Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps

V.S Melezhik,Gh Adam,J Buša,M Hnatič

doi:10.1051/epjconf/201610801008

Abstract

We discuss computational aspects of the developed mathematical models for ultracold few-body processes in atomic traps. The key element of the elaborated computational schemes is a nondirect product discrete variable representation (npDVR) we have suggested and applied to the time-dependent and stationary Schrodinger equations with a few spatial variables. It turned out that this approach is very effcient in quantitative analysis of low-dimensional ultracold few-body systems arising in confined geometry of atomic traps. The effciency of the method is demonstrated here on two examples. A brief review is also given of novel results obtained recently.

Highlights

The impressive progress in the physics of the ultracold quantum gases has demanded the elaboration of quantitative models for resonant and multichannel processes occurring in confined geometries of atomic traps
The key element of the elaborated computational schemes is a nondirect product discrete variable representation we have suggested and applied to the time-dependent and stationary Schrödinger equations with a few spatial variables
In our works we have developed computational methods [1,2,3] for pair collisions in tight atomic waveguides and have found several novel effects in its applications: the confinement-induced resonances (CIRs) in multimode regimes including effects of transverse excitations and deexcitations [2], the so-called dual CIR yielding a complete suppression of the quantum scattering [1], and resonant molecule formation with transferring energy relies to center-of-mass excitation while forming molecules [4]

Summary

Introduction

The impressive progress in the physics of the ultracold quantum gases has demanded the elaboration of quantitative models for resonant and multichannel processes occurring in confined geometries of atomic traps. In our works we have developed computational methods [1,2,3] for pair collisions in tight atomic waveguides and have found several novel effects in its applications: the confinement-induced resonances (CIRs) in multimode regimes including effects of transverse excitations and deexcitations [2], the so-called dual CIR yielding a complete suppression of the quantum scattering [1], and resonant molecule formation with transferring energy relies to center-of-mass excitation while forming molecules [4]. We have calculated the Feshbach resonance shifts and widths induced by atomic waveguides [7,8] and predicted dipolar CIRs [9]. Such a problem arises when calculating the Feshbach resonance shifts and widths induced by atomic waveguides.

Nondirect Product Discrete-Variable Representation

Splitting-up Method for 3D Time-Dependent Schrödinger Equation

Shifts and Widths of Feshbach Resonances in Atomic Waveguides

Conclusion