Few-body quantum physics with strongly interacting Rydberg polaritons

TL;DR

This paper develops a microscopic Hamiltonian model for one-dimensional Rydberg polaritons, analyzing their scattering, bound states, and decoherence effects, with exact solutions for single and two-body problems in weakly interacting regimes.

Contribution

It extends previous work by deriving a detailed microscopic Hamiltonian and solving key two-body problems analytically, including decoherence effects.

Findings

Exact solution for a single polariton in an external potential.

Analytical solution for the two-body problem in a weakly interacting regime.

Inclusion of decoherence processes via a Master equation approach.

Abstract

We present an extension of our recent paper [Bienias et al., Phys. Rev. A 90, 053804 (2014)] in which we demonstrated the scattering properties and bound-state structure of two Rydberg polaritons, as well as the derivation of the effective low-energy many-body Hamiltonian. Here, we derive a microscopic Hamiltonian describing the propagation of Rydberg slow light polaritons in one dimension. We describe possible decoherence processes within a Master equation approach, and derive equations of motion in a Schroedinger picture by using an effective non-Hermitian Hamiltonian. We illustrate diagrammatic methods on two examples: First, we show the solution for a single polariton in an external potential by exact summation of Feynman diagrams. Secondly, we solve the two body problem in a weakly interacting regime exactly.