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.

Figure 1

Excitation blockade and Tonks gas. Ground-state atoms within a blockade radius $l_{\mathrm{b}}$ from a Rydberg atom (red solid circle) cannot be excited to a Rydberg state. This defines a blockade volume of size $2l_{\text{b}}$ around each excited atom (orange ellipses), in which a single Rydberg excitation is shared between all particles. Certain sites may be located in the intersection of two blockade volumes (gray circles). In order to count the number of possible arrangements of Rydberg atoms, it is convenient to map the system to a Tonks gas of nonoverlapping hard rods (blue rectangles) of length $l_{\text{b}}$.

Figure 2

Probability for finding configurations with a given density $\rho$ of Rydberg atoms for different values of $\sigma l_{\mathrm{b}}$ in a system of length $L=200\times l_{\mathrm{b}}$. For a small number of ground state atoms within a blockade radius ($\sigma l_{\mathrm{b}}$), the function peaks at small densities $\rho \ll l_{\mathrm{b}}^{-1}$ (see top left panel for three typical configurations). When $\sigma l_{\mathrm{b}}$ grows, the relative weight of configurations with a large Rydberg density $\rho \sim l_{\mathrm{b}}^{-1}$ increases dramatically. Here a huge number of configurations with nearly crystalline arrangement exist (see top right panel for three examples). Hence, when all configurations are populated with equal probability, a state with high density and enhanced spatial correlations is entropically favored.

Figure 3

Density-density correlation function obtained from a Monte Carlo simulation for a sample of length $L=10\times l_{\mathrm{b}}$ (periodic boundary conditions) and atomic densities corresponding to $\sigma l_{\mathrm{b}}=\{1,5,30\}$. The larger the number of ground state atoms per blockade radius $\sigma l_{\mathrm{b}}$, the more pronounced become the oscillations of the spatial correlations.

Figure 4

Density-density correlation function for a sample of length $L=10\times l_{\mathrm{b}}$ (periodic boundary conditions) and an atomic density of $\sigma l_{\mathrm{b}}=7$. The crosses are obtained from a time-averaged quantum calculation using Hamiltonian (2) and the empty state $\left|0\right.〉$ as an initial state. The solid curve interpolates data obtained from a (classical) Monte Carlo simulation for the same parameters.