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arXiv:1805.08128 · Nature Communications

Reaction kinetics of ultracold molecule-molecule collisions

Daniel Kai Hoffmann, Thomas Paintner, W. Limmer, Dmitry S. Petrov, Johannes Hecker Denschlag

Published Dec 3, 2018• 27 citations
arXivHTMLPDF

Abstract

Abstract Studying chemical reactions on a state-to-state level tests and improves our fundamental understanding of chemical processes. For such investigations it is convenient to make use of ultracold atomic and molecular reactants as they can be prepared in well defined internal and external quantum states. Here, we investigate a single-channel reaction of two Li2-Feshbach molecules where one of the molecules dissociates into two atoms 2AB ⇒ AB + A + B. The process is a prototype for a class of four-body collisions where two reactants produce three product particles. We measure the collisional dissociation rate constant of this process as a function of collision energy/temperature and scattering length. We confirm an Arrhenius-law dependence on the collision energy, an a4 power-law dependence on the scattering length a and determine a universal four body reaction constant.

DOI
10.1038/s41467-018-07576-1

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Abstract Studying chemical reactions on a state-to-state level tests and improves our fundamental understanding of chemical processes. For such investigations it is convenient to make use of ultracold atomic and molecular reactants as they can be prepared in well defined internal and external quantum states. Here, we investigate a single-channel reaction of two Li2-Feshbach molecules where one of the molecules dissociates into two atoms 2AB ⇒ AB + A + B. The process is a prototype for a class of four-body collisions where two reactants produce three product particles. We measure the collisional dissociation rate constant of this process as a function of collision energy/temperature and scattering length. We confirm an Arrhenius-law dependence on the collision energy, an a4 power-law dependence on the scattering length a and determine a universal four body reaction constant.
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II. Inelastic atom -molecule collisions 2 A. Vibrational and rotational relaxation 2 1. Collisions at cold and ultracold temperatures 2 2. Shape resonances in molecular collisions 6 3. Feshbach resonances in molecular collisions 6 B. Quasi-resonant transitions 7 C. Atom -molecular ion collisions 8 III.Chemical Reactions at ultracold temperatures 9 A. Tunneling dominated reactions 9 1.Reactions at zero temperature 10 2. Feshbach resonances in reactive scattering 12 B. Barrierless reactions 14 1.Collision systems of three alkali metal atoms 14 2. Role of PES in determining ultracold reactions 16 3.Relaxation of vibrationally excited alkali metal dimers 18 4. Reactions of heteronuclear and isotopically substituted alkali-metal dimer systems 19 IV.Inelastic molecule -molecule collisions 20 A. Molecules in the ground vibrational state 20 B. Vibrationally inelastic transitions 22 V. Summary and outlook 24 References 24 I. A. Vibrational and rotational relaxation 1. Collisions at cold and ultracold temperatures
Dynamics play an important role in physics. From classical mechanics, astrophysics, hydrodynamics to quantum physics, the dynamics of physical systems have crucial impact on our understanding of nature. For simple configurations such as in the two-body problem the dynamics can be calculated analytically. However, things get more complicated once the number of contributors in a system increases such as in few- or many-body systems. One way to study such an ensemble is to use a model system where decisive parameters can be controlled. In this thesis I make use of an ultracold cloud of fermionic Lithium-6 atoms close to zero temperature to study dynamics of few- and many-body systems. Two experimental studies to this topic are presented. In the first study, I produced a gas of di-atomic molecules (dimers), consisting of two Lithium-6 atoms in different states, to study the reaction kinetics of the four-body process of a dimer-dimer collision. At temperatures close to absolute zero the internal and external degrees of freedom of the dimers can be well controlled. This allowed us to investigate the kinetics of a single-channel reaction. To resolve the dynamics of the process we heated a gas of molecules and tracked the state of the system as a function of time. We determined the reaction-rate constant of the process for various thermal energies which allowed us to verify the Arrhenius law for molecule-molecule reactions in the ultracold regime. Additionally, we provided first insight into the dependence of this four-body process on the particle interaction. In the second experimental work, I focused on the thermodynamical properties of the ultracold gas. Cooling the gas of Lithium-6 atoms close to zero temperature the gas undergoes a phase transition and superfluidity is established. To study the dynamics in such a gas, we used a local perturbation to produce sound waves. Depending on the excitation scheme we either excited first sound, i.e. a pressure wave, known from classical mechanics, or second sound, i.e. an entropy wave. In the study we focused on second sound and determined the second sound speed as a function of the particle interaction. We found agreement of our results with both - a numerical and an analytical description of the interaction strength dependence of the second sound speed. Besides the experimental work, a theoretical proposal for a novel imaging technique for a 2D ultracold gas in an optical lattice is presented. The scheme is based on a holographic approach and enables the detection of individual particles with only a few hundred scattered photons per atom.
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).
Ultracold polar molecular quantum gases promise to open new research directions ranging from the study of ultra-cold chemistry, precision measurements to novel quantum phase transitions. Based on the preparation of high-phase space density gases of polar KRb molecules [1–3], I will discuss the control of dipolar collisions and chemical reactions of polar molecules in a regime where quantum statistics, single scattering partial waves, and quantum threshold laws play a dominant role [4]. In particular, I will point out the crucial role of electric dipole-dipole interactions [5] and external confinement [6] in determining the chemical reaction rate. Finally, I will discuss prospects of reaching quantum degeneracy in bialkali samples of polar molecules and prospects for these systems as novel dipolar quantum many-body systems.