Arrested relaxation in an isolated molecular ultracold plasma

Spontaneous avalanche to plasma splits the core of an ellipsoidal Rydberg gas of nitric oxide. Ambipolar expansion first quenches the electron temperature of this core plasma. Then, long-range, resonant charge transfer from ballistic ions to frozen Rydberg molecules in the wings of the ellipsoid quenches the ion-Rydberg-molecule relative velocity distribution. This sequence of steps gives rise to a remarkable mechanics of self-assembly, in which the kinetic energy of initially formed hot electrons and ions drives an observed separation of plasma volumes. These dynamics adiabatically sequester energy in a reservoir of mass transport, starting a process that anneals separating volumes to form an apparent glass of strongly coupled ions and electrons. Short-time electron spectroscopy provides experimental evidence for complete ionization. The long lifetime of this system, particularly its stability with respect to recombination and neutral dissociation, suggests that this transformation affords a robust state of arrested relaxation, far from thermal equilibrium.

Figure 1

Top: experimental setup for the imaging of the molecular beam. The beam enters the experiment chamber through the skimmer and impacts on a MCP stack after a free flight of 468 mm. Free electrons are created, multiplied, and viewed as photons by a CCD camera. Bottom left: CCD response of molecular beam impacting on phosphor screen detector (at a distance of 468 mm from the skimmer) without laser light present. Bottom right: vertical summation over image pixel and fit; fitted Gaussian width is 4.35 mm.

Figure 2

(a) Moving grid time-of-flight molecular-beam plasma spectrometer. Copropagating laser beams, ${\omega }_1$ and ${\omega }_2$, cross the molecular beam between entrance aperture, $G_1$, and grid, $G_2$. (b) Level diagram for double-resonant preparation of a state-selected $n_{0}f\left(2\right)$ Rydberg gas. (c) Excitation spectrum of late-peak intensity as a function of ${\omega }_2$ frequency; structure assigned to the $nf\left(2\right)$ Rydberg series.

Figure 3

(Upper frame) Set of traces showing the charge density and width in $z$ of a plasma formed by avalanche from a $50f\left(2\right)$ Rydberg gas as a function of flight time for a sequence of flight distances to grid $G_2$, in the apparatus pictured in Fig. 2. (Lower frame) Integrated plasma signal obtained as the areas of the traces in the upper frame, plotted as a function of arrival time at $G_2$.

Figure 4

(Left) Selective field-ionization spectra of NO. contour plots showing SFI signal as a function the applied field for an $nf\left(2\right)$ Rydberg gas with an initial principal quantum number, $n_0=44$. Each frame represents 4000 SFI traces, sorted by initial Rydberg gas density. Ramp field potential applied to $G_1$, beginning from left to right, 0, 150, 300, and 450 ns after the ${\omega }_2$ laser pulse. The two bars of signal most evident at early ramp field delay times represent the field ionization of the $44f\left(2\right)$ Rydberg state respectively to ${\mathrm{NO}}^{+}$ $X$ ${}^1{\mathrm{\Sigma }}^{+}$ cation rotational states, $N^{+}=0$ and 2. This signal shifts to higher field with increasing ramp-field delay owing to $\ell$ mixing [31]. The signal waveform extracted near zero applied field represents the growing population of plasma electrons. Refer to Fig. 6 for a false-color scale bar.

Figure 5

Rate equation simulations of the electron-impact avalanche of a Rydberg gas. (Upper curves) Predicted growth in electron density and temperature on a microsecond time scale for a $n_0=50$ Rydberg gas with initial density $\rho =1\times {10}^{10}$ ${\mathrm{cm}}^{-3}$. (Lower curves) Change in electron density and temperature on a nanosecond time scale for Rydberg gases with principal quantum numbers $n_0=30,35,40,50$, and 60 with an initial density $\rho =1\times {10}^{12}$ ${\mathrm{cm}}^{-3}$.

