Optical realization of nonlinear quantum dynamics
  In a cavity filled with a Kerr medium it is possible to generate the superposition of coherent states, i.e. Schroodinger cat states may be realized in this system. We show that such a medium may be mimicked by the propagation of a conveniently shaped Gaussian beam in a GRIN device. This is attained by introducing a second order correction to the paraxial propagation of the beam. An additional result is that a Gaussian beam propagating in GRIN media, may split into two Gaussian beams. 
F. Soto-Eguibar, V. Arrizon, A. Z\'u\~niga-Segundo, and H.M.   Moya-Cessa
physics.optics