Theoretical Study On Collision Characteristics Of Ultracold Three-body System

Quantum three-body system,as the simplest few body system,is the starting point for the study of quantum few body problems.The novel quantum phenomenon in few body system,Efimov effect,was proposed by Russian nuclear physicist Efimov in 1970.It has attracted many scholars’ research with its unique discrete scale invariance and universality.Magnetic Feshbach resonance technology and ultracold atom and molecule technology provides an ideal platform for the experimental study of Efimov effect.The development of these technologies not only confirms the Efimov effect in homonuclear Bose system and heteronuclear system,but also promotes exploration of the universal behavior in Efimov effect.The collision between ultracold atoms and molecules is a significant research direction in atomic and molecular physics.The three-body recombination,atomic and molecular vibrational relaxation and collision induced dissociation are important factors affecting gas stability and the main reason for the loss of the ultracold atoms.At the same time,the loss of particle is also the considerable experimental observables.Therefore,the theoretical calculation of physical observables in ultracold three-body collision such as the three-body recombination rate,atom-dimer scattering length and the vibrational relaxation rate is particularly important.They can be combined with the particle number loss information in the experiment to reveal the novel quantum effects in ultracold atoms and molecules.In this thesis,a program package for accurately solving the binding,resonance and scattering characteristics of ultracold three-body system is developed by combining the slow variable discretization method,the hyperspherical adiabatic approximation and the R-matrix propagation method in the framework of hyperspherical coordinates.With the model potential including finite range effect and van der Waals asymptotic behavior,the universality of three-body parameters in heteronuclear Efimov effect,the characteristics of three-body recombination around d-wave resonant and Efimov effect in non-zero angular momentum system are carried out.The main results are as follows:(1)The effects of the attractive homonuclear interaction on the Efimov resonance position in the three-body systems consisting of two heavy bosons and one other atom is studied.The universal behavior of the first Efimov resonance position determined by the mass ratio of light and heavy atoms and van der Waals interaction is obtained.A universal formula is given which can predict the position of Efimov resonance with the mass ratio,scattering length between homonuclear atoms and van der Waals interaction as inputting parameters.This formula can effectively predict the first Efimov resonance position in heteronuclear systems with mass ratio between 2-30,and provides a theoretical range for experiments exploring Efimov effects in unknown system.(2)We have studied the three-body recombination characteristics of heteronuclear three-body system with d-wave resonant interactions.The mechanism of three-body recombination enhancement peaks in this system is revealed.Our result supports the existing prediction that there is a universal three-body resonant state associated with the d-wave resonant interaction in the homonuclear system maintained by the d-wave resonant interaction.It is also proved that whether the three-body resonant state appears in the heteronuclear three-body system depends on the details of the interaction between the homonuclear atoms.Our work has implications for the experimental study of threebody states in ultracold quantum gas mixtures dominated by d-wave resonance.(3)In the three-body system composed of two identical fermions and one other atom with the total angular momentum and parity of JΠ=1-,the van der Waals universality of the first Efimov resonance is studied.At the same time,the influence of the p-wave interaction between two identical fermions on the Efimov resonance is considered.It is found that the absolute value of the two-body scattering length producing the first Efimov resonance is inversely proportional to the mass ratio of the system,and decreases with the enhancement of the p-wave interaction between Fermi.With the increasing of mass ratio,the influence of Fermi interaction on Efimov resonance decreases gradually.