Quantum morphogenesis: Spontaneous transverse-pattern formation in the wave function of an atomic beam interacting with a light field

Summary

By coupling a microscopic quantum system to a dissipative field, a self-organized phase pattern emerges in the wave function of the microscopic system. The system is a supercooled atomic beam, crossing a laser beam, so that a local dephasing is induced on the wave function at each transverse coordinate, depending on the local field intensity. As the dephased wave function is propagated along a closed loop, diffraction provides a phase-to-amplitude conversion inducing local modifications of the atomic probability density. This in its turn modifies the field pattern. Thus, beyond a threshold controlled by the atomic intensity and the laser frequency, the uniform transverse phase of the wave function destabilizes towards a pattern. The symmetries of the pattern can be studied in terms of the symmetry changes induced on the laser beam. These spontaneous transverse patterns have nothing to do with the forced patterns induced by optical standing waves which define a preassigned confining potential, nor do they have to be confused with an alternative proposal for longitudinal-pattern formation (Zhang W.et al., Phys. Rev. Lett.,72 (1994) 60). The coupling here considered of a microscopic system obeying a Schrodinger equation for an atomic beam with a dissipative field obeying a diffusion equation appears as a generalization of the Hartree-Fock approximation.