Evolution dynamics of a dense frozen Rydberg gas to plasma

Dense samples of cold Rydberg atoms have previously been observed to spontaneously evolve to a plasma, despite the fact that each atom may be bound by as much as $100{\mathrm{cm}}^{-1}$. Initially, ionization is caused by blackbody photoionization and Rydberg-Rydberg collisions. After the first electrons leave the interaction region, the net positive charge traps subsequent electrons. As a result, rapid ionization starts to occur after $1\mu \mathrm{s}$ caused by electron-Rydberg collisions. The resulting cold plasma expands slowly and persists for tens of microseconds. While the initial report on this process identified the key issues described above, it failed to resolve one key aspect of the evolution process. Specifically, redistribution of population to Rydberg states other than the one initially populated was not observed, a necessary mechanism to maintain the energy balance in the system. Here we report new and expanded observations showing such redistribution and confirming theoretical predictions concerning the evolution to a plasma. These measurements also indicate that, for high $n$ states of purely cold Rydberg samples, the initial ionization process which leads to electron trapping is one involving the interactions between Rydberg atoms.

Figure 1

Binned data showing the dependence of plasma ion number on the total detected ion signal (plasma ions + field ions) for Rb $36d$ at delays of $2\mu \mathrm{s}$ (◆), $5\mu \mathrm{s}$ (●), and $12\mu \mathrm{s}$ (∎) from the laser pulse.

Figure 2

(a) Log-log plots of the threshold number of Rydberg atoms, $N_T$, needed to initiate avalanche ionization for Cs states from $26d$ through $55d$ and $48s$ through $59s$, in a sample with approximately 1% of 300 K Rydberg atoms. These data were obtained at delays between the laser and beginning of the field pulse of $1\mu s$ (∎), $2\mu s$ (•), $5\mu s$ (●), $10\mu s$ (◆), and $20\mu s$ (★) for $nd$ states, and $5\mu s$ (엯) for $ns$ states. (b) Log-log plots of $N_T$ versus $n$ at a delay of $10\mu s$ for purely cold Rydberg samples (◆), and for mixed samples containing approximately 1% of thermal Rydberg atoms (엯). As can be seen, the threshold Rydberg atom numbers are approximately a factor of 2 higher for a purely cold sample. Also shown are fits of $N_T$ versus $n$, which shows $N_T\propto n^{-3.2}$ for a purely cold sample (—) and $N_T\propto n^{-2.1}$ for a mixed sample (---).

Figure 3

Electric field dependence of the plasma ion signal for two different Rydberg states, $41d$ (a) and $32d$ (b). Each graph plots several different initial Rydberg population densities, which are, from top to bottom in each of (a) and (b), $2.5\times {10}^9{\mathrm{cm}}^{-3}$, $1.5\times {10}^9{\mathrm{cm}}^{-3}$, $1.0\times {10}^9{\mathrm{cm}}^{-3}$, and (for $41d$ only) $0.4\times {10}^9{\mathrm{cm}}^{-3}$. The data were obtained at a delay of $10\mu \mathrm{s}$ from the laser pulse, and each data point is averaged over 30 laser shots.

Figure 4

Binned data at a delay of $10\mu \mathrm{s}$ for Rb $$ showing the effect of rf fields on the spontaneous plasma formation process. Data taken with no rf present are denoted by ◆, while data taken with a 100 MHz, 0.5 V∕cm field are shown thus: ★. The data are plotted vs the total detected ion signal (plasma ions + field ions) on the $x$ axis, which is assumed to be equal to the initial Rydberg population.

Figure 5

Averaged positive ion signals (plasma ions plus field ions) from the Rb $44d$ state as a function of delay for different field pulse maximum amplitudes: 310 V∕cm (—), 620 V∕cm (- - -), and 1500 V∕cm (⋯). The adiabatic threshold for ionization of the Rb $44d$ state is 97 V∕cm, and zero on the $y$ axis corresponds to the signal when the dye laser is blocked.

