Radiation trapping in a dense cold Rydberg gas

Cold atomic gases resonantly excited to Rydberg states can exhibit strong optical nonlinearity at the single-photon level. We observe that in such samples radiation trapping leads to an additional mechanism for Rydberg excitation. Conversely we demonstrate that Rydberg excitation provides an in situ probe of the spectral, statistical, temporal, and spatial properties of the trapped rescattered light. We also show that absorption can lead to an excitation saturation that mimics the Rydberg blockade effect. Collective effects due to multiple scattering may coexist with cooperative effects due to long-range interactions between the Rydberg atoms, adding a new dimension to quantum optics experiments with cold Rydberg gases.

Figure 1

(a) A dense cloud of ground state $|g\rangle =5s^2{}^{1}S_0$ Sr atoms is excited by probe and coupling lasers to the Rydberg state $|r\rangle =5s48s{}^{1}S_0$ via the intermediate state $|e\rangle =5s5p{}^{1}P_1$. An autoionization beam provides spatially resolved Rydberg detection. Rydberg atoms are also excited by rescattered probe light trapped in the cloud leading to (b) a broad component in the excitation spectrum [red (dark gray) shading] in addition to the narrow laser-excited component [blue (light gray) shading]. (c) Increasing optical depth $[b=3$ (red, solid), 6 (blue, dashed) and 14 (purple, dotted)] leads to attenuation of the probe beam (relative intensity $s$) with propagation distance $x$, leading to (d) the confinement of laser-excited Rydberg atoms (density $n_{\mathrm{Ryd}}$) to the edge of the cloud (gray shaded area).

Figure 2

(Left) Mean number of detected ions $\langle N\rangle$ and (right) $Q$ parameter as a function of ${\mathrm{\Delta }}_{\mathrm{P}}$. Gray dashed lines indicate $\pm W_{\mathrm{L}}$. (a) $b=0.7$, solid black line is the OBE model. (b) $b=3$, (c) $b=6$, and (d) $b=14$ (peak ground state density $n_0=1.5\times {10}^{12}{\mathrm{cm}}^{-3}$). Solid blue lines show the two-component OBE model, with blue (light gray) and red (dark gray) shading indicating the laser-excited and pedestal components, respectively. Here $x_0=89\pm 3\mu \mathrm{m}$.

Figure 3

(a) ${\langle N\rangle }_{\mathrm{Max}}$ versus $b$ for the narrow (blue diamonds) and pedestal (red triangles) components for the data in Fig. 2 ($x_0=89\mu \mathrm{m}$). Solid lines indicate the propagation model for the narrow component (upper, purple) and the OBE model for the pedestal (lower, red). (b) $\langle N\rangle$ at ${\mathrm{\Delta }}_{\mathrm{P}}=0$ versus $y$ (gray circles) and corresponding ground-state density profile (shaded area) for a cloud with $x_0=380\pm 4\mu \mathrm{m}$ and $b=8.4$ ($n_0=2\times {10}^{11}{\mathrm{cm}}^{-3}$). Solid purple line is the propagation model fitted to the data at $\left|y\right|>0.1$ mm.

Figure 4

$\langle N\rangle$ as a function of ${\mathrm{\Delta }}_{\mathrm{P}}$ for $\tau =0.5\mu \mathrm{s}$ (a) and $4\mu \mathrm{s}$ (b) (gray circles). Here $x_0=350\pm 4\mu \mathrm{m}$ and $b=17$ ($n_0=4\times {10}^{11}{\mathrm{cm}}^{-3}$). Solid lines are two-component fits with dashed lines indicating the Gaussian pedestal. (c) ${\langle N\rangle }_{\mathrm{Max}}$ versus $\tau$ for the narrow (blue diamonds) and pedestal (red triangles) components. Gray circles are ${\langle N\rangle }_{\mathrm{Max}}$ (narrow) at low $b$. Black solid and dashed lines indicate fits of the OBE model to the narrow component data at low and high $b$, respectively. The red (dark gray) solid line is the pedestal OBE model scaled to fit the data. The blue (light gray) solid line is the result of the MC simulation. (d) Normalized $\langle N\rangle$ versus ${\mathrm{\Delta }}_{\mathrm{P}}$ from the MC simulations, for densities $5\times {10}^9{\mathrm{cm}}^{-3}$ (purple, solid), $5\times {10}^{10}$ (blue, dashed), and $5\times {10}^{11}{\mathrm{cm}}^{-3}$ (red, dotted).

Figure 5

Energy level diagrams for (a) laser excitation of Rydbergs, which form the narrow feature, and (b) excitation of Rydbergs with rescattered field, which form the pedestal feature.