Generalized equipartition for nonlinear multiplicative Langevin dynamics: application to laser-cooled atoms

TL;DR

This paper extends the virial and equipartition theorems to nonequilibrium Langevin systems with nonlinear friction and multiplicative noise, specifically applied to laser-cooled atoms, enabling experimental insights into dissipation and confinement deviations.

Contribution

It generalizes the equipartition theorem for nonlinear Langevin dynamics, providing a new relation for laser-cooled atoms that reveals dissipation and confinement deviations.

Findings

Derived a generalized equipartition relation for laser-cooled atoms.

Showed how to measure dissipation in experiments using the new relation.

Identified how deviations from harmonic confinement affect the system.

Abstract

The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize the equipartition theorem for confined laser-cooled atoms in the semi-classical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semi-classical regime.