Effective Field Theory for Rydberg Polaritons

Photons can be made to strongly interact by dressing them with atomic Rydberg states under conditions of electromagnetic induced transparency.~ Probing Rydberg polaritons in the few-body limit, recent experiments were able to observe non-perturbative two-body effects including: single photon switching and the formation of bound states.~ Although the two-body problem is amenable to exact solutions, such approaches quickly become intractable for more than two particles.~ To overcome this problem, we study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT).~ For attractive interactions, we show how a suitably long medium can be used to prepare shallow N-body bound states in one dimension.~ We verify this prediction for two and three photons using full numerical simulations.~ We then consider conditions under which the effective interactions are repulsive and study two and three photon transmission.~ Finally, we show how to go beyond EFT by measuring the three-body contact force or, alternatively, scattering at high relative momenta.