Rydberg Polaritons in a Cavity: A Superradiant Solid

We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atom-atom interaction and atom-light coupling induces a rich phase diagram. A novel superradiant solid (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance transition, here both the solid-$1/2$ and SRS to SR phase transitions are first order. These results are confirmed by large scale quantum Monte Carlo simulations.

Figure 1

(a) Schematic diagram of a 1D lattice of atoms trapped inside an ultrahigh finesse optical cavity. Each site is tuned to locate at the antinode of the cavity mode and occupied by a single atom with the ground state $|g⟩$ coupled to a high-lying Rydberg state $|e⟩$ via a two-photon transition process. (b) Setup for the internal energy levels of the atoms, where the cavity mode transits the ground state $|g⟩$ to an intermediate state $|p⟩$ with a large detuning ${\Delta }_p={\omega }_c-{\omega }_{g-p}$ (${\omega }_{g-p}$ is the transition frequency between $|g⟩$ and $|p⟩$ states), while the transition $|p⟩\to |e⟩$ of frequency ${\omega }_{p-e}$ is driven by a laser with Rabi frequency ${\Omega }_l$ and frequency ${\omega }_l$ detuned by ${\Delta }_e={\omega }_l-{\omega }_{p-e}$.

Figure 2

Variational phase diagram for (a) $\Delta =3$, (b) $\Delta =2$, (c) $\Delta =1$, and (d) $\Delta =0.5$. All the parameters are in units of $V$.

Figure 3

(a) The $\mu \mathrm{\text{−}}\overline{g}$ phase diagram obtained by different methods for $V=1$ and $\Delta =3$ in the grand-canonical ensemble. The red solid vertical lines are the traces evaluated in Fig. 4. (b) The $\rho \mathrm{\text{−}}\overline{g}$ phase diagram obtained by QMC simulation. Here, PS denotes the phase separation between the solid-$1/2$, SRS, and SR phase transitions, see the context for detail. (c) The enlarged region of the SRS phase, where the red arrow marks the tricritical point among the SRS, SR, and solid-$1/2$ phases.

Figure 4

The structure factor $S(Q)/N$ (solid line) and compressibility ${\kappa }_T/10$ (dashed line) along the trajectories of the lower (left panel) and upper (right panel) vertical cuts indicated by solid bars in Fig. 3a. Here, the red arrows mark the critical points with $\tilde{\mu }={\tilde{\mu }}_c$. For all cases $V=1$, $\beta =500$, $N=100$, and $\Delta =3$ ($\Delta =2.5$). The inset shows the corresponding average excitation density $\rho$. For simplicity, the small error bars for the observables are not shown here.