Superradiance in ultracold Rydberg gases

Experiments in dense, ultracold gases of rubidium Rydberg atoms show a considerable decrease of the radiative excited state lifetimes compared to dilute gases. This accelerated decay is explained by collective and cooperative effects, leading to superradiance. A formalism to calculate effective decay times in a dense Rydberg gas shows that for these atoms the decay into nearby levels increases by up to three orders of magnitude. Excellent agreement between theory and experiment follows from this treatment of Rydberg decay behavior.

Figure 1

(Color online) Measured and calculated decay of the number of atoms in Rydberg states with $n\ge 27$ following excitation to $n=43p$. The initial density of Rydberg atoms in the experiment is $5\times {10}^8{\mathrm{cm}}^{-3}$. The dots are experimental points with the vertical dashed line showing the start of experimental measurements, and the solid line theoretical simulation. The fitting parameter in this calculation was the number of atoms present at the start of the measurement, i.e., 1400 Rydberg atoms at $6\mathrm{\mu }\mathrm{s}$.

Figure 2

(Color online) Calculated output intensity as function of time for a sample with density $5\times {10}^8{\mathrm{cm}}^{-3}$ for the transition from state $40p$ to $39s$, $37s$, and $6s$, respectively. The initial increase in intensity over time is the sign for superradiance, i.e., the decay into $39s$ and $37s$ qualifies as superradiant, whereas the (very nearly exponential) decay into $6s$ does not.

Figure 3

(Color online) Decay times from $40P$ into various $nS$ states $(◇)$ in a dense gas $(\mathcal{N}=5\times {10}^8{\mathrm{cm}}^{-3})$ and in vacuum $(+)$. The decay times from $40P$ into the corresponding $nD$ states are nearly the same and are therefore not shown.

Figure 4

(Color online) Map of critical parameters of $\mathcal{C}$ and $\varrho$ (solid line). Above the critical curve (shaded area) are the parameters for which superradiance happens. Also shown are the $\mathcal{C}$ and $\varrho$ for the decay to $ns$ states from 40$p$ state $(+)$. Density of atoms is the same as above.