Achieving one-dimensionality with attractive fermions

TL;DR

This paper evaluates the accuracy of effective one-dimensional theories for ultracold fermionic atoms in quantum wires, deriving a many-body Hamiltonian and analyzing beyond-mean-field corrections to understand their validity.

Contribution

It derives a comprehensive many-body effective Hamiltonian for ultracold fermions in 1D traps, including corrections from virtual excitations and finite-range effects.

Findings

Finite-range corrections are larger than three-body interactions due to Pauli principle.

Effective 1D theory accurately describes the ground state over a wide range of parameters.

Beyond-mean-field corrections are significant for understanding system energetics.

Abstract

In this article we discuss the accuracy of effective one-dimensional theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive within a fully many-body approach the effective Hamiltonian describing this class of systems and we calculate the beyond-mean field corrections to the energy of the ground state arising from virtual transitions towards excited state of the confining potential. We find that, due to the Pauli principle, effective finite-range corrections are one of magnitude larger than effective three-body interactions.By comparing to exact solutions of the purely 1D problem, we conclude that a 1D effective theory provides a good description of the ground state of the system for a rather large range of interaction parameters.