Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment

Tomasz Grining,Robert Moszynski,Pietro Massignan,Monika Musiał,Michał Tomza,Michał Lesiuk,Maciej Lewenstein,Michał Przybytek

doi:10.1088/1367-2630/17/11/115001

Abstract

We employ ab initio methods of quantum chemistry to investigate spin-1/2 fermions interacting via a two-body contact potential in a one-dimensional harmonic trap. The convergence of the total energy with the size of the one-particle basis set is analytically investigated for the two-body problem and the same form of the convergence formula is numerically confirmed to be valid for the many-body case. Benchmark calculations for two to six fermions with the full configuration interaction method equivalent to the exact diagonalization approach, and the coupled cluster (CC) method including single, double, triple, and quadruple excitations are presented. The convergence of the correlation energy with the level of excitations included in the CC model is analyzed. The range of the interaction strength for which single-reference CC methods work is examined. Next, the CC method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed to study a two-component Fermi gas composed of 6–80 atoms in a one-dimensional harmonic trap. The density profiles of trapped atomic clouds are also reported. Finally, a comparison with experimental results for few-fermion systems is presented. Upcoming possible applications and extensions of the presented approach are discussed.

Highlights

Ultracold gases are highly controllable systems ideal for investigating different phenomena of quantum manybody physics [1,2,3,4,5,6]
It turned out that the CCSD(T) method is very accurate for many properties of atoms and molecules and, as for it is considered as the golden standard of quantum chemistry. As we show this method can be applied with success to the system of ultracold atoms in a one-dimensional harmonic trap interacting via a short-range contact type potential
There we show the absolute error with respect to the complete basis set limit in the ground state energy for the 2 + 2 and 3 + 3 systems (N + N means N atoms with the spin projection 1/2, and N atom with the spin projection -1 2) as a function of the number of one-particle basis functions for several interaction strengths obtained with the full configuration interaction (FCI) method, as well as the error plotted as a function of nb according to equation (20)

Summary

26 October 2015

We employ ab initio methods of quantum chemistry to investigate spin-1/2 fermions interacting via a and DOI. Two-body contact potential in a one-dimensional harmonic trap. Benchmark calculations for two to six fermions with the full configuration interaction method equivalent to the exact diagonalization approach, and the coupled cluster (CC) method including single, double, triple, and quadruple excitations are presented. The convergence of the correlation energy with the level of excitations included in the CC model is analyzed. The range of the interaction strength for which single-reference CC methods work is examined. The CC method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed to study a two-component. Fermi gas composed of 6–80 atoms in a one-dimensional harmonic trap. Upcoming possible applications and extensions of the presented approach are discussed

Introduction

Theoretical framework

Numerical results and discussion

Findings

Summary and conclusions