Theoretical Investigation Of Ultracold Bose Molecular Scattering And Suppressing Reactivity In Degenerate Fermi Molecular Gas

Ultracold molecules provide an important platform for investigation of quantum computation,quantum simulators,precision mearurement and ultracold chemistry.The quantum effect of molecule scattering is obvious at ultra-low temperature.It is necessary for researchers to understand properties of ultracold Bose and Fermi molecule scattering from the basic principles of quantum mechanics.In this thesis,three theoretical models are presented in order to study the quantum scattering process of ultracold Bose and Fermi molecules.Its main contents are summarized as follows:A theoretical model is presented for investigating the quantum reflection and quantum coherence in ultracold Bose molecular s-wave scattering.Analytical expressions of shortrange S matrix,transition matrix T,reflection and transmission coefficients are derived for the hard core plus van der Waals potential in the vicinity of threshold.The formula of phase difference between different reflection paths is given.The quantum coherent effect between different reflection paths is discussed.We find that the effect of quantum coherence on the loss rate K of Bose molecule depends on the scattering length a and short-range loss parameter y.As an applied example of the theoretical model,we calculate the loss rate K of ultracold 23Na87Rb molecules in the scattering process.It is found that the quantum coherence has a significant influence on the loss rate of 23Na87Rb molecules.We interpret the experimental results of the ultracold 23Na87Rb molecular scattering.An analytical model is presented to study arbitrary-order partial-wave scattering,especially high-partial-wave scattering for ultracold molecules.The threshold formulas of the transmission and reflection coefficients for arbitrary-order partial-wave scattering are given.For high-partial-wave scattering,shape resonance will take place because of the existence of a centrifugal barrier.We investigate the effect of shape resonance and short-range interaction on high-partial-wave scattering of ultracold molecules.The calculation results of partial-wave scattering near threshold by using the analytical model consistent with those by using the numerical procedure of the quantum defect theory.Moreover,we find a method to fit the loss parameter y for ultracold Bose molecular scattering from the experimental data.As an applied example,we calculate the thermally average loss rate K for ultracold 87Rb133Cs molecule.Our results agree with the experimental observation and numerical results.On the premise of ensuring accuracy,the use of analytical models greatly reduces the amount of computation.A theoretical model is presented for describing the suppressing reactivity of ultracold Fermi molecular gas in degenerate regime by introducing the statistical potential.The statistical potential describes the spatial correlation between particles,and can be obtained by calculating diagonal elements of the density matrix of the system.The formula of the statistical potential of non-ideal Fermi molecular gas is derived.The magnitude of the statistical potential is related to the temperature of gas and the interparticle spacing.We interpret the experiment of ultracold 40K87Rb molecule in degenerate regime by using our theoretical model,and simulate quantitatively the reaction rate observed in experiment.The p-wave scattering volume of 40K87Rb molecules is fitted according to experimental data.The effect of the statistical correlation between molecules in ultracold Fermi molecular gas on properties of molecular scattering is discussed.