Statistical quantum mechanical approach to diatom–diatom capture dynamics and application to ultracold KRb + KRb reaction

Abstract

A general and rigorous quantum method is proposed for studying capture dynamics between two diatomic molecules in full dimensionality. By solving the time-independent Schrödinger equation with proper boundary conditions, this method is ideally suited for studying quantum dynamics of cold and ultracold reactions. To illustrate its applicability, the capture dynamics between ultracold KRb molecules is characterized in full six dimensions for the first time using a first-principles based long-range interaction potential. The calculated capture rates for collisions involving distinguishable and indistinguishable 40K87Rb molecules are in good agreement with the experiment and exhibit clear Wigner threshold behaviors. Predictions for ultracold collisions between internally excited 40K87Rb suggest minor changes in the loss rate, consistent with experimental observations in similar systems.

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

“…202,203 The application of a full-dimensional SQM method to the KRb + KRb reaction showed excellent reproduction of the experimental observations (Figure 4a), describing accurately the tunneling through the centrifugal barrier in the p-wave capture (Figure 4d). 203 This method is also able to predict loss rates for internally excited reactants (Figure 4b,c), as well as product state distributions. 204 Advances in treating the dynamics dominated by quantum effects are needed to gain further insight into the emerging field of cold chemistry.…”

Precision test of statistical dynamics with state-to-state ultracold chemistry

“…The details of the implementation for diatom-diatom systems have been published in Ref. [38]. In brief, the time-independent Schrödinger equation was solved in diatom-diatom Jacobi coordinates (R,r 1 ,r 2 ,θ 1 ,θ 2 ,φ) using the log-derivative method [55,56] with the Wentzel-Kramers-Brillouin (WKB) approximation [57] to damp the wavefunction within the capture radius.…”

“…The interaction potential was determined using a similar method as in Ref. [38]. In the calculations, only the p-wave (L reac = 1) and = −1 were considered, given the fermionic nature of the KRb reactants.…”

“…The breakdown of the state-counting model for the most near-threshold state-pair highlights the importance of considering the escape process of the products. To this end, we calculate the product escape probabilities for the remaining 56 state-pairs by explicitly following their dynamics over the long-range potential [38] (SM). The results show near unit probabilities (>0.999) for all 56, indicating a lack of any barriers or bottlenecks that impede product formation in these states.…”

Quantum spin state selectivity and magnetic tuning of ultracold chemical reactions of triplet alkali-metal dimers with alkali-metal atoms

“…using classical probabilities) [26][27][28]. Statistical (or universal) models [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] have been successfully applied to calculate the rate of ultracold chemical reactions of alkali-metal dimers [30,[32][33][34]37] and the density of states of the (KRb) 2 reaction complex [41]. However, the previous calculations have been limited to the case of zero magnetic field and did not account for electron spins, hyperfine interactions, and non-adiabatic effects, all of which we will consider in the present work.…”