Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement

• URL: http://arxiv.org/abs/2002.02168v4
• Date: Wed, 19 Feb 2020 14:26:14 GMT
• Title: Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement
• Authors: Yue Chen, Da-Wu Xiao, Ren Zhang and Peng Zhang
• Abstract summary: We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the equation J_3D(E) = 1/a_3D (J_2D(E) = ln a_2D) for the eigen-energy E of this system in the 3D (2D) case, with a_3D and a_2D being the corresponding s-wave scattering lengths.
• Score: 12.864072516318716
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the algebraic equation J_{3D}(E) = 1/a_{3D} (J_{2D}(E) = ln a_{2D}) for the eigen-energy E of this system in the 3D (2D) case, with a_{3D} and a_{2D} being the corresponding s-wave scattering lengths, and provide the analytical expressions of the functions J_{3D}(E) and J_{2D}(E). In previous researches 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. Liang and C. Zhang, Phys. Scr. 77, 025302 (2008)). Our results in this work are applicable for arbitrary eigen-energy of this system, and can be used for the studies of dynamics and thermal-dynamics of interacting ultracold atoms in this trap, e.g., the calculation of the 2nd 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.

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