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Physical Review A

Anomalous lifetimes of ultracold complexes decaying into a single channel

James F. E. Croft, John L. Bohn, Goulven Quéméner

Published Feb 3, 2023• 10 citations
Publisher

Abstract

We investigate the lifetimes of complexes formed in ultracold molecule collisions. Employing both transition-state theory and a non-Hermitian microscopic model, we examine processes that can extend the lifetime of complexes beyond that predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) theory. We focus on complexes that possess only one open channel, and find that the extreme distribution of widths for this case favors low decay rates. Thus, decay from a complex into a single energetically available channel can be anomalously slow, even orders of magnitude slower than the RRKM rate, and moreover the decay may be nonexponential in time.

DOI
10.1103/physreva.107.023304

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We investigate the lifetimes of complexes formed in ultracold molecule collisions. Employing both transition-state theory and a non-Hermitian microscopic model, we examine processes that can extend the lifetime of complexes beyond that predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) theory. We focus on complexes that possess only one open channel, and find that the extreme distribution of widths for this case favors low decay rates. Thus, decay from a complex into a single energetically available channel can be anomalously slow, even orders of magnitude slower than the RRKM rate, and moreover the decay may be nonexponential in time.
We investigate the lifetimes of complexes formed in ultracold molecule collisions. Employing both transition-state-theory and an optical model approach we examine processes that can extend the lifetime of complexes beyond that predicted by Rice-Ramsperger-Kassel-Marcus theory. We focus on complexes that possess only one open channel, and find that the extreme distribution of widths for this case favors low decay rates. Thus decay from a complex into a single energetically available channel can be anomalously slow, and moreover nonexponential in time. We apply the theory to two systems of current experimental interest, RbCs and NaRb, finding qualitatively that the empirical time scales can be accounted for in the theory.
The puzzle of "sticky collisions," in which molecular collision complexes exhibit unexpectedly long lifetimes, remains an unresolved mystery. A central challenge to solving this mystery is that traditional close-coupling calculations remain limited by the vast computational cost needed to take into account all the degrees of freedom involved in the collision. In this work, we propose a statistical model designed to simulate the result of full close-coupling calculations, with the goal of collecting statistics about reasonable lifetimes of collision complexes. To do so, we numerically sample resonances using random matrix theory and utilize results from quantum defect theory to calculate scattering properties and lifetimes. We find that in the limit of dense resonances, our theory agrees well with the Rice-Ramsperger-Kassel-Markus (RRKM) prediction, whereas in the limit of sparse resonances, the physics is governed by threshold behavior rather than resonant effects. By comparing these predictions to experimental results in two limits, we argue that close-coupling calculations alone may be insufficient to resolve the issue of long lifetimes.
A thorough understanding of molecular scattering in the ultralow temperature regime is crucial for realizing long coherence times and enabling tunable interactions in molecular gases, systems which offer many opportunities in quantum simulation, quantum information, and precision measurement.Of particular importance is the nature of the long-lived intermediate complexes which may be formed in ultracold molecular collisions, as such complexes can dramatically affect the stability of molecular gases, even when exothermic reaction channels are not present.Here, we investigate collisional loss in an ultracold mixture of 40 K 87 Rb molecules and 87 Rb atoms, where chemical reactions between the two species are energetically forbidden.Through direct detection of the KRb 2 Ã intermediate complexes formed from atom-molecule collisions, we show that a 1064 nm laser source used for optical trapping of the sample can efficiently deplete the complex population via photoexcitation, an effect which can explain the strong twobody loss observed in the mixture.By monitoring the time evolution of the KRb 2 Ã population after a sudden reduction in the 1064 nm laser intensity, we measure the lifetime of the complex [0.39(6) ms], as well as the photoexcitation rate for 1064 nm light [0.50ð3Þμs -1 ðkW=cm 2 Þ -1 ].The observed lifetime, which is ∼10 5 times longer than recent estimates based on the Rice-Ramsperger-Kassel-Marcus statistical theory, calls for new theoretical insight to explain its origin.
Collisional complexes, which are formed as intermediate states in molecular collisions, are typically short-lived and decay within picoseconds. However, in ultracold collisions involving bialkali molecules, complexes can live for milliseconds, completely changing the collision dynamics. This can lead to unexpected two-body loss in samples of nonreactive molecules. During the past decade, such "sticky" collisions have been a major hindrance in the preparation of dense and stable molecular samples, especially in the quantum-degenerate regime. Currently, the behavior of the complexes is not fully understood. For example, in some cases, their lifetime has been measured to be many orders of magnitude longer than recent models predict. This is not only an intriguing problem in itself but also practically relevant, since understanding molecular complexes may help to mitigate their detrimental effects. Here, we review the recent experimental and theoretical progress in this field. We treat the case of molecule-molecule as well as molecule-atom collisions.
By using an exact analytical approach to the time evolution of decay we investigate the tunneling decay of ultracold single atoms to discuss the conditions for deviations of the exponential decay law. We find that RRR, given by the ratio of the energy of the decaying fragment Er{\mathcal{E}}_{r}Er​ to its corresponding width ${\mathrm{\ensuremath{\Gamma}}}_{r}$, is the relevant quantity in this study. When RRR is less than 0.30.30.3, the decay of the atom goes to a good approximation for the first few lifetimes as $exp(\ensuremath{-}{\mathrm{\ensuremath{\Gamma}}}_{r}t/2\ensuremath{\hbar}){t}^{\ensuremath{-}3/2}$. We also find that for values of $R\ensuremath{\sim}1$, the nonexponential behavior occurs in a postexponential regime that goes as ${t}^{\ensuremath{-}3}$ after around a dozen lifetimes. The above conditions depend on suitably designed potential parameters and suggest that for values $R\ensuremath{\lesssim}1$, the experimental verification of nonexponential decay might be possible.