Two-body Förster resonance involving Rb $nD$ states in a quasi-electrostatic trap

In this work, we excite $n{D}_{5/2}$ Rydberg states in a dense and cold Rb atomic sample held in a 10.6 $\mu \mathrm{m}$ quasi-electrostatic trap using narrow-bandwidth laser pulses. Our goal is to study the Förster resonance process $n{D}_{5/2}+n{D}_{5/2}\to (n-2)F+(n+2)P_{3/2}$ at zero electric field as a function of the total atomic density using pulsed-field ionization in the range $n=37–47$. Such a process is almost degenerate for $n=43$. Younge and coworkers studied this process [K. C. Younge, A. Reinhard, T. Pohl, P. R. Berman, and G. Raithel, Phys. Rev. A 79, 043420 (2009)] and attributed the observed saturation to many-body effects. Our results show that as the ground-state atomic density increases, the $n{D}_{5/2}$ state population and the population transfer starts to saturate, which is consistent with the onset of Rydberg atom blockade and previously published results. However, since our experiment allows the independent measurement of the $n{D}_{5/2}$ and $(n+2)P_{3/2}$ state populations, we were able to obtain the $(n+2)P_{3/2}$ state population density dependence. Our results clearly show that the $(n+2)P_{3/2}$ state population depends quadratically on the total Rydberg atomic population, and consequently, the Förster resonance is a two-body process for a ground-state atomic density below $3\times {10}^{11}$ ${\mathrm{cm}}^{-3}$.

Figure 1

(a) Experimental time sequence. The QUEST phase may be varied up to 2 s. (b) Typical $45P_{3/2}$ signal obtained as a function of QUEST decay time using a boxcar gate.

Figure 2

(a) State-mixing fraction of the $43D_{5/2}$ state and (b) $43D_{5/2}$ and $45P_{3/2}$ populations as function of the ground-state atomic density.

Figure 3

$43D_{5/2}$ population as a function of the ground-state atomic density. The dashed (red) line is obtained from a theoretical classical hard sphere model in the steady state [21, 22]. From this fit, we obtain a blockade radius of about 4 $\mu \mathrm{m}$ for the $43D_{5/2}$ state.

Figure 4

Normalized $45P_{3/2}$ population as a function of the normalized total Rydberg atomic population for $n=43$. The full line is a power-law fit to the total Rydberg atom density at $n=43$, ${\rho }_{43}^{\delta }$, where $\delta$ is a fitting parameter. The fit gives $\delta =1.9\pm 0.2$. The inset shows $\delta$ as a function of $(n+2)$, the full line is obtained considering a two-body interaction.