Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Scattering of Molecules

Abstract

Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.

Determination of CaOH and CaOCH3 vibrational branching ratios for direct laser cooling and trapping

“…Release of as little as 100 nK of additional kinetic energy into the motion of dissociation products has been achieved with ultracold Sr 2 molecules [76], and an efficient pathway for SrOH zero-kinetic-energy dissociation is currently being developed using ab initio molecular potentials [77]. Moreover, modern theoretical approaches to molecular quantum scattering calculations are reaching the regime of larger polyatomic molecules [78] and, therefore, experimental results on collisions would play a crucial role in further developing the field.…”

Numerical solution of time-dependent three-particle Faddeev equations: Calculation of rearrangement S matrices

“…Differential form of Faddeev equations in coordinate space or Faddeev-AGS integral equations in momentum space has been the usual tool to study the three-body problems in the context of nuclear physics [1][2][3]. During the last two decades, however, the time-dependent wave-packet (TDWP) approach has emerged as a viable alternative to time-independent approach, especially for reactive scattering of few-atom systems in chemical physics [4][5][6][7]. For few-body problems in the context of nuclear physics, although some earlier explorations [8][9][10][11][12][13] of the time-dependent approach have been made, it has not so far attracted sufficient interest.…”

“…The time-dependent approach is usually implemented in the form of numerical time evolution of a given initial wave packet in coordinate space or momentum space. TD approaches to reactive scattering in the context of chemical physics are usually formulated in coordinate space [4][5][6][7]. For few-atom problems within chemical physics, the TDWP approach, compared to the time independent methods, scales more favorably with respect to number of grid points and/or basis functions used to discretize the spatial degrees of freedom.…”

“…For few-atom problems within chemical physics, the TDWP approach, compared to the time independent methods, scales more favorably with respect to number of grid points and/or basis functions used to discretize the spatial degrees of freedom. As a result, the TDWP approach to scattering has in fact become a real competitor to time-independent methods for such systems [4,5]. The possibility of using momentum space in time-dependent scattering calculations was explored in Refs.…”

“…This spatial discretization is achieved by requiring that the TDSE is satisfied, in a weighted-residual sense, either on a set of grid points, or on an approximation space. Time propagation may then be done by a number of well-known algorithms [4][5][6][7]. The specification of the approximation space, or of the discretization grid, entails, first, the selection of an appropriate set of coordinates (or momenta).…”