Entropic enhancement of spatial correlations in a laser-driven Rydberg gas

Laser-driven Rydberg gases are many-body quantum systems that exhibit a pronounced collective excitation behavior due to the strong interaction between atoms in high-lying electronic states. Atoms located within a so-called blockade volume share a single Rydberg excitation, which is dynamically created and annihilated. For sufficiently long times, this driven system approaches a steady state, which lends its properties from a maximum entropy state of a Tonks gas. Using this connection, we show that spatial correlations between Rydberg atoms are controlled by the number of atoms contained within a blockade volume. For a small number, the system favors a disordered arrangement of Rydberg atoms, whereas in the opposite limit, Rydberg atoms tend to arrange in an increasingly ordered configuration. We argue that this is an entropic effect which is observable in current experiments. Our work demonstrates how ordered structures can spontaneously emerge in a strongly interacting, closed many-body system out of equilibrium.