Two-component few-fermion mixtures in a one-dimensional trap: numerical versus analytical approach

TL;DR

This paper investigates few-fermion mixtures in a one-dimensional trap, comparing numerical MCTDH results with an analytical pair wave-function approach across different population imbalances and interaction strengths, revealing detailed correlation and density behaviors.

Contribution

It extends the MCTDH method to few-fermion systems and generalizes a bosonic pair wave-function Ansatz to fermionic mixtures, providing a comprehensive analysis of interaction effects.

Findings

Density profiles show splitting into peaks with increasing interaction.

Correlation properties change significantly from weak to strong coupling.

Numerical and analytical results agree well across the interaction spectrum.

Abstract

We explore a few-fermion mixture consisting of two components which are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi-sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multi-configurational time-dependent Hartree (MCTDH) method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our Ansatz for a correlated pair wave-function proposed in [1] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single impurity atom shows rich behaviour of the energy and density as we approach fermionization, and is directly connected to recent experiments [2-4].