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Physical Review A

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

Yan-Peng Bai, Jing-Lun Li, Gao‐Ren Wang, Shu‐Lin Cong

Published Jul 10, 2019• 16 citations
Publisher

Abstract

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 $\ensuremath{\theta}$ between reflection paths. As an applied example, we calculate the loss rate of $^{23}\mathrm{Na}^{87}\mathrm{Rb}$ molecules in the ultracold $^{23}\mathrm{Na}^{87}\mathrm{Rb}\ensuremath{-}^{23}\mathrm{Na}^{87}\mathrm{Rb}$ 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.

DOI
10.1103/physreva.100.012705

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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 SSS matrix, and transition matrix TTT 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 \ensuremathθ\ensuremath{\theta}\ensuremathθ between reflection paths. As an applied example, we calculate the loss rate of 23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb molecules in the ultracold 23Na87Rb\ensuremath−23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}\ensuremath{-}^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb\ensuremath−23Na87Rb collision. We can well interpret the experimental results of the ultracold 23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb 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 23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb 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 87Rb133Cs+87Rb133Cs^{87}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{133}\mathrm{Cs}+^{87}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{133}\mathrm{Cs}87Rb133Cs+87Rb133Cs collision, our results are consistent with the recent experimental and theoretical results of Gregory et al. [Nat. Commun. 10, 3104 (2019)].
A simple quantum-defect model gives analytic expressions for the complex scattering length and threshold collision rates of ultracold molecules. If the probability of reaction in the short-range part of the collision is high, the model gives universal rate constants for s- and p-wave collisions that are independent of short-range dynamics. This model explains the magnitudes of the recently measured rate constants for collisions of two ultracold 40K87Rb molecules, or an ultracold 40K atom with the 40K87Rb molecule [S. Ospelkaus et al., Science 327, 853 (2010).
We consider losses in collisions of ultracold molecules described by a simple statistical short-range model that explicitly accounts for the limited lifetime of classically chaotic collision complexes. This confirms that thermally sampling many isolated resonances leads to a loss cross section equal to the elastic cross section derived by Mayle et al. [Phys. Rev. A 85, 062712 (2012)] and this makes precise the conditions under which this is the case. Surprisingly, we find that the loss is nonuniversal. We also consider the case that loss broadens the short-range resonances to the point that they become overlapping. The overlapping resonances can be treated statistically even if the resonances are sparse compared to kBT{k}_{B}TkB​T, which may be the case for many molecules. The overlap results in Ericson fluctuations which yield a nonuniversal short-range boundary condition that is independent of energy over a range much wider than is sampled thermally. Deviations of experimental loss rates from the present theory beyond statistical fluctuations and the dependence on a background phase shift are interpreted as nonchaotic dynamics of short-range collision complexes.
We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of near-threshold four-body bound states, systematically studying the effects of molecular properties, such as interaction strength, interaction range, and atomic mass. It is found that the adiabatic potential's nearest-neighbor energy level distribution transitions from significant level repulsion characteristic of chaos (Brody distribution) to nonchaotic (Poisson distribution) as the two molecules are separated. For the near-threshold four-atom bound states, the case where all atoms have equal masses shows a Poissonian spacing distribution, while the unequal-mass system exhibits significant level repulsion characterized by a nonzero Brody parameter. We derive a semiclassical formula for the density of states and extract from it simple scaling laws with potential depth and range. We find good agreement between the semiclassical predictions for the density of states and the full quantum mechanical calculations.
Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photoexcitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecular transition, we are able to test this hypothesis with light intensities three orders of magnitude lower than what is typical in red-detuned dipole traps. This allows us to investigate light-induced collisional loss in a gas of nonreactive fermionic 23Na40K^{23}\mathrm{Na}^{40}\mathrm{K}23Na40K molecules. Even for the lowest intensities available in our experiment, our results are consistent with universal loss, meaning unit loss probability inside the short-range interaction potential. Our findings disagree by at least two orders of magnitude with latest theoretical predictions, showing that crucial aspects of molecular collisions are not yet understood and provide a benchmark for the development of new theories.
We investigate the behaviour of single-channel theoretical models of cold and ultracold collisions that take account of inelastic and reactive processes using a single parameter to represent short-range loss. We present plots of the resulting energy-dependence of elastic and inelastic or reactive cross-sections over the full parameter space of loss parameters and short-range phase shifts. We then test the single-channel model by comparing it with the results of coupled-channel calculations of rotationally inelastic collisions between LiH molecules and Li atoms. We find that the range of cross-sections predicted by the single-channel model becomes increasingly accurate as the initial LiH rotational quantum number increases, with a corresponding increase in the number of open loss channels. The results suggest that coupled-channel calculations at very low energy (in the s-wave regime) could in some cases be used to estimate a loss parameter and then to predict the range of possible loss rates at higher energy, without the need for explicit coupled-channel calculations for higher partial waves.