Aberrations in (3+1)D Bragg diffraction using pulsed Gaussian laser beams

TL;DR

This paper investigates the effects of aberrations, pulse shapes, and velocity on the efficiency of 3D atomic Bragg beam splitters formed by pulsed Gaussian laser beams, combining numerical simulations, analytical models, and experimental data.

Contribution

It provides a comprehensive analysis of aberrations and pulse shape effects on Bragg diffraction efficiency, including analytical solutions and experimental validation.

Findings

Transfer efficiency depends on residual atomic velocity and diffraction order losses.

Gaussian beam aberrations significantly affect diffraction performance.

Different pulse shapes influence the transfer efficiency, with analytical models matching experimental data.

Abstract

We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Gaussian beam envelope, studied with (3+1)D numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular-, Gaussian-, Blackman- and hyperbolic secant pulses. For the latter, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the $\pi$-pulse time is explained from a renormalization of the simple Pendell\"osung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)D numerical simulations for pulsed Gaussian beams, as well as experimental data and find very good agreement, considering a mixture of Bose-Einstein condensate and thermal cloud.