Role of multilevel Rydberg interactions in electric-field-tuned Förster resonances

In this work, we investigate the dc electric-field dependence of two Förster resonant processes in ultracold ${}^{85}\mathrm{Rb}$, $37D_{5/2}+37D_{5/2}\to 35L(L=O,Q)+39P_{3/2}$, as a function of the atomic density. At low densities, the $39P_{3/2}$ yield as a function of electric field exhibits resonances. With increasing density, the linewidths increase until the peaks merge. Even under these extreme conditions, where the Förster resonance processes show little electric-field dependence, the $39P_{3/2}$ population depends quadratically on the total Rydberg atom population, suggesting that a two-body interaction is the dominant process. In order to explain our results, we implement a theoretical model which takes into account the multilevel character of the interactions and Rydberg atom blockade process using only atom pair interactions. The comparison between the experimental data and the model is very good, suggesting that the Förster resonant processes are dominated by two-body interactions up to atomic densities of $3.0\times {10}^{12}{\mathrm{cm}}^{-3}$.

Figure 1

State-mixing fraction as a function of dc electric field as a function of the atomic density. The resonances involving $L=O,Q$ are labeled. In the inset, we show the normalized $39P_{3/2}$ population as a function of the normalized total Rydberg atomic population for two different electric fields, off resonance at $1.51\text{V}{\text{cm}}^{-1}$ and on resonance at $1.61\text{V}{\text{cm}}^{-1}$.

Figure 2

$37D_{5/2}$ and $39P_{3/2}$ state normalized populations as a function of the Rydberg excitation laser frequency on the Förster resonance at $1.61\text{V}{\text{cm}}^{-1}$. The $37D_{5/2}$ state population shows saturation behavior, which is due to the Rydberg atom blockade. The points are the experimental data and the line is the theoretical model. The density for this measurement is $3\times {10}^{12}{\mathrm{cm}}^{-3}$. The signals are normalized to the peak $37D_{5/2}$ signal. No other free parameters are used to generate the theoretical graphs. The frequency zero is set at the $37D_{5/2}$ atomic resonance at zero electric field.

Figure 3

Experimental and calculated state-mixing fraction as a function of electric field, with an excitation laser detuning of $0\mathrm{MHz}$ from the $37D_{5/2}$ resonance at densities ranging from $1.2\times {10}^{10}\mathrm{t}\mathrm{o}3\times {10}^{12}{\mathrm{cm}}^{-3}$. Two resonances appear in the density range shown; as the density is increased these resonances merge. The dashed lines represent the lower and upper boundary of the atomic density uncertainty.