Thermalization in a Coherently Driven Ensemble of Two-Level Systems

We investigate the coherent quantum time evolution of a driven mesoscopic chain of two-level systems that interact via the van der Waals interaction in their excited state. The Hamiltonian is the sum of a classical lattice gas Hamiltonian and an off-diagonal driving term without classical counterpart. Starting from a product state we observe-beyond a certain interaction strength-thermalization of the system with respect to observables of the classical lattice gas. This transition can be studied experimentally with Rydberg atoms, ions, or polar molecules. We suggest how to experimentally determine the temperature of the thermal state which should allow for thermometry of the internal degrees of freedom of cold Rydberg gases whose external dynamics is frozen.