Accelerating Self-Imaging: The Airy-Talbot Effect.

We present a new type of self-imaging phenomenon: self-imaging along curved trajectories. Unlike the Talbot effect, where self-imaging occurs for periodic wave patterns propagating along a straight line, here the field is generally not periodic and is self-imaged along curved trajectories. In the paraxial regime, self-imaging along a parabolic trajectory can ideally go on indefinitely. In the nonparaxial regime the self-imaging is along a circular trajectory and lasts as long as the beam bends. We demonstrate this accelerating self-imaging effect experimentally, and discuss generalizations to higher dimensions.

Quantum vortices of strongly interacting photons.

Vortices are topologically nontrivial defects that generally originate from nonlinear field dynamics. All-optical generation of photonic vortices-phase singularities of the electromagnetic field-requires sufficiently strong nonlinearity that is typically achieved in the classical optics regime. We report on the realization of quantum vortices of photons that result from a strong photon-photon interaction in a quantum nonlinear optical medium. The interaction causes faster phase accumulation for copropagating photons, producing a quantum vortex-antivortex pair within the two-photon wave function. For three photons, the formation of vortex lines and a central vortex ring confirms the existence of a genuine three-photon interaction. The wave function topology, governed by two- and three-photon bound states, imposes a conditional phase shift of π per photon, a potential resource for deterministic quantum logic operations.