Study On The Universality In The Reaction Of ²³Na⁴⁰K Feshbach Molecules

Universality in complex system presents an important topic in physics.With the development of research on ultracold atoms,universality of different kinds,especially Efimov effect,is verified or discovered in few-body systems under very low tempera-ture.Based on the ultracold mixture of 23Na40K,in this thesis we investigate the atom-exchange reaction in the vicinity of Feshbach resonances,among which we have ob-served possible universality.We introduce the theory and construction of the new apparatus of 23Na40K ultra-cold polar molecule,including a modified control system and imaging software with user-friendly interface and great flexibility.We successfully create two-species degen-erate mixture gases and Feshbach molecules on this platform.By exploiting the overlapped Feshbach resonances and manipulating the energy difference between the reactants and products,we observe the threshold behavior of the rate coefficient as the reaction energy changes.For two different Feshbach overlaps,the behavior of rate coefficients as a function of magnetic field can be described by the same three-body parameter in the universal model,which indicates possible existence of universality.In order to analyze the reaction universality quantitatively,we try to caculate the three-body problem with weakly-bound molecules in the hyperspherical coordinate.Among the numerical challenges,we investigate the solution of weakly bound state in hyperangle when the hyperradius is large.Using simplified T-spline and heuristic mesh generation method,we are able to obtain accurate eigenvalues and wavefunctions.Our method paves the way towards solving the atom-exchange reaction for weakly bound molecules.The next research will focus on ground state molecules.Hence,we calculate the coupling strength between Feshbach molecules and excited states in the stimulated Ra-man adiabatic passage(STIRAP).Using the properties of Feshbach molecules,we pro-pose a simple method for the calculation of their overlap with wavefunctions of excited states.With the detailed results,we can identify proper Feshbach molecule states and excited states quickly and prepare the needed ground hyperfine states through the STI-RAP directly.