Multiband dispersion and warped vortices of strongly-interacting photons

TL;DR

This paper theoretically investigates the complex multiband dispersion and warped vortex structures in strongly-interacting photons via Rydberg polaritons, revealing new multi-photon correlation phenomena.

Contribution

It introduces a multiband dispersion model with warped band structures for interacting photons, extending beyond the single-band approximation.

Findings

Band structure includes one massive and multiple massless modes with Dirac points.

The dispersion is warped, deviating from simple parabolic models.

Numerical simulations confirm the analytical multiband dispersion results.

Abstract

We present a theoretical study of quantum correlations between interacting photons realized through co-propagating Rydberg polaritons. We show that the spatial evolution of the $n$-photon wavefunction is governed by a multiband dispersion featuring one massive mode and multiple massless modes with degenerate Dirac points and $n$-fold rotational symmetry. The resulting band structure is warped, departing from the single-band, parabolic approximation commonly assumed for interacting polaritons. Our analytical results are supported by rigorous numerical modeling that fully accounts for photon propagation inside the finite atomic medium. These findings advance the understanding of multi-photon interactions and support the development of future multi-photon control tools.