Dipole-Dipole Excitation and Ionization in an Ultracold Gas of Rydberg Atoms

In cold dense Rydberg atom samples, the dipole-dipole interaction strength is effectively resonant at the typical interatomic spacing in the sample, and the interaction has a $1/R^3$ dependence on interatomic spacing $R$. The dipole-dipole attraction leads to ionizing collisions of initially stationary atoms, which produces hot atoms and ions and initiates the evolution of initially cold samples of neutral Rydberg atoms into plasmas. More generally, the strong dipole-dipole forces lead to motion, which must be considered in proposed applications.

Figure 1

(a) Potential energy curves for the coupled $46d46d$, $48p44f$, and $47p45f$ pairs. The dipole-dipole coupling exceeds the zero field $46d46d\mathrm{\text{−}}48p44f$ splitting at $R_{\mathrm{vdw}}=2.5\mu \mathrm{m}$, shown by the arrow. Pairs on the attractive potential spaced by $R$ less than $1.7\mu \mathrm{m}$ move to small separation, collide, and ionize in less than 300 ns. (b) Potentials for the $48s48s$ and $47p48p$ pairs. In this case, $R_{\mathrm{vdw}}=1.1\mu \mathrm{m}$, as shown by the arrow. Pairs on the attractive potential spaced by $1.7\mu \mathrm{m}$ require 500 ns to collide.

Figure 2

Time resolved electron signals with the field ionization pulse 250 ns delayed from the laser excitations. (a) $48s$ initial state at density of $5\times {10}^9$ (solid line), $1.5\times {10}^9$ (dashed line), and $2\times {10}^8$ (dotted line) $\mathrm{\text{atoms}}/{\mathrm{cm}}^3$, respectively; (b) $46d$ initial state at density of $5\times {10}^9$ (solid line), $1.5\times {10}^9$ (dashed line), and $4\times {10}^8$ (dotted line) $\mathrm{\text{atoms}}/{\mathrm{cm}}^3$. The population transferred to the high angular momentum states while the plasma is formed is not seen in this spectrum due to the low field ionization field.

Figure 3

Ratio of the free $\mathrm{\text{ion}}+(n+2)p$ signals produced by the resonant dipole-dipole interaction to the total signal 250 ns after laser excitation of the $46d$ (●) and $33d$ (▲) states. The inset shows the time resolved signal for the $46d$ state when the total number of atoms is $5\times {10}^9\mathrm{\text{atoms}}/{\mathrm{cm}}^3$. The slopes of the ratios are linear in the number of atoms, as expected for a binary process, and the ratio of the slopes is 3.4, in agreement with the expected $n^4$ scaling.

Figure 4

(a) Energy levels for the $39s39s\mathrm{\text{−}}39s39p$ transition vs interatomic spacing $R$. (b) Free ion signal vs microwave frequency. A signal is observed only on the low frequency side of the atomic frequency, 68.378 GHz; i.e., only transitions to the attractive curve of (a) are observed. (c) Time resolved electron signals after a $3.5\mu \mathrm{s}$ delay subsequent to exciting the $39s$ state with (solid line) and without (dotted line) the microwave pulse. Without the microwaves, only the $39s$ field ionization signal is observed. With the microwave, a plasma signal at $0.5\mu \mathrm{s}$ relative to the start of the field ionization pulse and the redistribution of the remaining Rydberg population are evident.