Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps

Abstract

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 Schrödinger equations with a few spatial variables. It turned out that this approach is very efficient in quantitative analysis of low-dimensional ultracold few-body systems arising in confined geometry of atomic traps. The efficiency of the method is demonstrated here on two examples. A brief review is also given of novel results obtained recently.

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

“…Detailed description of this method one can find in our previous paper published in the EPJ (Web of conferences) [15].…”

“…Therefore, the conventional theory is no longer valid here and the development of the low-dimensional theory, including the influence of the confinement, is needed. In our works we have developed computational methods [9,10,14,15] for pair collisions in tight atomic waveguides and have found several novel effects in its applications: the CIRs in multimode regimes including effects of transverse excitations and deexcitations [10], the so-called dual CIR yielding a complete suppression of quantum scattering [9], and resonant molecule formation with transferring energy relies to center-of-mass excitation while forming molecules [16]. The last effect was recently confirmed in the Heidelberg experiment [3].…”

“…The matrix Y jν and its inverse (Y −1 ) ν j are defined on the grid Ω j as described in [9,10,15,24] (here one can also find the procedure of construction of the 2D angular grid Ω j and the definition of the weights λ j ).…”

Numerical Solution of the Time Dependent 3D Schrödinger Equation Describing Tunneling of Atoms from Anharmonic Traps

“…To integrate (1) we use the split-operator method the basic ideas of which have been proposed in [8] and which has been developed in [2,3,9] in connection with the solution of confined ultracold atom-atom collisions in waveguide-like traps:…”

“…Pair correlation plays a major role in quantum tunneling and there are a only few works in the context of ultracold physics which accurately take into account the interatomic interaction [1][2][3][4][5][6][7]. In the present paper, we consider a tunneling of two interacting atoms from an anharmonic optical trap.…”