Figure 6

(Left) Self-similar expansion of Gaussian ultracold plasmas. (Gray lines) Ambipolar expansion of a model Gaussian plasma core ellipsoid of cold ions and $T_e=180$ K electrons with ${\sigma }_y\left(0\right)={\sigma }_z\left(0\right)=83\mu \mathrm{m}$ and ${\sigma }_x\left(0\right)=250\mu \mathrm{m}$. Ions rapidly attain ballistic velocities, ${\partial }_t{\sigma }_y={\partial }_t{\sigma }_z=272$ m ${\mathrm{s}}^{-1}$ and ${\partial }_t{\sigma }_x=132$ m ${\mathrm{s}}^{-1}$. (Blue line with red data points) Experimental measure of ${\partial }_t{\sigma }_z\left(t\right)$ fit by Vlasov model for a Gaussian spherical expansion for $T_e=5$ K. (Right) Electron signal as a function of flight time to $G_2$ and Rydberg gas principal quantum number observed in the moving grid apparatus diagramed in Fig. 2 with a constant reverse bias on $G_1$ of 1.20, 0.60, 0.48, and 0.24 V (top row), and forward bias of 0.0, $-0.12$, $-0.24$, and $-0.36$ V, all with a flight distance to $G_2$ of 56 mm.

Figure 7

Plasma bifurcation and recoil: $x,y$ detector images of ultracold plasma volumes produced by 2:1 aspect ratio ellipsoidal Rydberg gases with selected initial state, $40f\left(2\right)$, after a flight time of 402 $\mu \mathrm{s}$ over a distance of 575 mm. Charge distributions bifurcate with increasing recoil velocity as a function of ${\omega }_1$ laser pulse energies of 1.5, 3, 4.5, 6, 7.5, 9, and 12 $\mu \mathrm{J}$. Inset: measured recoil velocity plotted as a function of ${\omega }_1$ laser power. Refer to Fig. 6 for a false-color scale bar.

Figure 8

Long-time dynamics of recoiling plasma volumes. (Left) Electron signal waveforms in $z$ obtained for $n_0=65$ at short and long flight distances. (Right) Expansion measured by ${\sigma }_z\left(t\right)$ compared with the short-time expansion observed in the moving grid spectrometer, and the 14 m ${\mathrm{s}}^{-1}$ expansion in $z$ of the ellipsoidal volume marked by ${\omega }_1$.

Figure 9

Bifurcated traces giving absolute sums of imaging detector columns in $y$ as a function of $x$ for the images pictured in Fig. 7, with centered traces integrating to define a lost electron component that accounts for the charge missing in the image traces as the ${\omega }_1$ power approaches saturation of the $X$ ${}^2\mathrm{\Pi }\to$ $A$ ${}^2{\mathrm{\Sigma }}^{+}$ transition in NO. Missing charge distributed arbitrarily as a Gaussian with the ${\sigma }_x$ of the molecular beam at the point of laser interaction propagated by the beam divergence over the 600 mm flight distance to the detector.

Figure 10

Results of coupled rate-equation simulations describing the relaxation of an $n_0=80$ Rydberg gas of NO (left) and an ultracold plasma of ${\mathrm{NO}}^{+}$ ions and electrons with $T_e\left(0\right)=5$ K (center). Both simulations represent the initial density distribution of particles by a $5\sigma$ Gaussian ellipsoid with principal axis dimensions, ${\sigma }_x=1.0$ mm, ${\sigma }_y=0.55$ mm, and ${\sigma }_z=0.7$ mm, as measured for the plasma represented in Fig. 3 after an expansion of 10 $\mu \mathrm{s}$. Evolution proceeds in 100 concentric shells enclosing set numbers of kinetically coupled particles, linked by a common electron temperature that evolves to conserve energy globally. Upper frames describe the change in electron temperature as a function of time. Lower frames show changes in the total number of ions and electrons, Rydberg molecules, and neutral dissociation products N(${}^{4}S$) and O(${}^{3}P$). The rightmost frame gives the results of a shell-model hydrodynamic simulation of the expansion of a Gaussian ellipsoid with the dimensions measured at 10 $\mu \mathrm{s}$ for the arrested plasma in Fig. 3, assuming an electron temperature that rises to 60 K, with curves, reading from the bottom on the left, for ${\sigma }_y\left(t\right)$, ${\sigma }_x\left(t\right)$, and ${\sigma }_x\left(t\right)$.