Photons are particles with rather special properties. They are easily created by a light source, absorbed by matter, and may repel or attract each other when in contact with a suitable material. The idea of feeding photons into crystal-like structures in which photons move between preferred positions and interact with each other, has recently captured the interest of many physicists. Such photon lattices provide us with the enticing opportunity to learn more about many-body physics under nonequilibrium conditions. First experiments with such systems are currently underway, but making theoretical predictions for their behavior poses a great challenge. In our paper now published in PRX, we introduce a theoretical framework which allows for reliable predictions whenever a particular form of the interaction can be identified as “weak.”
Our perturbative formalism is directly built upon the Lindblad master equation, and thus applies to a large class of open quantum systems. We show that accuracy is significantly improved by resummation of an infinite subset of perturbative corrections. The resummation, organized by diagrams, is applied to an open Jaynes-Cummings lattice – the model investigated experimentally within the circuit QED architecture. Perturbation theory and resummation allow us to treat different lattice dimensionalities and sizes, including infinite ones.
Open-system perturbation theory enhanced by resummation will be of use in many contexts. For photon lattices, it provides an important toolbox for validating experimental data from novel open-system quantum simulators. Lindblad perturbation theory comes with minimal technical overhead, can easily handle bosons as well as (pseudo-)spins, and opens new vistas for future studies of nonequilibrium many-body systems.