Quasiclassical method for calculating the density of states of ultracold collision complexes

Abstract

We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, N -atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the K 2 -Rb and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.124 µK −1 , with an associated Rice-Ramsperger-Kassel-Marcus (RRKM) sticking time of 6.0 µs. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies, and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We estimate dispersion coefficients and collision rates between molecules and complexes. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments. * gerritg@theochem.ru.nl arXiv:1905.06691v2 [cond-mat.quant-gas]

Photoinduced Two-Body Loss of Ultracold Molecules

“…Mayle et al obtain the RRKM sticking time using multichannel quantum defect theory (MQDT) [ [25,26], which treats the long range fully quantum mechanically but uses a simplified short range, parametrized by the DOS. However, in the accompanying paper [28] we show that there was an error in the DOS calculation, leading to sticking times of 2 to 3 orders of magnitude too large. A quasiclassical equation to accurately calculate the DOS for arbitrary potentials is found…”

“…These calculations result in a DOS of 0.37 μK −1 (for J ¼ 1) and a sticking time of about 18 μs. We showed that this lifetime is not long enough for complex-diatom collisions to explain the experimental losses [28].…”

“…The complex has D ¼ 6 internal degrees of freedom. The constant C Nm , parity factor g NJp , and geometry factor GðqÞ are defined in the accompanying paper [28]. The factor g NJp ¼ 1=2 for collisions of heteronuclear diatoms.…”

“…We include both the laser excitation loss mechanism and sticking-amplified three-body loss with a rate of 1.1 × 10 −10 cm −3 s −1 , as described in Ref. [28]. The estimated lifetime of the complex with respect to complex-molecule collisions τ 3b ¼ 1=½nð0Þk 3b , where nð0Þ is the initial molecular density and k 3b the molecule-complex collision rate.…”

Loss of Ultracold Rb87Cs133 Molecules via Optical Excitation of Long-Lived Two-Body Collision Complexes

“…Christianen et al predict a lifetime for the (RbCs) 2 complex of 0.253 ms [50]. Their prediction is extrapolated from a detailed calculation for (NaK) 2 using approximate scaling laws.…”