# Focus: Modeling Ultracold Chemistry

Phys. Rev. Focus 25, 11
The rate at which ultracold molecules react is limited by quantum mechanical effects not seen in ordinary chemistry, according to calculations that agree with recent experiments.

When two very cold molecules chemically react, the quantum states of their nuclei–which are normally invisible to chemistry–have a dramatic influence on the reaction rate, according to recent experiments. In the 19 March Physical Review Letters, theorists devise a scheme for calculating reaction rates of molecules at ultralow temperatures, where such quantum effects become important. The team calculates that the reaction rate is determined by the initial approach of the molecules at intermediate distances, rather than by the details of their final chemical reaction at close range. Experimenters need such detailed understanding if they hope to exploit ultracold molecules for fundamental studies and quantum computers.

Atomic physicists have steadily improved their ability to cool atoms to temperatures where quantum effects reign, and in the past decade they have also trapped loosely bound pairs of atoms. But only in 2008 did they produce large numbers of ultracold pairs that were bound strongly enough to properly be called molecules. Each of these molecules is in its lowest possible state of vibration and rotation, and their overall motion corresponds to temperatures under a millionth of a degree above absolute zero. Bose-Einstein condensation of ultracold atoms 14 years ago spawned a continuing flurry of physics experiments and garnered a Nobel Prize, but researchers expect even richer quantum behavior from ultracold molecules. Understanding how ultracold molecules interact is critical to the experiments.

To observe these interactions, an experimental team recently measured the rate at which ultracold potassium-rubidium (KRb) molecules swapped atoms in pairs to form $Rb2$ and $K"2$ molecules [1]. The rate was as much as 100 times slower when the nuclear spins of all the molecules were aligned (all pointing up, for example) than when some spins were in different orientations. Paul Julienne of the Joint Quantum Institute of the University of Maryland in College Park and the National Institute of Standards and Technology in Gaithersburg, Maryland, was a co-author of that work and now teams up with Zbigniew Idziaszek of the University of Warsaw to formally calculate the reaction rate.

Because of the low temperatures, the calculation has to account for quantum effects such as the spin states of the nuclei and the molecules’ wavelike properties. In principle, if you imagine one molecule as fixed in space, then the outgoing, scattered molecular waves that came close but failed to react with it can interfere with the incoming molecular wave approaching at a later time.

For the KRb reactions, however, this complexity can be ignored, because the molecules are almost certain to react if they get close enough. “It’s like the drain in the bathtub,” Julienne says, so that the reaction rate depends only on the long-range van der Waals forces that all molecules experience. “Where the quantum mechanics comes in is that you have to figure out the probability that they’re going to get pulled in to each other, given that the size of the quantum wave is many hundreds of times larger than the length of a chemical bond.”

That probability of approach depends in part on the precise orientations of the spins of the nuclei–even though the final reaction involves only electrons. The nuclear orientations matter because these molecules are fermions, which means that two of them cannot have the same quantum state at the same location in space. In the calculation, this effect appears as a repulsive barrier that molecules can only traverse by quantum-mechanically “tunneling” through it. The calculations confirmed the dramatic increase in rate observed in the experiments when the trap contained molecules with a mixture of nuclear orientations.

The calculated reaction rate agrees with experiment and doesn’t depend on the details of the chemistry. “That universality is surprising,” says Jeremy Hutson of the University of Durham, England. “It gives an enormous simplification, but it’s not a simplification that would have been expected.” Although “some things come out simple,” he says, “the theory is a very sophisticated one.”

–Don Monroe

Don Monroe is a freelance science writer in Murray Hill, New Jersey.

## References

1. S. Ospelhaus, K.-K. Ni, D. Wang, M.H.G. de Miranda, B. Neyenhuis, G. Quéméner, P.S. Julienne, J.L. Bohn, D.S. Jin, and J. Ye, “Quantum-State Controlled Chemical Reactions of Ultracold Potassium-Rubidium Molecules,” Science 327, 853 (2010)

## Subject Areas

Atomic and Molecular Physics

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