in the momentum distribution show remarkable correlation between particles on the two sides of the split.