We investigate the deflection of light by a cold atomic cloud when the light-matter interaction is locally tuned via the Zeeman effect using magnetic field gradients. This lighthouse effect is strongest in the single-scattering regime, where deviatio
n of the incident field is largest. For optically dense samples, the deviation is reduced by collective effects, as the increase in linewidth leads to a decrease of the magnetic field efficiency.
We present a fully quantum scheme to perform 2D atomic lithography based on a cross-cavity optical Stern-Gerlach setup: an array of two mutually orthogonal cavities crossed by an atomic beam perpendicular to their optical axes, which is made to inter
act with two identical modes. After deriving an analytical solution for the atomic momentum distribution, we introduce a protocol allowing us to control the atomic deflection by manipulating the amplitudes and phases of the cavity field states.
