Self-organization in dissipative optical lattices

TL;DR

This paper demonstrates that atomic transport in dissipative optical lattices exhibits self-organization during the transition from Gaussian to q-Gaussian distributions, constrained by the finiteness of the second moment and supported by experimental data.

Contribution

It introduces a modified Klimontovich's S-theorem to interpret self-organization in optical lattices and constrains the nonadditivity parameter q within a specific range.

Findings

Self-organization occurs only where the second moment <p^{2}> is finite.

The nonadditivity parameter q is confined to 1<q<5/3.

Experimental results support the theoretical q-range.

Abstract

We show that the transition from Gaussian to the q-Gaussian distributions occurring in atomic transport in dissipative optical lattices can be interpreted as self-organization by recourse to a modified version of Klimontovich's S-theorem. As a result, we find that self-organization is possible in the transition regime, only where the second moment <p^{2}> is finite. Therefore, the nonadditivity parameter q is confined within the range 1<q<5/3, although whole spectrum of q values i.e., 1<q<3, is considered theoretically possible. The range of q values obtained from the modified S-theorem is also confirmed by the experiments carried out by Douglas et al. [Phys. Rev. Lett. 96, 110601 (2006)].