Mesoscopic Rydberg ensembles: Beyond the pairwise-interaction approximation

We examine state mixing in a dense, cold Rydberg gas. Cold Rb atom clouds in an optical dipole trap are excited into $n{D}_{5/2}$ Rydberg levels using narrow-bandwidth laser pulses. For $n=43$, two atoms excited to $43D_{5/2}$ states can be converted to $41F_{7/2}$ and $45P_{3/2}$ product states via a Förster resonance. We find, unexpectedly, that up to 50% of the Rydberg atoms are detected in such product states after only 100 ns of interaction time. The experiment is modeled using many-body quantum simulations. To reproduce the mixing fractions measured near Förster resonances, we use an exact, nonperturbative many-atom Hamiltonian in which product states are treated on an equal basis with the laser-excited $n{D}_{5/2}$ Rydberg level. Simplified many-body interaction models based on sums over pairwise atomic potentials cannot reproduce the measured mixing fractions.

Figure 1

(Color online) Trap images and corresponding field ionization signals for varying trap densities. (a) Shadow images of the dipole trap for expansion times ranging from $10\mu \text{s}$ to $160\mu \text{s}$. Extending the expansion time allows the trap density to be continuously varied. Densities shown range from approximately $1\times {10}^{10}{\text{cm}}^{-3}$ to $4\times {10}^{11}{\text{cm}}^{-3}$. (b) State-selective field ionization (SSFI) signals for (a) high, (b) intermediate, and (c) low density. The SSFI electric field ramp is shown on the right axis. The signals are normalized to equalize the area under each curve.

Figure 2

(Color online) Lorentzian fits for two typical experimental data points. The shaded blue areas are Lorentzian fits to the $P$ signals. (a) Excitation of $43D_{5/2}$ at high density. The individual Lorentzians shown are for the $P$ and $D$ signals. (b) Fitting for nonresonant states $\left(n\ne 43\right)$. To illustrate the overall agreement of the fit with the experimental results, we show the $P$ signal Lorentzian along with the sum of the Lorentzians.

Figure 3

(Color online) Time evolution of theoretical results for a peak density of $4\times {10}^{11}{\text{cm}}^{-3}$ and for the state $43D_{5/2}$. The shaded curve illustrates the Gaussian envelope of the excitation pulse having a peak Rabi frequency of 3 MHz. The solid lines show the calculated time evolution obtained from the CBMBT and the dashed lines show the evolution obtained with theory based on sums over pairwise interactions. (a) Theoretical state mixing fraction calculated via the two presented theories and experimental result for the final mixing value shown as a horizontal bar. The width of the bar reflects experimental uncertainty. (b) Theoretical Rydberg excitation number.

Figure 4

(Color online) Comparison of mixing predicted by theory based on sums over pairwise interactions (green circles), CBMBT (red diamonds), and experimental results (blue line with open circles). (a) Mixing vs density for excitation of $43D_{5/2}$. (b) Mixing vs principal quantum number $n$ for excitation of states near the resonance of Eq. (1). Error bars are given by the uncertainty in fit parameters as discussed in the text.