Heating and cooling of electrons in an ultracold neutral plasma using Rydberg atoms

E. V. Crockett, R. C. Newell, F. Robicheaux, and D. A. Tate

Phys. Rev. A 98, 043431 – Published 24 October 2018

Abstract

We have experimentally demonstrated both heating and cooling of electrons in an ultracold neutral plasma (UNP) by embedding Rydberg atoms into the plasma soon after its creation. We have determined the relationship between the initial electron temperature, $T_{e, i}$ , and the binding energy of the added Rydberg atoms, $E_{b}$ , at the crossover between heating and cooling behaviors (that is, the binding energy of the atoms, which, when they are added to the plasma, neither accelerate nor slow down the plasma expansion). Specifically, this condition is $| E_{b} | \approx 2.7 \times k_{B} T_{e, i}$ when the diagnostic used is the effect of the Rydberg atoms on the plasma asymptotic expansion velocity. Additionally, we have obtained experimental estimates for the amount of heating or cooling which occurs when the Rydberg binding energy does not satisfy the crossover condition. The experimental results for the crossover condition, and the degree of heating or cooling away from the crossover, are in agreement with predictions obtained from numerical modeling of the interactions between Rydberg atoms and the plasma. We have also developed a simple intuitive picture of how the Rydberg atoms affect the plasma, which supports the concept of a “bottleneck” in the Rydberg state distribution of atoms in equilibrium with a coexisting plasma.

Received 15 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.043431

Physics Subject Headings (PhySH)

Electronic excitation & ionization Single- and few-photon ionization & excitation

Rydberg atoms & molecules Ultracold gases

Atomic, Molecular & Optical

Authors & Affiliations

E. V. Crockett^1,*, R. C. Newell^1,†, F. Robicheaux², and D. A. Tate^1,‡

¹Department of Physics and Astronomy, Colby College, Waterville, Maine 04901, USA
²Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA

