From conditional phase to quantum vortices of photons

Vortices are a hallmark of topologically nontrivial dynamics in nonlinear physics. They appear in optics as phase twists in the electromagnetic field resulting from light-matter interactions. Quantum vortices, characterized by phase singularities in the wavefunction, are typically associated with strongly interacting many-particle systems, particularly superfluids. However, the emergence of vortices through the effective interaction of light with itself, a phenomenon requiring strong optical nonlinearity, was previously limited to the classical regime until recent advancements.

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 co-propagating photons, producing a quantum vortex-antivortex pair within the two-photon wave function.

For counter-propagating photons, a conditional phase and a non-trivial intensity correlation between the photons are also observed. Furthermore, if the photons have different parity, they exchange their parity by the long-range dipole-dipole exchange interaction by imprinting a pi/2 conditional phase.

For three photons, the strong interaction leads to an even richer topological structure of the three-photon wavefunction. The point vortices lead to the formation of vortex lines, and a central vortex ring attests to a genuine three-photon interaction. It also produces chiral asymmetric interactions between the photons.

The wavefunction topology, governed by two- and three-photon bound states, imposes a conditional phase shift of pi-per-photon, a potential resource for deterministic quantum logic operations.