arXiv:0803.1341 · Physica Scripta

Two ultracold atoms in a completely anisotropic trap

Jun-Jun Liang, Chao Zhang

Published Feb 1, 2008• 14 citations

Abstract

As a limiting case of ultracold atoms trapped in deep optical lattices, we consider two interacting atoms trapped in a general anisotropic harmonic oscillator potential, and obtain exact solutions of the Schrödinger equation for this system. The energy spectra for different geometries of the trapping potential are compared.

DOI: 10.1088/0031-8949/77/02/025302

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arXiv:0803.1341 · Physica Scripta

Two ultracold atoms in a completely anisotropic trap

Jun-Jun Liang, Chao Zhang

Published Feb 1, 2008• 14 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0031-8949/77/02/025302

Related papers

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arXiv:quant-ph/0410163Physical Review AMay 23, 200579 citations

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We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the transcendental equation

{J}_{3\mathrm{D}}(E)=1/{a}_{3\mathrm{D}}

(

{J}_{2\mathrm{D}}(E)=ln{a}_{2\mathrm{D}}

) for the eigenenergy

E

of this system in the 3D (2D) case, with

{a}_{3\mathrm{D}}

and

{a}_{2\mathrm{D}}

being the corresponding

s

-wave scattering lengths, and provide the analytical expressions of the functions

{J}_{3\mathrm{D}}(E)

and

{J}_{2\mathrm{D}}(E)

. In previous research, this type of equation was obtained for spherically or axially symmetric harmonic traps [T. Busch et al., Found. Phys. 28, 549 (1998); Z. Idziaszek and T. Calarco, Phys. Rev. A 74, 022712 (2006)]. However, for our cases with a completely anisotropic trap, only the equation for the ground-state energy of some cases has been derived [J.-J. Liang and C. Zhang, Phys. Scr. 77, 025302 (2008)]. Our results in this work are applicable for arbitrary eigenenergy of this system and can be used for the study of dynamics and thermal dynamics of interacting ultracold atoms in this trap, e.g., the calculation of the second virial coefficient or the evolution of two-body wave functions. In addition, our approach for the derivation of the above equations can also be used for other two-body problems of ultracold atoms.