Quantum States of Interacting Atoms in Quasi-One-Dimensional Ultracold Trapped Gases

Polyanna Guimarães E Miranda,André Luiz Mota,Débora Nazaré De Freitas

doi:10.4236/jmp.2018.93031

Abstract

We theoretically investigate the quantum states of a Hamiltonian model for quasi-one-dimensional ultracold trapped gases. From the ansatz given by the numerical solution of the Schrödinger equation of the system, we develop a scattering potential functional form and an approximate solution for the analytical approach of the model. We obtain the set of approximate eigenstates and eigenenergies that can be used in future improvements on the study of atomic scattering in low dimensional ultracold gases. We also show that there is a parity inversion of the ground state of the model as the interaction strength increases.

Highlights

The current ability in developing experiments in low dimensional systems has recently renewed the interest for both experimental and theoretical studies of such systems
In this paper we will turn our attention to the low energy eigenstates of the atoms in these quasi-1D traps including the scattering potential effects—a nontrivial issue, despite the simplicity of the model we will employ. The aim of such procedure is to provide a set of wave functions that can be used as a basis for the scattering wave function expansion, allowing future refinements on the results previously obtained by employing the eigenstates of the unperturbed Hamiltonian
We present both a numerical and an analytical analysis of the eigenstates and eigenenergies of a simple model for atomic scattering of ultracold atoms confined in quasi-1D optical traps

Summary

Introduction

The current ability in developing experiments in low dimensional systems has recently renewed the interest for both experimental and theoretical studies of such systems. The strength of the Huang’s potential corresponds to the theoretical representation of the tunable interaction between the atoms by Feshbach resonance [18] [19] [20] in actual experiments In these approaches, the scattering amplitude is determined by means of the expansion of the scattering wave function [8] [15] [21] into the eigenstates of the transverse unperturbed (Huang’s potential independent) Hamiltonian. In this paper we will turn our attention to the low energy eigenstates of the atoms in these quasi-1D traps including the scattering potential effects—a nontrivial issue, despite the simplicity of the model we will employ The aim of such procedure is to provide a set of wave functions that can be used as a basis for the scattering wave function expansion, allowing future refinements on the results previously obtained by employing the eigenstates of the unperturbed Hamiltonian.

The Quasi-1D Model for a Scattering Atom Confined in an Optical Trap

Numerical Results on a Discrete Lattice

Analytical Approximation—1D Solution

Analytical Approximation—Quasi-1D Solution

Conclusion