Thermalization of a strongly interacting 1D Rydberg lattice gas

When Rydberg states are excited in a dense atomic gas the mean number of excited atoms reaches a stationary value after an initial transient period. We shed light on the origin of this steady state that emerges from a purely coherent evolution of a closed system. To this end we consider a one-dimensional ring lattice, and employ the perfect blockade model, i.e. the simultaneous excitation of Rydberg atoms occupying neighboring sites is forbidden. We derive an equation of motion which governs the system’s evolution in excitation number space. This equation possesses a steady state which is strongly localized. Our findings show that this state is to a good accuracy given by the density matrix of the microcanonical ensemble where the corresponding microstates are the zero energy eigenstates of the interaction Hamiltonian. We analyze the statistics of the Rydberg atom number count providing expressions for the number of excited Rydberg atoms and the Mandel Q-parameter in equilibrium.

💡 Research Summary

The paper investigates why, after an initial transient, the mean number of excited atoms in a dense gas of Rydberg atoms settles to a stationary value even though the system evolves under purely coherent dynamics without any external bath. To address this, the authors consider a one‑dimensional ring lattice populated by atoms and adopt the perfect blockade model, which forbids simultaneous excitation of neighboring sites. This model captures the essential physics of the strong van‑der‑Waals interaction that makes two Rydberg excitations within a blockade radius energetically forbidden.

The total Hamiltonian is split into a laser‑driven term that flips ground‑state atoms to the Rydberg state and an interaction term that assigns infinite energy to any configuration violating the blockade constraint. Because of the constraint, the Hilbert space decomposes into subspaces labelled by the number n of Rydberg excitations. Within each subspace the states are orthogonal and all have zero interaction energy.

The authors then construct a transition matrix that connects subspaces with different excitation numbers. By tracing out the internal degrees of freedom they derive a master‑equation‑like evolution for the probabilities P_n(t) of finding n excitations: \