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

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 Fermisea 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][3][4].

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

“…One-dimensional (1D) systems are among the most widely studied problems in physics, especially due to their invaluable pedagogical properties and their more friendly manipulation of mathematical expressions both analytically and numerically, which often guide us through the understanding of interesting physical systems [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. Furthermore, 1D structures such as nanotubes and nanowires, among others, may be highly relevant in technological applications [23].…”

Three interacting atoms in a one-dimensional trap: a benchmark system for computational approaches

“…These authors investigated the dimensional crossover from a three-dimensional to a quasi one-dimensional trap but reported partial data for stricly one-dimensional fermions and no data for bosons. Other approaches for three particles in a trap in one dimension include group-theoretical [67] and geometrical analyses [68], multiconfigurational time-dependent Hartree method [63,[69][70][71], ansatz correlated wave functions [63,71], effective-interaction approaches [29,70], density functional theory [72], as well as exact results in the limit of infinite repulsion [34,73,74].…”

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

“…The experimental progress has generated great interest for few-body problems in one-dimensional geometries for both bosonic [21][22][23][24][25][26][27][28], fermionic [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], and mixed systems [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Recently, it has been shown that for strong short-range repulsive interactions a 1D two-component Fermi system in a harmonic trap exhibits strong magnetic correlations already at the three-body level [37,40].…”