Efficient three-body calculations with a two-body mapped grid method

Abstract

We investigate the prospects of combining a standard momentum space approach for ultracold three-body scattering with efficient coordinate space schemes to solve the underlying two-body problem. In many of those schemes the two-body problem is numerically restricted up to a finite interparticle distance $r_{\mathrm{b}}$. We analyze effects of this two-body restriction on the two- and three-body level using pairwise square-well potentials that allow for analytic two-body solutions and more realistic Lennard-Jones van der Waals potentials to model atomic interactions. We find that the two-body $t$-operator converges exponentially in $r_{\mathrm{b}}$ for the square-well interaction. Setting $r_{\mathrm{b}}$ to 2000 times the range of the interaction, the three-body recombination rate can be determined accurately up to a few percent when the magnitude of the scattering length is small compared to $r_{\mathrm{b}}$, while the position of the lowest Efimov features is accurate up to the percent level. In addition we find that with the introduction of a momentum cut-off, it is possible to determine the three-body parameter in good approximation even for deep van der Waals potentials.

References in corpus (31)

• Feshbach Resonances in Ultracold Gases
• Universality in Few-body Systems with Large Scattering Length
• Evidence for Efimov quantum states in an ultracold gas of cesium atoms
• Efimov Physics: a review
• Observation of an Efimov spectrum in an atomic system
• Universality in Three- and Four-Body Bound States of Ultracold Atoms
• Contact Measurements on Atomic BEC
• Universal few-body physics and cluster formation
• Three-body recombination in Bose gases with large scattering length
• Observation of universality in ultracold 7Li three-body recombination
• Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium
• Origin of the Three-body Parameter Universality in Efimov Physics
• Three-body recombination into deep bound states in a Bose gas with large scattering length
• Observation of the Second Triatomic Resonance in Efimov's Scenario
• Efimov Resonances in Ultracold Quantum Gases
• Universality of the three-body Efimov parameter at narrow Feshbach resonances
• Nuclear-spin-independent short-range three-body physics in ultracold atoms
• The Dilute Bose-Einstein Condensate with Large Scattering Length
• Microscopic Origin and Universality Classes of the Efimov Three-Body Parameter
• Few-body physics in resonantly interacting ultracold quantum gases
• Physical Origin of the Universal Three-body Parameter in Atomic Efimov Physics
• Excited Thomas-Efimov levels in ultracold gases
• Enhanced Dimer Relaxation in an Atomic/Molecular BEC
• Precision Test of the Limits to Universality in Few-Body Physics
• Three-Body Recombination of Identical Bosons with a Large Positive Scattering Length at Nonzero Temperature
• Efimov-van-der-Waals universality for ultracold atoms with positive scattering lengths
• Van der Waals universality near a quantum tricritical point
• Collisional relaxation of Feshbach molecules and three-body recombination in 87Rb Bose-Einstein condensates
• Finite-range effects in Efimov physics beyond the separable approximation
• Scattering hypervolume for ultracold bosons from weak to strong interactions
• Quantum unbinding near a zero temperature liquid-gas transition

Cited by in corpus (7)

• Three-body recombination in physical chemistry
• Multichannel effects in the Efimov regime from broad to narrow Feshbach resonances
• Strong spin-exchange recombination of three weakly interacting ${}^7$Li atoms
• Efimovian three-body potential from broad to narrow Feshbach resonances
• Emergent inflation of the Efimov spectrum under three-body spin-exchange interactions
• Three-body spin mixing in spin-1 Bose-Einstein condensates
• Accurate simulation of Efimov physics in ultracold atomic gases with realistic three-body multichannel interactions