Wave-packet dynamical analysis of ultracold scattering in cylindrical waveguides

Abstract

A wave-packet propagation method is developed and applied to investigate the quantum dynamics of scattering processes of identical and distinguishable atoms in harmonic waveguides. The quantum dynamics of the confinement-induced resonances ͑CIRs͒ for ultracold collisions of identical particles, s-wave CIRs for bosons and p-wave CIRs for fermions, is explored in detail. Our multigrid approach allows us to fully take into account the coupling between the center-of-mass ͑c.m.͒ and relative motions in the case of distinguishable atoms. The latter includes, in particular, s-and p-partial-wave mixing, caused by the confining trap, which acts differently on the different atomic species. Specifically, we explore in detail the recently discovered ͓J. I. Kim, V. S. Melezhik, and P. Schmelcher, Phys. Rev. Lett. 97, 193203 ͑2006͔͒ dual CIR, which is based on a destructive interference mechanism leading to complete transmission in the waveguide, although the corresponding scattering in free space exhibits strong s-and p-wave scattering.

Shifts and widths of Feshbach resonances in atomic waveguides

“…CIRs have also been extensively studied e.g. in the context of three-body [10,11], and four-body [12] scattering in confining traps, fermionic p-wave scattering [13], distinguishable atom scattering [7,[14][15][16] or multichannel scattering [8,17,18] in atomic waiveguides. Two novel effects were predicted for distinguishable atoms: the so-called dual CIR yield- * saeidian@iasbs.ac.ir † melezhik@theor.jinr.ru ‡ peter.schmelcher@physnet.uni-hamburg.de ing a complete suppression of quantum scattering [14], and the resonant molecule formation in tight waveguides [16].…”

Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps

“…To overcome this difficulty, we have suggested [18,19] to use the basis of the orthogonalized combinations of the spherical harmonics on the two-dimensional grid over θ and φ variables. It turned out that this idea was very efficient for the time-dependent Schrödinger equation with three [18][19][20][21][22][23][24] and four [1,4,25,26] nonseparable spatial variables. Especially productive it was for the quantitative description of the ultracold pair atomic collisions in confined geometry of harmonic traps (low-dimensional few-body systems) [1,2,4,9,[25][26][27].…”

“…Actually, the conventional few-body theory is no longer valid here and the development of a low-dimensional theory, including the influence of the confinement is needed. 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]. The last effect was recently confirmed in a Heidelberg experiment [5].…”

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.…”