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 ${}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}$ molecules in the ultracold ${}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}-{}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}$ collision. We can well interpret the experimental results of the ultracold ${}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}$ 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 ${}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}$ molecules in ultracold molecule-molecule collisions.

The investigation of ultracold atomic or molecular collision is important for us to understand the essence of a chemical reaction. We present a simple analytical model of arbitrary-order partial-wave scatterings for ultracold molecular collision in the threshold regime. The threshold formulas of the transmission and reflection coefficients are given. For high-partial-wave collision, 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 molecular collisions. Moreover, we find a method to fit the loss parameter from the experimental data of ultracold bosonic molecular collision. As an applied example, we calculate the thermally average loss rate for the ultracold ${}^{87}\mathrm{Rb}{}^{133}\mathrm{Cs}+{}^{87}\mathrm{Rb}{}^{133}\mathrm{Cs}$ collision, our results are consistent with the recent experimental and theoretical results of Gregory et al. [ Nat. Commun. 10, 3104 (2019)].

We demonstrate that final states of ultracold molecules by scattering with atoms can be selectively produced using dynamic magnetic fields of multiple frequencies. We develop a multifrequency Floquet coupled channel method to study the channel selection by dynamic magnetic field control, which can be interpreted by a generalized quantum Zeno effect for the selected scattering channels. In particular, we use an atom-molecule spin-flip scattering to show that the transition to certain final states of the molecules in the inelastic scattering can be suppressed by engineered coupling between the Floquet states.

We investigate theoretically the formation of ultracold ground-state CsYb molecules on the lowest vibrational level via the Feshbach-optimized photoassociation process. Three s-wave Feshbach resonances of CsYb are found. The probability density of the scattering state in the short-range internuclear distance is significantly enhanced near the resonance positions. The population transfer efficiency reaches its maximum when the pulse duration equals half a period of the Rabi oscillation. By using the optimized laser parameters including the peak intensity and detuning, the final population of the lowest vibrational level of the ground electronic state reaches order of 10 ⁻¹ in the four-laser scheme.