Quantum atomic lithography via cross-cavity optical Stern-Gerlach setup

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.