Repeated interaction model for diffusion-induced Ramsey narrowing

Yanhong Xiao,Ronald L Walsworth,David F Phillips,Irina Novikova

doi:10.1364/oe.16.014128

Abstract

In a recent paper [Y. Xiao et al., Phys. Rev. Lett. 96, 043601 (2006)] we characterized diffusion-induced Ramsey narrowing as a general phenomenon, in which diffusion of coherence in-and-out of an interaction region such as a laser beam induces spectral narrowing of the associated resonance lineshape. Here we provide a detailed presentation of the repeated interaction model of diffusion-induced Ramsey narrowing, with particular focus on its application to Electromagnetically Induced Transparency (EIT) of atomic vapor in a buffer gas cell. We compare this model both to experimental data and numerical calculations.

Highlights

Atomic motion can affect the lineshape of an atomic transition
In the case of Electromagnetically Induced Transparency (EIT) for an atomic vapor constrained to diffuse in a buffer gas which only weakly perturbs ground state coherence in a collision, the interaction time is usually estimated by the lowest order diffusion mode, which leads to the typical Lorentzian lineshape but implicitly assumes that atoms diffuse out of the laser beam and do not return [1, 2, 3]
We provided a detailed description of the repeated interaction model of diffusioninduced Ramsey narrowing: an intuitive analytical model based on a weighted average of distinct atomic histories arising from the diffusion of coherence in and out of an interaction region

Summary

Introduction

Atomic motion can affect the lineshape of an atomic transition. For example, transit-time broadening often sets a limit on the narrowest linewidth obtainable in the interaction of a thermal atomic vapor with a collimated laser beam. In recently published work [4] we characterized an important but heretofore overlooked line narrowing process — “diffusion-induced Ramsey narrowing” — in which atoms diffuse out of the interaction region and return before decohering. In this process, atoms evolve coherently in the dark (outside of the laser beam) between periods of interaction (inside the laser beam), in analogy to Ramsey spectroscopy [5]. The model consists of (i) solving the time evolution of the atomic density matrix as a function of the history (“Ramsey sequence”) of time spent in and out of the laser beam (See Fig. 1b); (ii) evaluating the probability distributions for the in and out periods from the underlying diffusion equation; and (iii) integrating the density matrix solutions over the probability distributions to determine the ensemble average lineshape

Atomic density matrix following a Ramsey sequence

Probability distributions for Ramsey sequences

Integration over all Ramsey sequences

Comparison with experiment

Comparison with numerical calculations

Conclusions