Dilute Bose gases interacting via power-law potentials

Abstract

Neutral atoms interact through a van der Waals potential which asymptotically falls off as r^{-6}. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise that depend on the characteristic length of the van der Waals potential. We parameterize these corrections by analyzing the energies of two- and few-atom systems under external harmonic confinement, obtained by numerically and analytically solving the Schrodinger equation. We generalize our results to particles interacting through a longer-ranged potential which asymptotically falls off as r^{-4}.Comment: 7 pages, 4 figure

Ultracold atoms in quasi-one-dimensional traps: A step beyond the Lieb-Liniger model

“…which leads to much better agreement with numerical calculations in which the Schrödinger equation was solved with a model potential and compared to the constant pseudopotential ( 5) predictions [23,25,[35][36][37][38]. This is equivalent to replacing the scattering length by its energy-dependent generalization…”

Scattering length for Lennard-Jones potentials

“…There are, however, particular forms of potentials whose scattering length is susceptible of being computed algebraically. Examples are the hard-core potential with a r −n tail [2,3,4,5], and the potentials discussed by Pade [6,7]. These, besides of being analytical at any distance, are able to reproduce the general trend of experimental data.…”

Studies of a single component Fermi gas near a p-wave resonance with the lowest order constrained variational method

“…where V is volume of the system, k F is the Fermi momentum and the density is n = k 3 F /6π 2 . From the above normalization condition, we could see the difference between the p-wave case and the s-wave case for the LOCV method [39,43]. For any paired particles in the p-wave case, the relative momentum is non-zero while the relative momentum is zero for the s-wave case.…”

“…The LOCV method has the advantage that it is much simpler in numerical calculation. The energy per particle for the Bose and the two-component Fermi system with higher partial waves is also obtained with the LOCV method although p-wave calculation is unphysical because the trial wave function does not obey the correct statistical properties of identical particles [43].…”