Quasi-thermalization of collisionless particles in quadrupole potentials

TL;DR

This paper explains how noninteracting particles in quadrupole traps reach a quasi-thermal state with persistent anisotropy, due to dephasing and conservation laws, without collisions, supported by models of symmetric and pancake traps.

Contribution

It introduces models that explain anisotropic quasi-thermalization in collisionless gases in quadrupole and related traps, revealing the role of angular momentum and potential shape.

Findings

Particles reach a stationary state without collisions due to dephasing.

Anisotropy persists at long times, with different effective temperatures.

The models explain experimental observations of temperature anisotropy.

Abstract

We analyze several puzzling features of a recent experiment with a noninteracting gas of atoms in a quadrupole trap. After an initial momentum kick, the system reaches a stationary, quasi-thermal state even without collisions, due to the dephasing of individual particle trajectories. Surprisingly, the momentum distribution remains anisotropic at long times, characterized by different "temperatures" along the different directions. In particular, there is no transfer of the kick energy between the axial and radial trap directions. To understand these effects we discuss and solve two closely related models: a spherically symmetric trap $V(r)\simeq r^\alpha$ and a strongly confined gas along one direction (a "pancake" trap). We find that in the isotropic trap, the gas unexpectedly also preserves the anisotropy of the kick at long times, which we are able to explain using the conservation of angular momentum and the virial theorem. Depending on the value of $\alpha$ we find that the kick can cool or heat the orthogonal directions. The pancake trap case is quantitatively similar to the quadrupole one. We show that for the former, the temperature anisotropy and memory of the kick direction are due to the change in the 2D effective potential resulting from the kick, thereby also explaining the quadrupole experimental results.