Collective Excitation of Rydberg-Atom Ensembles beyond the Superatom Model

In an ensemble of laser-driven atoms involving strongly interacting Rydberg states, the steady-state excitation probability is usually substantially suppressed. In contrast, here we identify a regime in which the Rydberg excited fraction is enhanced by the interaction. This effect is associated with the buildup of many-body coherences induced by coherent multiphoton excitations between collective states. The excitation enhancement should be observable under currently existing experimental conditions and may serve as a direct probe for the presence of coherent multiphoton dynamics involving collective quantum states.

Figure 1

(a) Illustration of the setup: Three-level atoms with the Rydberg state $|r⟩$. The blockade radius exceeds the trap size such that at most one atom can be in the Rydberg state. (b) Steady-state values of the Rydberg fraction for $N=4$ atoms as a function of the probe Rabi frequency ($\mathrm{\Delta }=0$). The coherent laser driving is strong compared to the decay rate $\mathrm{\Gamma }$ of the intermediate level. Solid black line: Rydberg fraction $f_r$ predicted by the exact ME solution. Red dashed line: Result $f_{\mathrm{SA}}$ of a SA model with $\sqrt{N}$-enhanced ${\mathrm{\Omega }}_p$. Blue dot-dashed line: Rydberg fraction $f_0$ for noninteracting atoms. Black dotted line: Analytical expansion of $f_r$ in the weak probe limit. The gray shading denotes the region of interaction-induced enhancement beyond the noninteracting value.

Figure 2

(a) Level scheme of symmetrized (Dicke) states. Diagonalizing the horizontal couplings (${\mathrm{\Omega }}_c$) in a perfectly blockaded ensemble, a dressed state picture is obtained. (b),(c) Dressed state energies as a function of the detuning from the intermediate state $\mathrm{\Delta }$ in the (b) noninteracting and (c) blockaded cases. In the blockaded case resonances between the state $|G⟩$ and the doubly excited dressed states (red) occur at $\mathrm{\Delta }\approx \pm {\mathrm{\Omega }}_c/2$ (circles). Gray dotted lines show bare energies (or asymptotes). (d) Rydberg fraction as a function of $\mathrm{\Delta }$. The parameters are as in Fig. 1. Solid black line: Exact ME solution. Red dashed line: Result of the SA model. Blue dot-dashed line: $f_0$. Black dotted line: Analytical model. The resonances between the dressed Dicke states result in a large excitation enhancement in comparison to the noninteracting Rydberg fraction.

Figure 3

(a) Dissipative phase diagram showing the enhancement factor $f_r/f_0$ as a function of Rabi frequencies for $N=4$ atoms and $\mathrm{\Delta }=0$. For strong coherent driving and weak probe field, a region of $f_r>f_0$ is encountered. The dashed line shows the transition from suppressed to enhanced excitation ($f_r=f_0$). The arrow marks the critical value of ${\mathrm{\Omega }}_c/\mathrm{\Gamma }\approx 1.27$. (b) Maximal value of $f_r/f_0$ as a function of atom number $N$. (c) Few atoms ($N=4$) in a spherical volume of varying radius with random position sampling. The possibility for multiple Rydberg excitations is included in the simulation, and realistic values for the laser dephasings and the spontaneous decay rate of the Rydberg state have been used (see text for details). The parameters correspond to the black cross (lower black curves) and plus sign (upper red curves) in (a). For the higher Rabi frequencies, the excitation enhancement is present at all sphere radii (densities). Dashed lines show the predictions of the rate equation model, which coincide with the SA model in the case of full blockade (dotted lines).