Coherent Population Trapping with Controlled Interparticle Interactions

We investigate coherent population trapping in a strongly interacting ultracold Rydberg gas. Despite the strong van der Waals interactions and interparticle correlations, we observe the persistence of a resonance with subnatural linewidth at the single-particle resonance frequency as we tune the interaction strength. This narrow resonance cannot be understood within a mean-field description of the strong Rydberg–Rydberg interactions. Instead, a many-body density matrix approach, accounting for the dynamics of interparticle correlations, is shown to reproduce the observed spectral features.

Figure 1

(a) Excitation scheme (${}^{87}\mathrm{Rb}$). ${\Omega }_1$ and ${\Omega }_2$ are the Rabi frequencies at 780 and 480 nm, respectively, $\delta$ is the detuning of the upper transition; (b) calculated Rydberg state population, produced by the two-step sequence described in the text. The upper panel shows the result of a mean-field calculation, which predicts a strong shift and broadening of the resonance line. On the contrary, the exact result within a two-atom model (lower panel) yields an unshifted narrow interaction independent resonance and an additional resonance at $\delta =V(R)/h$ with $V(R)$ being the (repulsive) two-body interaction energy at an interparticle distance $R$.

Figure 2

Excitation blockade of the Rydberg state $61S$ (filled squares) in comparison to the excitation of the $30S$ state (filled circles) after the first (resonant) excitation pulse. While the $30S$ state shows no saturation, the solid line in the $61S$ data shows a heuristic saturation function $\propto 1/(1+{\rho }_{\mathrm{bl}}/\rho )$ from which a blockade density ${\rho }_{\mathrm{bl}}\approx 1.3\times {10}^9{\mathrm{cm}}^{-3}$ is derived.

Figure 3

(a) Probe scan of the $30S$ Rydberg state (upper graph) and simulation using one-atom optical bloch equations (lower graph), averaged over the Gaussian distribution of ${\Omega }_2$. The $30S$ state is subject to stronger decay and redistribution than the $61S$ state, which is why the dip in the signal around the central peak is less pronounced. (b) Upper graphs: Similar scans for the $61S$ Rydberg state at different densities. Middle graphs: Theoretical spectra, obtained from the density matrix expansion (red dots) and from the mean-field calculation (green dashed lines). Lower graphs: Theoretical spectra considering only interacting pairs. All calculations have been performed using the experimental parameters. Densities are given relative to ${\rho }_{\mathrm{bl}}=1.3\times {10}^9{\mathrm{cm}}^{-3}$.

Figure 4

The width of the narrow line in the measured $61S$ spectra (red squares) shows a weak density dependence and lies below the natural linewidth of the intermediate state. In comparison, the noninteracting $30S$ state does not show a significant change of the linewidth with density (blue circles). The many-body simulation (solid red curve) reproduces the slight increase of the linewidth for $61S$ whereas the mean-field model (dashed green line) predicts a much stronger density dependence. The black dash-dotted line shows the simulation results for vanishing laser linewidths. All values are FWHM determined from fitting the sum of two Gaussians of opposite sign.