Hyperspherical approach to atom--dimer collision with the Jacobi boundary condition

一维系统中二聚体-二聚体散射的超球面分析

Hyperspherical Analysis of Dimer-Dimer Scattering in One-Dimensional Systems

本研究针对一维量子系统二聚体-二聚体散射问题，采用绝热超球面表示结合慢变量离散化方法解决数值难题，经可积区域验证有效，并在不可积区域发现散射长度共振增强新特征，为低维少体量子物理研究提供了可靠工具。

Hyperspherical asymptotics of a system of four charged particles

We present a detailed analysis of the charged four-body system in hyperspherical coordinates in the large hyperradial limit. In powers of $R^{-1}$ for any masses and charges, the adiabatic Hamiltonian is expanded to third order in the dimer-dimer limit and to first order in the particle-trimer limit.

Magnetically Controlled Exchange Process in an Ultracold Atom-Dimer Mixture

We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schrödinger equation in the adiabatic hyperspherical representat…

Three-body rf association of Efimov trimers

We present a theoretical analysis of rf association of Efimov trimers in a 2-component Bose gas with short-range interactions. Using the adiabatic hyperspherical Green's function formalism to solve the quantum 3-body problem, we obtain universal expressions for 3-body rf association rates as a function of the s-wave scattering length $a$. We find that the association rates scale as $a^{-2}$ in the limit of large $a$, and diverge as $a^3 a_{ad}^{3}$ whenever an Efimov state crosses the atom-dimer threshold (where $a_{ad}$ stands for the atom-dimer scattering length). Our calculations show that …

Correlation diagrams in collisions of three identical particles

We discuss collision of three identical particles and derive scattering selection rules from initial to final states of the particles. We use either laboratory-frame, hyperspherical, or Jacobian coordinates depending on which one is best suited to describe three different configurations of the particles: (1) three free particles, (2) a quasi-bound trimer, or (3) a dimer and a free particle. We summarize quantum numbers conserved during the collision as well as quantum numbers that are appropriate for a given configuration but may change during the scattering process. The total symmetry of the …

Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures

Few-body correlations emerging in two-dimensional harmonically trapped mixtures, are comprehensively investigated. The presence of the trap leads to the formation of atom-dimer and trap states, in addition to trimers. The Tan's contacts of these eigenstates are studied for varying interspecies scattering lengths and mass ratio, while corresponding analytical insights are provided within the adiabatic hyperspherical formalism. The two- and three-body correlations of trimer states are substantially enhanced compared to the other eigenstates. The two-body contact of the atom-dimer and trap states…