The dynamics of atoms and ions expanding in the magnetic nozzle of a Helicon plasma thruster is experimentally studied by means of near-infrared laser-induced fluorescence spectroscopy and a retarding potential analyzer. The two techniques are compared in measuring Xe and Kr ion velocity for different thruster working parameters. Fluorescence spectra are recorded for several operating conditions inside and outside the thruster discharge chamber. In the near-field plume, the relatively intense magnetic field induces the Zeeman effect on the probed optical transitions. Hence, modeling of the atomic lineshapes is addressed to accurately compute the Doppler shift and infer the velocity. The first direct measurements of the neutral flow in a magnetic nozzle reveal that atoms are accelerated to supersonic velocities downstream the thruster exit. The ions acceleration region extends several centimeters downstream the exit plane. Larger axial ion speeds are attained when the thruster operates at lower mass flow rates and higher levels of input power.