Inspired by Wannier's threshold law, we recognize that collision-complex decay meets the requirements of quantum-classical correspondence in sufficiently exothermic ultracold reactions. We make use of this correspondence to elucidate the classical foundations of ultracold reactions and to help bring calculations currently beyond the capabilities of quantum mechanics within reach. A classical method with a simplified model of many-body interactions is provided for the determination of the collision-complex lifetime and demonstrated for a reduced-dimensional system, as preliminary to the calculation of collision-complex lifetimes in the full-dimensional system.
Inspired by Wannier's threshold law, we recognize that collision-complex decay meets the requirements of quantum-classical correspondence in sufficiently exothermic ultracold reactions. We make use of this correspondence to elucidate the classical foundations of ultracold reactions and to help bring calculations currently beyond the capabilities of quantum mechanics within reach. A classical method with a simplified model of many-body interactions is provided for the determination of the collision-complex lifetime and demonstrated for a reduced-dimensional system, as preliminary to the calculation of collision-complex lifetimes in the full-dimensional system.
Ultracold atoms and molecules provide an unprecedented view into the role of quantum effects in chemical reactions. However, these same quantum effects make ultracold chemical reactions notoriously difficult to simulate. Contrary to conventional wisdom that ultracold systems necessitate quantum approaches, with classical mechanics offering a rough approximation at best, the past three decades have seen an explosion in classical, quasiclassical, and semiclassical approaches that yield near-exact results for ultracold systems─including in cases where today's quantum methods would be computationally intractable. This review illustrates the power of these approaches with 30 years' worth of numerical and experimental evidence. The review provides a comprehensive account of the successes of universal classical post-threshold laws for low-energy atomic and molecular scattering systems, as well as the cutting edge in quasiclassical approaches that unravel the ongoing controversy surrounding long-lived collision complex lifetimes in ultracold collisions. Special attention is placed on atomic systems where classical scaling laws hold directly at zero Kelvin, which underline the predictive power classical methods can offer even in the most extreme quantum chemical environments. The review culminates with a discussion of broader implications for classically inspired approaches to prototypically quantum chemistry in the second quantum revolution.
Ultracold chemistry, the science of chemical reactions below one milliKelvin, has the potential to expedite technologies from controlled reactions to quantum computation. Experimental investigation of the ultracold KRb dimer reaction (2KRb → [K2Rb2]⋆ → K2 + Rb2) has been central to the field. Despite recent experimental and theoretical work on the reaction, it remains an open question how cold products (14 K) are formed from the hot collision complex (4,000 K). The answer to this question has been obstructed by the computational intensity of quantum mechanical simulations at cold temperatures. This dissertation makes use of the analogy of an “ultracold inferno” to circumvent the computationally intensive quantum mechanical treatments typically applied near threshold. The thesis reveals that, unexpectedly, classical mechanics is expected to be exact for elements of the ultracold KRb dimer reaction and many threshold processes previously thought to be the sole province of quantum mechanics. Classical behaviors can thus be observed in certain systems at extremely low temperatures, and classical mechanics can be employed to bring computational simulation of many threshold systems within reach. To identify when classical mechanics is valid near threshold, two semiclassical criteria of quantum-classical correspondence are presented. The criteria are then put into practice to calculate the rate of product formation in a reduced-dimensional model with the essence of the ultracold KRb dimer reaction via classical analytic phase-space counting and classical numerical dynamics simulations. A hybrid semiclassical-quantum method is also proposed to bring simulation of many full-dimensional exothermic ultracold reactions within reach. Classical “post-threshold” laws are derived and shown to operate in a plethora of cold and ultracold systems. Quantum and classical threshold behavior is unified from across physics and chemistry to emphasize the wide-reaching importance of classical mechanics near threshold. This thesis concludes classical mechanics has broad applications in threshold phenomena in fields such as ultracold and cold physics and chemistry, intense laser science, plasma science, nuclear physics, positron and positronium scattering, electron detachment and attachment, and astrochemistry. Classical techniques can be used to facilitate calculations and to better understand the mechanisms behind these threshold processes. These findings illustrate the power of time-honored classical mechanics in the age of the quantum leap.
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.
A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanoKelvin. In this work we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. For the first time we map out an accurate ab initio ground state potential energy surface of the KRbK complex in full dimensionality and report numerically exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome. We compare this with a lighter system with a smaller density of states (here the LiYbLi trimer) which displays random, and not chaotic, behavior.
Estimates for the lifetime of collision complexes formed during ultracold molecular collisions based on density-of-states arguments are shown to be consistent with similar estimates based on classical trajectory calculations. In the classical version, these collisions are shown to exhibit chaos and their fractal dimension is calculated versus collision energy. From these results, a picture emerges that ultracold collisions are likely classically ergodic, justifying the density-of-states estimates for lifetimes. These results point the way toward using the techniques of classical and quantum chaos to interpret molecular collisions in the ultracold regime.
A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them are possible in ultracold molecular gases, and as such this model will allow the rigorous parametrization of experimental results. In addition we show how, once extracted, these parameters can be related to the physical properties of the system, shedding light on fundamental aspects of molecular collision dynamics.