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

Three ultracold fermions in a two-dimensional anisotropic harmonic confinement

“…Furthermore, in the previous work [43], we obtained the behavior of 0 ; , 2D ( ) r   in the short-range limit, i.e.…”

“…Due to the above reasons, theoretical calculations for few-body problems of ultracold atoms have attracted much attention. For confined atoms, so far people have obtained analytical solutions of two-body energy spectra for the systems in various harmonic confinements with arbitrary dimensions and anisotropicity [39][40][41][42][43]. The three-body energy spectra have also been derived for the ultracold atoms in a two-dimensional (2D) [44] or 3D [45] isotropic harmonic confinement, or a 3D axial symmetric anisotropic harmonic confinement [2].…”

“…The eigen-energies of these three atoms are calculated as functions of a 2D and the trapping frequencies in the two spatial directions. Our approach is based on the analytical solution of the corresponding two-body problem, which was obtained in our previous work [43], as well as the method of [2] for the construction of the transcendental equation for the three-body eigen-energy with the solution of the two-body problem. Our results can be used for the study of many-body, or few-body physics of 2D ultracold gases, e.g.…”

Quantum Register of Fermion Pairs

“…The energy spectrum of two identical atoms in a 3D, anisotropic harmonic trap interacting via a delta function potential can be calculated exactly, given the 3D scattering length and the harmonic trap frequencies 40,74 . The trap frequencies ω x /2π=96.84(4) kHz, ω y /2π=96.55(4) kHz, and ω z /2π=25.09(4) kHz are measured via lattice intensity modulation spectroscopy.…”