  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 interact 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.
