Figure 2: Schematics of the experiment and the beam parameters.

(a) A holographic fork mask generates a row of vortex beams with different azimuthal indices m=..., −5, −3, −1, 0, 1, 3, 5, ... (refs 19, 20). These beams are focused by a magnetic lens and are studied in the region of maximal quasi-uniform magnetic field. The focal plane is shifted few Rayleigh ranges below the observation plane z=0 to reduce the Gouy-phase rotation46,47. A knife-edge stop is placed at zk<0, where it blocks half of each of the beams. Varying the position zk of the knife edge, we observe spatial rotational dynamics of the cut beams propagating to the observation plane (see Fig. 1). (b) Intensity distribution in the |m|=1 beams. The radius w of the focused beams varies slowly with z. In the highlighted range zε(−80, −30) μm, the beam radius approaches the magnetic radius, w(z)≃wB, and the beams acquire the Landau-state properties (see Figs 3 and 4).