Nonadiabatic quantum chaos in atom optics

TL;DR

This paper investigates nonadiabatic quantum chaos in atom optics, showing how wave packet dynamics and chaos emerge from nonadiabatic transitions in atomic motion within standing-wave laser fields, linking quantum and classical chaos regimes.

Contribution

It introduces the concept of nonadiabatic quantum chaos in atom optics and connects quantum wave packet proliferation with classical chaotic motion through the Landau--Zener parameter.

Findings

Wave packet splitting occurs at the Landau--Zener parameter around 1.

Chaotic center-of-mass motion correlates with wave packet proliferation.

Quantum and classical chaos regimes are linked via the Landau--Zener parameter.

Abstract

Coherent dynamics of atomic matter waves in a standing-wave laser field is studied. In the dressed-state picture, wave packets of ballistic two-level atoms propagate simultaneously in two optical potentials. The probability to make a transition from one potential to another one is maximal when centroids of wave packets cross the field nodes and is given by a simple formula with the single exponent, the Landau--Zener parameter $\kappa$. If $\kappa \gg 1$, the motion is essentially adiabatic. If $\kappa \ll 1$, it is (almost) resonant and periodic. If $\kappa \simeq 1$, atom makes nonadiabatic transitions with a splitting of its wave packet at each node and strong complexification of the wave function as compared to the two other cases. This effect is referred as nonadiabatic quantum chaos. Proliferation of wave packets at $\kappa \simeq 1$ is shown to be connected closely with chaotic center-of-mass motion in the semiclassical theory of point-like atoms with positive values of the maximal Lyapunov exponent. The quantum-classical correspondence established is justified by the fact that the Landau--Zener parameter $\kappa$ specifies the regime of the semiclassical dynamical chaos in the map simulating chaotic center-of-mass motion. Manifestations of nonadiabatic quantum chaos are found in the behavior of the momentum and position probabilities.