Brian Kendrick
The Geometric Phase Controls Ultracold Chemistry
The unique properties of ultracold ($T < 1\,{\rm mK}$) atom-molecule collisions
often lead to unprecedented quantum interference effects that effectively
control the collision outcome. As the collision energy approaches absolute zero,
the cross sections obey the Wigner threshold laws and the rate coefficients
for barrierless exothermic reactions approach a constant (non-zero) value. Many of
the molecules of experimental interest, exhibit a conical intersection (degeneracy)
between the ground and first excited electronic states. This degeneracy gives
rise to a $U(1)$ gauge potential analogous to that of a magnetic solenoid centered
at the degeneracy. During the collision process, quantum interference occurs between
the two components of the scattering wavefunction that encircle the conical
intersection. In the ultracold regime, this interference can approach its maximal
values (via Levinson's theorem) effectively acting as a quantum switch turning
the reaction on or off. The geometric (Berry) phase associated with the conical intersection
reverses the nature of the quantum interference (i.e., constructive becomes destructive
and vice versa) and therefore gives the opposite theoretical prediction for the
collision outcome relative to a calculation that ignores the phase. We will discuss
all of these effects in detail and present results from accurate numerical quantum
scattering calculations that demonstrate these effects for several molecular systems
of experimental interest.
