QUANTUM MORPHOGENESIS - SPONTANEOUS TRANSVERSE-PATTERN FORMATION IN THE WAVE-FUNCTION OF AN ATOMIC-BEAM INTERACTING WITH A LIGHT-FIELD

By coupling a microscopic quantum system to a dissipative field, a sel f-organized phase pattern emerges in the wave function of the microsco pic system. The system is a supercooled atomic beam, crossing a laser beam, so that a local dephasing is induced on the wave function at eac h transverse coordinate, depending on the local field intensity. As th e dephased wave function is propagated along a closed loop, diffractio n provides a phase-to-amplitude conversion inducing local modification s of the atomic probability density. This in its turn modifies the fie ld pattern. Thus, beyond a threshold controlled by the atomic intensit y and the laser frequency, the uniform transverse phase of the wave fu nction destabilizes towards a pattern. The symmetries of the pattern c an be studied in terms of the symmetry changes induced on the laser be am. These spontaneous transverse patterns have nothing to do with the forced patterns induced by optical standing waves which define a preas signed confining potential, nor do they have to be confused with an al ternative proposal for longitudinal-pattern formation (Zhang W. et al, Phys. Rev. Lett., 72 (1994) 60). The coupling here considered of a mi croscopic system obeying a Schrodinger equation for an atomic beam wit h a dissipative field obeying a diffusion equation appears as a genera lization of the Hartree-Fock approximation.