^*Present address: Lincoln Financial Group, Boston, MA 02110, USA.
^†Present address: Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA.
^‡duncan.tate@colby.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 4 — October 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Experimental electron TOF spectra of bare and embedded plasmas. (a) Electron signal detected by the MCP for UNPs with initial average ion density $ρ_{i o n} = 4.4 \times 10^{7} {cm}^{- 3}$ and $T_{e, i} = 20$ , 50, and 90 K with no Rydberg atoms added (solid red line) and with $40 d$ atoms added with $N_{R} / N_{i o n} = 0.28$ (blue dashed line). At top is the TOF signal with only the NBPL laser exciting the $40 d$ state, multiplied by 10, showing that there is no spontaneous plasma formation from a sample of cold $40 d$ atoms with density $1.2 \times 10^{7} {cm}^{- 3}$ . The short fat black $↑$ and $↓$ arrows on the 20 K and 90 K TOF spectra represent the change (increase or decrease, respectively) in the electron signal at early and late times when Rydberg atoms are added. The red (solid) and blue (dashed) arrows represent the approximate lifetimes of the bare plasma, and the embedded plasma, respectively. (b) Data for UNPs embedded with $40 d$ Rydberg atoms, plotted in terms of a $y$ coordinate which is the remaining electron fraction, $δ$ , defined using Eq. (6). The red (open) symbols show the results for the bare plasma, while the blue (filled) symbols show the results for the plasma when Rydberg atoms are added, and the $T_{e, i}$ values are as shown in the legend. The uncertainty of the $δ$ values at a given flight time is at the $\pm 0.01$ level, approximately equivalent to the symbol size in each plot (see Sec. 3a for a discussion of how these uncertainties are obtained). (c) Plot of $δ$ vs time for UNPs with different $T_{e, i}$ values when $27 d_{5 / 2}$ atoms are added, for $ρ_{i o n} = 2.1 \times 10^{7} {cm}^{- 3}$ and $N_{R} / N_{i o n} = 0.19$ . (d) Enlargement of the data in panel (c) in the region around $δ = 0.5$ [the data set in panel (d) is more extensive than that in panel (c)]. The black $- \cdot -$ line shows the approximate location of the crossover condition, where the addition of the Rydberg atoms does not affect the electron TOF signal and the horizontal black dashed line shows the condition $δ = 0.5$ . The black circle at the intersection of these lines is the crossover point, and $T_{C O}$ when $27 d_{5 / 2}$ atoms are added to a UNP is the value of $T_{e, i}$ for a bare plasma that reaches $δ = 0.5$ at a time of $40 μ s$ . From these data, using interpolation as described in the text, we obtain $T_{C O} = 94 \pm 11$ K for a UNP with $27 d_{5 / 2}$ atoms embedded in it.
Reuse & Permissions
Figure 2
Experimental ion TOF spectra for UNPs embedded with $40 d_{5 / 2}$ atoms ( $| E_{b} | / k_{B} = 106$ K). The red solid lines are the TOF signals for the bare (nonembedded) plasmas, and the blue dashed lines are for the embedded plasmas. The $T_{e, i}$ values defined using Eq. (2) are shown on each trace (the uncertainty in $T_{e, i}$ is $\pm 5$ K). As with the electron TOF spectra shown in Fig. 1, the crossover condition is somewhere in the range $T_{e, i} = 40$ –50 K. For these data, $N_{i o n} = 4 \times 10^{5}$ (initial average $ρ_{i o n} = 4.5 \times 10^{7} {cm}^{- 3}$ ), and $N_{R} / N_{i o n} = 0.18$ . These ion TOF spectra were averaged over 128 laser shots, and the TOF spectra were also subsequently smoothed by averaging them over five adjacent time points (the time resolution of the raw data was 128 ns).
Reuse & Permissions
Figure 3
(a) Experimental and numerical results for the crossover electron temperature, $T_{C O}$ , vs the magnitude of the binding energy of the added Rydberg atoms in units of K, $| E_{b} | / k_{B}$ . Inset (b) is an enlargement of the region $| E_{b} | / k_{B} \leq 200$ K, $T_{C O} \leq 110$ K on a log-log scale. In both graphs, the experimental results are shown for electrons ( $◊$ ) and ions ( $⧫$ ) when the effective initial electron temperature of the plasma, $T_{e, 0}$ , is the marker parameter. The average ion densities for these data are in the range $3 - 7 \times 10^{7} {cm}^{- 3}$ , and $σ_{0} \approx 550 μ m$ . The black dotted line is a weighted fit to the experimental electron data, and the black dash-dot-dashed line is a fit to the experimental ion data. The simulation results are for the crossover conditions for the marker parameters electron temperature and electron Coulomb coupling parameter at 100 ns, $T_{0.1}$ and $Γ_{0.1}$ respectively, the electron temperature and coupling parameter at $9.9 μ s, T_{9.9}$ and $Γ_{9.9}$ respectively, as well as the value of $T_{e, 0}$ found from the average expansion velocity over 9.9 to $19.9 μ s$ of evolution time. The simulations were run with ion densities in the range $0.3 - 3 \times 10^{8} {cm}^{- 3}$ and $σ_{0} = 354 μ m$ . The legend gives the average ion density, $ρ_{i o n}$ , and the ratio of Rydberg atoms to ions, $N_{R} / N_{i o n} = 0.2$ or 0.3, for the simulations. The experimental vertical error bars are as shown, while the horizontal error bars are negligible (see Secs. 3 A, B, and C for an explanation of how the error bars were obtained). The simulation error bars are not shown: The $T_{C O}$ values are known exactly since this was set as an initial condition in each simulation, while the uncertainty in the $| E_{b} | / k_{B}$ values is $\pm 2.5$ K for $| E_{b} | / k_{B} = 100$ K and $\pm 25$ K for $| E_{b} | / k_{B} = 500$ K, equivalent to one half of the adjacent Rydberg state energy spacing. The parameter space to the left of a line for a given marker on the graph corresponds to cooling of the plasma as measured using that marker (i.e., the marker reaches a particular value at a longer evolution time when Rydberg atoms are added to the plasma than for the bare plasma) while to the right of the line corresponds to heating.
Reuse & Permissions
Figure 4
(a) Experimental electron TOF spectra plotted in terms of the remaining electron fraction when $50 d$ Rydberg atoms are added to UNPs with various $T_{e, i}$ values as shown in the legend, when $N_{R} / N_{i o n} = 0.4$ and $ρ_{i o n} = 4.0 \times 10^{7} {cm}^{- 3}$ . The red (open) symbols show the results for the bare plasma, while the blue (filled) symbols show the results for the plasma when Rydberg atoms are added. (b) Ion TOF spectra when $32 d$ Rydberg atoms are added to UNPs with $T_{e, i}$ values as shown for $N_{R} / N_{i o n} = 0.7$ and $ρ_{i o n} = 4.4 \times 10^{7} {cm}^{- 3}$ . The TOF spectra for the bare plasmas are shown by a solid red line; the spectra for the UNPs embedded with Rydberg atoms are shown by the blue dashed lines. As can be seen in both the electron and the ion TOF spectra when Rydberg atoms are embedded, there is hardly any variation in the spectra with $T_{e, i}$ , indicating that the plasma behavior is almost completely controlled by the added Rydberg atoms.
Reuse & Permissions
Figure 5
(a) The effect of varying Rydberg atom density (relative to ion density) when $27 d_{5 / 2}$ atoms are added to UNPs with $T_{e, i}$ values as shown. The average ion density for these data is $(2.8 \pm 0.7) \times 10^{8} {cm}^{- 3}$ and $σ_{0} = 560 \pm 40 μ m$ . The $T_{e, i}$ values are set by the frequency of the photoionization laser, and $T_{e, 0}$ is found using Eq. (3) and the $v_{0}$ values obtained from fitting the ion TOF spectra (we assume $T_{i o n, 0} = 0$ ). The black dashed line corresponds to $T_{e, 0} = T_{e, i}$ , and the fact that the results with $N_{R} = 0$ are consistently 20 K above this line indicates a likely systematic effect in the measurement technique. (b) Slope of $T_{e, 0}$ vs $T_{e, i}$ found from straight line fits of the data in (a) vs $N_{R} / N_{i o n}$ . The black diamonds are the experimental data [i.e., those in panel (a), plus two additional data sets]. The other symbols, connected by the dashed lines, are results of simulations described in Sec. 4c with initial average ion density and $σ_{0}$ values as shown. The black dashed line is a fit to the experimental data with slope $= - 1.6 \pm 0.3$ and intercept $= 0.96 \pm 0.08$ . The vertical and horizontal error bars for the experimental data in panels (a) and (b) are discussed in Sec. 3d. The uncertainties of the simulation data in panel (b) are discussed in Sec. 4c.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information