Aberrations in (3+1)-dimensional Bragg diffraction using pulsed Laguerre-Gaussian laser beams

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