Cold-Rydberg-gas dynamics

Using state-selective field ionization, the state distributions of Rydberg atoms in cold Rydberg gases are measured for various initially excited Rydberg levels, populations, and evolution times. We provide direct experimental evidence for $l$-changing collisions that we previously observed indirectly [S. K. Dutta, D. Feldbaum, A. Walz-Flannigan, J. R. Guest, and G. Raithel, Phys. Rev. Lett. 86, 3993 (2001)]. We also observe $n$-mixing and find that its effects are largely in agreement with recent theoretical work on $n$-changing collisions between electrons and Rydberg atoms, thus enabling an estimation of the electron temperature. Unexpectedly large populations of atoms are found in states with principal quantum numbers much lower than that of the initially excited atoms. We explain this observation by collisions between high-$l$ Rydberg atoms, which are highly polar and can collide due to static electric-dipole forces between them.

Figure 1

(a) Top view, in cross section, and (b) side view of the experimental setup.

Figure 2

Field-ionization spectra for initially excited $51d$ states. Panel (a): FI signal and the FI pulse vs time. The FI pulse arrives $38\mu \mathrm{s}$ after the Rydberg excitation $\left(t\approx 0\right)$. The signal prior to the FI pulse is due to escaping plasma electrons. Panel (b): Field-ionization data of panel (a) mapped into a function of ionization electric field. Note that in (b) all signal prior to the application of the FI pulse is condensed into a single peak at $0\mathrm{V}∕\text{cm}$ (and therefore is hardly visible). The traces $A–E$ correspond to the following initial Rydberg-atom populations $N_{\mathrm{R}}$ and densities ${\rho }_{\mathrm{R}}$. $A$, $N_{\mathrm{R}}$ and ${\rho }_{\mathrm{R}}$ very small; $B$, $N_{\mathrm{R}}=5.5\times {10}^2$ and ${\rho }_{\mathrm{R}}=2.7\times {10}^8{\text{cm}}^{-3}$; $C$, $N_{\mathrm{R}}=5.4\times {10}^3$ and ${\rho }_{\mathrm{R}}=5.9\times {10}^8{\text{cm}}^{-3}$; $D$, $N_{\mathrm{R}}=7.0\times {10}^5$ and ${\rho }_{\mathrm{R}}=2.2\times {10}^9{\text{cm}}^{-3}$; $E$: $N_{\mathrm{R}}=3.3\times {10}^6$ and ${\rho }_{\mathrm{R}}=9.6\times {10}^8{\text{cm}}^{-3}$.

Figure 3

Field-ionization spectra for initially excited $65d$ states. Panel (a): FI signal and FI pulse vs time. The FI pulse, indicated by the dashed line, arrives $18\mu \mathrm{s}$ after the Rydberg excitation $(t\approx 0)$. Panel (b): FI data of panel (a) mapped as a function of ionization electric field. In (b), all signal arriving prior to the application of the FI pulse is condensed into a single peak at $0\mathrm{V}∕\text{cm}$ (and therefore is hardly visible). The traces $A–E$ correspond to the following initial Rydberg-atom populations $N_{\mathrm{R}}$ and densities ${\rho }_{\mathrm{R}}$. $A$, $N_{\mathrm{R}}$ and ${\rho }_{\mathrm{R}}$ very small; $B$, $N_{\mathrm{R}}=8.4\times {10}^2$ and ${\rho }_{\mathrm{R}}=1.0\times {10}^8{\text{cm}}^{-3}$; $C$, $N_{\mathrm{R}}=1.1\times {10}^4$ and ${\rho }_{\mathrm{R}}=7.6\times {10}^8{\text{cm}}^{-3}$; $D$, $N_{\mathrm{R}}=2.2\times {10}^5$ and ${\rho }_{\mathrm{R}}=2.7\times {10}^9{\text{cm}}^{-3}$; $E$, $N_{\mathrm{R}}=1.1\times {10}^6$ and ${\rho }_{\mathrm{R}}=1.1\times {10}^9{\text{cm}}^{-3}$. As indicated by the shaded regions, in traces $B$, $C$ and $D$ at least $29\%$, $33\%$, and $75\%$ of the remaining Rydberg atoms have been transferred to lower-$n$ states, respectively.

Figure 4

FI signal from a Rydberg gas with initial state $64d$ shown for the indicated delay times, $\tau$, between the Rydberg excitation and the FI pulse for fixed $N_{\mathrm{R}}=3.7\times {10}^6$ and ${\rho }_{\mathrm{R}}=7.8\times {10}^8{\text{cm}}^{-3}$. Panel (a): FI signal (solid lines) and FI pulse (dashed line) vs time. The onset of the FI pulse is at $\mathrm{t}\approx 0$. Panel (b): data of (a) represented as a function of ionization electric field. In all cases except trace $F$, the delay time $\tau$ is equivalent to the interaction time $t_{\mathrm{int}}$ between the trapped electrons and the Rydberg-atom gas. The shaded regions in panel (a) indicate the signal from atoms which have been transferred to states with $n⪡n_0$. The percentages of the latter vs the total Rydberg population at the onset of the FI pulse are at least $23\%$, $50\%$, $68\%$, $81\%$, $78\%$, $64\%$ for traces $A–F$, respectively [3, 5].

Figure 5

Simulations of FI signals due to inelastic collisions between electrons and $51d$ Rydberg atoms, compared with the experimental data in trace $B$ in Fig. 2a. Simulations for three different electron energies are shown: $k_{\mathrm{B}}{T}_{\mathrm{e}}=1\text{meV}$, $3\text{meV}$, and $10\text{meV}$. Each simulation result is scaled such that its integral equals that of the experimental result over the region of comparison.

Figure 6

Field-ionization spectra for initially excited $38d$ states, clearly showing population redistribution to several resolved higher-$n$ states. The FI pulse, indicated by the dashed line, starts at $35\mu \mathrm{s}$ after the Rydberg excitation. Trace $A$: Initial Rydberg atom population $N_{\mathrm{R}}=1.1\times {10}^6$ and density ${\rho }_{\mathrm{R}}=1.0\times {10}^9{\text{cm}}^{-3}$. Trace $B$: Reference signal obtained with very small $N_{\mathrm{R}}$ and ${\rho }_{\mathrm{R}}$.