Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps

Vladimir S Melezhik

doi:10.1051/epjconf/201817301008

Abstract

We discuss computational aspects of the developed mathematical models for resonant processes in confined geometry of atomic and atom-ion traps. The main attention is paid to formulation in the nondirect product discrete-variable representation (npDVR) of the multichannel scattering problem with nonseparable angular part in confining traps as the boundary-value problem. Computational efficiency of this approach is demonstrated in application to atomic and atom-ion confinement-induced resonances we predicted recently.

Highlights

During the last three decades one can observe an impressive development of the physics of ultracold atoms [1] and cold ions [2]
The control of interparticle interaction is performed in quantum gases with the help of magnetic Feshbach resonances [1] which, in confined geometry of atomic traps, transform into so-cold confinement-induced resonances (CIRs) [7,8,9,10,11,12,13]
We have calculated the Feshbach resonance shifts and widths induced by atomic waveguides [11, 12] and predicted dipolar CIRs [13]

Summary

Introduction

During the last three decades one can observe an impressive development of the physics of ultracold atoms [1] and cold ions [2] Different aspects of this investigations attract big interest from the side of theoreticians and experimentalists. Experimentalists have got a chance to work here with deterministically prepared quantum systems [3] with precise control of interparticle interaction, particle states and particle number [2, 3]. It opens a possibility for quantum simulation with fully controlled few-body systems in ultracold quantum gases [4,5,6]. We have calculated the Feshbach resonance shifts and widths induced by atomic waveguides [11, 12] and predicted dipolar CIRs [13]

Methods

Results

Conclusion