Figure 6

Averaged positive ion signals (plasma ions plus field ions) from the Rb $44d$ state as a function of delay for different initial Rydberg atom densities. These data were obtained with field ionization pulse amplitudes of 310 V∕cm, a value that is 3.2 times the adiabatic ionization threshold for $44d$. Zero on the $y$ axis corresponds to the signal when the dye laser is blocked. Each data trace was obtained by placing different neutral density filters in the dye laser beam. The average Rydberg atom densities are (from top to bottom) $4.0\times {10}^9{\mathrm{cm}}^{-3}$, $1.3\times {10}^9{\mathrm{cm}}^{-3}$, $7.2\times {10}^8{\mathrm{cm}}^{-3}$, and $4.0\times {10}^8{\mathrm{cm}}^{-3}$.

Figure 7

Averaged electron field ionization signals from the $44d$ state at a delay of 100 ns between the laser pulse and the beginning of the field ionization pulse, obtained with a maximum field of 1500 V∕cm. Data were obtained with different initial Rydberg atom densities using neutral density filters placed in the pulsed laser beam. The atom densities relative to that when the laser was unattenuated are given by ${10}^{-D}$, where $D$ is the filter density. We show data for (a) $D=2.5\Rightarrow 1.3\times {10}^7{\mathrm{cm}}^{-3}$, (b) $D=1.5\Rightarrow 1.3\times {10}^8{\mathrm{cm}}^{-3}$, (c) $D=1.0\Rightarrow 4.0\times {10}^8{\mathrm{cm}}^{-3}$, (d) $D=0.5\Rightarrow 1.3\times {10}^9{\mathrm{cm}}^{-3}$, and (e) no ND filter, $D=0\Rightarrow 4.0\times {10}^9{\mathrm{cm}}^{-3}$. We also show the field ionization pulse (f), which has a maximum amplitude of 1500 V∕cm. The horizontal dashed lines in (d) and (e) show the zero level of the electron signal.

Figure 8

Averaged electron field ionization signals from the $44d$ state at various delays between the laser pulse and the beginning of the field ionization pulse, obtained with a maximum field of 1500 V∕cm and a density of $4.0\times {10}^9{\mathrm{cm}}^{-3}$ [except for the dotted line in (a)]. Data were obtained at delays of (a) 100 ns, for which data are shown with the dye laser pulse unattenuated (solid line), and attenuated with a $D=2.5$ filter to a density of $1.3\times {10}^7{\mathrm{cm}}^{-3}$ (dotted line), (b) $1\mu \mathrm{s}$, (c) $5\mu \mathrm{s}$, and (d) $30\mu \mathrm{s}$. The horizontal dashed lines in (b), (c), and (d) show the zero level of the electron signal.

Figure 9

Averaged electron field ionization signals from the $44d$ state at various delays between the laser pulse and the beginning of the field ionization pulse and various initial Rydberg-atom number densities, obtained with a maximum field of 105 V∕cm. We show data for (a) a delay of 100 ns and $D=2.0\Rightarrow 4.0\times {10}^7{\mathrm{cm}}^{-3}$, (b) a 100 ns delay and $D=1.5\Rightarrow 1.3\times {10}^8{\mathrm{cm}}^{-3}$, (c) a delay of 100 ns and $D=1.0\Rightarrow 4.0\times {10}^8{\mathrm{cm}}^{-3}$, (d) a delay of 100 ns and no ND filter $\Rightarrow 4.0\times {10}^9{\mathrm{cm}}^{-3}$, (e) a delay of $1\mu \mathrm{s}$ and no ND filter, and (f) a delay of $5\mu \mathrm{s}$ and no ND filter. For reference, we also show the field ionization pulse (g), which has a maximum amplitude of 105 V∕cm. The horizontal dashed lines show the zero levels of the electron signal.