Model for investigating quantum reflection and quantum coherence in ultracold molecular collisions

We present a simple model used for investigating the quantum reflection and quantum coherence in ultracold molecular collisions. Analytical expressions of reflection and transmission coefficients, short-range S matrix, and transition matrix T are derived for the hard-core plus inverse power potentials in the vicinity of the threshold. The effect of the quantum reflection and coherence on the loss rate depends on the scattering length and short-range loss parameter. The quantum coherence results from the phase difference theta between reflection paths. As an applied example, we calculate the loss rate of (NaRb)-Na-23-Rb-87 molecules in the ultracold (NaRb)-Na-23-Rb-87-(NaRb)-Na-23-Rb-87 collision. We can well interpret the experimental results of the ultracold (NaRb)-Na-23-Rb-87 molecular collision [Ye et al., Sci. Adv. 4, eaaq0083 (2018)]. It is found that the quantum coherence has a significant influence on the loss rate of (NaRb)-Na-23-Rb-87 molecules in ultracold molecule-molecule collisions.