Crossover between few and many fermions in a harmonic trap

TL;DR

This paper investigates the transition from few to many fermions in a one-dimensional harmonic trap using the coupled cluster method, providing insights into energy, pairing, and density properties across different system sizes.

Contribution

It demonstrates the effectiveness of the coupled cluster method in studying large fermionic systems and maps the crossover from few to many-body regimes in a harmonic trap.

Findings

Energy converges rapidly to many-body results across interaction strengths.

More particles are needed to observe non-analytic pairing gap behavior.

Pronounced even-odd oscillations diminish with increasing particle number.

Abstract

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the non-analytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.