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arXiv:1702.01463 · Physical Review A

Expansion of an ultracold Rydberg plasma

Gabriel Forest, Y. Li, Edwin Ward, Anne L. Goodsell, Duncan Tate

Published Apr 2, 2018• 4 citations
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Abstract

We report a systematic experimental and numerical study of the expansion of ultracold Rydberg plasmas. Specifically, we have measured the asymptotic expansion velocities, ${v}_{0}$, of ultracold neutral plasmas (UNPs) which evolve from cold, dense samples of Rydberg rubidium atoms using ion time-of-flight spectroscopy. From this, we have obtained values for the effective initial plasma electron temperature, ${T}_{e,0}={m}_{\mathrm{ion}}{v}_{0}^{2}/{k}_{B}$ (where ${m}_{\mathrm{ion}}$ is the ${\mathrm{Rb}}^{+}$ ion mass), as a function of the original Rydberg atom density and binding energy, ${E}_{b,i}$. We have also simulated numerically the interaction of UNPs with a large reservoir of Rydberg atoms to obtain data to compare with our experimental results. We find that for Rydberg atom densities in the range ${10}^{7}--{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}$, for states with principal quantum number $n>40, {T}_{e,0}$ is insensitive to the initial ionization mechanism which seeds the plasma. In addition, the quantity ${k}_{B}\phantom{\rule{0.16em}{0ex}}{T}_{e,0}$ is strongly correlated with the fraction of atoms which ionize, and is in the range $0.6\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|\ensuremath{\lesssim}{k}_{B}{T}_{e,0}\ensuremath{\lesssim}2.5\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|$. On the other hand, plasmas from Rydberg samples with $n\ensuremath{\lesssim}40$ evolve with no significant additional ionization of the remaining atoms once a threshold number of ions has been established. The dominant interaction between the plasma electrons and the Rydberg atoms is one in which the atoms are deexcited, a heating process for electrons that competes with adiabatic cooling to establish an equilibrium where ${T}_{e,0}$ is determined by their Coulomb coupling parameter, ${\mathrm{\ensuremath{\Gamma}}}_{e}\ensuremath{\sim}0.01$.

DOI
10.1103/physreva.97.043401

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We report a systematic experimental and numerical study of the expansion of ultracold Rydberg plasmas. Specifically, we have measured the asymptotic expansion velocities, v0{v}_{0}v0​, of ultracold neutral plasmas (UNPs) which evolve from cold, dense samples of Rydberg rubidium atoms using ion time-of-flight spectroscopy. From this, we have obtained values for the effective initial plasma electron temperature, Te,0=mionv02/kB{T}_{e,0}={m}_{\mathrm{ion}}{v}_{0}^{2}/{k}_{B}Te,0​=mion​v02​/kB​ (where mion{m}_{\mathrm{ion}}mion​ is the Rb+{\mathrm{Rb}}^{+}Rb+ ion mass), as a function of the original Rydberg atom density and binding energy, Eb,i{E}_{b,i}Eb,i​. We have also simulated numerically the interaction of UNPs with a large reservoir of Rydberg atoms to obtain data to compare with our experimental results. We find that for Rydberg atom densities in the range 107−−109cm\ensuremath−3{10}^{7}--{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}107−−109cm\ensuremath−3, for states with principal quantum number n>40,Te,0n>40, {T}_{e,0}n>40,Te,0​ is insensitive to the initial ionization mechanism which seeds the plasma. In addition, the quantity kBTe,0{k}_{B}\phantom{\rule{0.16em}{0ex}}{T}_{e,0}kB​Te,0​ is strongly correlated with the fraction of atoms which ionize, and is in the range 0.6\ifmmode×\else\texttimes\fi∣Eb,i∣\ensuremath≲kBTe,0\ensuremath≲2.5\ifmmode×\else\texttimes\fi∣Eb,i∣0.6\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|\ensuremath{\lesssim}{k}_{B}{T}_{e,0}\ensuremath{\lesssim}2.5\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|0.6\ifmmode×\else\texttimes\fi∣Eb,i​∣\ensuremath≲kB​Te,0​\ensuremath≲2.5\ifmmode×\else\texttimes\fi∣Eb,i​∣. On the other hand, plasmas from Rydberg samples with n\ensuremath≲40n\ensuremath{\lesssim}40n\ensuremath≲40 evolve with no significant additional ionization of the remaining atoms once a threshold number of ions has been established. The dominant interaction between the plasma electrons and the Rydberg atoms is one in which the atoms are deexcited, a heating process for electrons that competes with adiabatic cooling to establish an equilibrium where Te,0{T}_{e,0}Te,0​ is determined by their Coulomb coupling parameter, \ensuremathΓe\ensuremath∼0.01{\mathrm{\ensuremath{\Gamma}}}_{e}\ensuremath{\sim}0.01\ensuremathΓe​\ensuremath∼0.01.
We report a systematic experimental and numerical study of the expansion of ultra-cold Rydberg plasmas. Specifically, we have measured the asymptotic expansion velocities, v0v_0v0​, of ultra-cold neutral plasmas (UNPs) which evolve from cold, dense samples of Rydberg rubidium atoms using ion time-of-flight spectroscopy. From this, we have obtained values for the effective initial plasma electron temperature, Te,0=mionv02/kBT_{e,0} = m_{ion} v_0^2/k_BTe,0​=mion​v02​/kB​ (where mionm_{ion}mion​ is the Rb+^++ ion mass), as a function of the original Rydberg atom density and binding energy, Eb,iE_{b,i}Eb,i​. We have also simulated numerically the interaction of UNPs with a large reservoir of Rydberg atoms to obtain data to compare with our experimental results. We find that for Rydberg atom densities in the range 107−10910^7 - 10^9107−109 cm−3^{-3}−3, for states with principal quantum number n>40n > 40n>40, Te,0T_{e,0}Te,0​ is insensitive to the initial ionization mechanism which seeds the plasma. In addition, the quantity kB Te,0k_B \, T_{e,0}kB​Te,0​ is strongly correlated with the fraction of atoms which ionize, and is in the range 0.6×∣Eb,i∣≲kBTe,0≲2.5×∣Eb,i∣0.6 \times |E_{b,i}| \lesssim k_BT_{e,0} \lesssim 2.5 \times |E_{b,i}|0.6×∣Eb,i​∣≲kB​Te,0​≲2.5×∣Eb,i​∣. On the other hand, plasmas from Rydberg samples with n≲40n \lesssim 40n≲40 evolve with no significant additional ionization of the remaining atoms once a threshold number of ions has been established. The dominant interaction between the plasma electrons and the Rydberg atoms is one in which the atoms are deexcited, a heating process for electrons that competes with adiabatic cooling to establish an equilibrium where Te,0T_{e,0}Te,0​ is determined by their Coulomb coupling parameter, Γe∼0.01\Gamma_e \sim 0.01Γe​∼0.01.
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, Te,i{T}_{e,i}Te,i​, and the binding energy of the added Rydberg atoms, Eb{E}_{b}Eb​, 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 $|{E}_{b}|\ensuremath{\approx}2.7\ifmmode\times\else\texttimes\fi{}{k}_{B}{T}_{e,i}$ 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.
By photoionizing samples of laser-cooled atoms with laser light tuned just above the ionization limit, plasmas can be created with electron and ion temperatures below 10 K. These ultracold neutral plasmas have extended the temperature bounds of plasma physics by two orders of magnitude. Table-top experiments, using many of the tools from atomic physics, allow for the study of plasma phenomena in this new regime with independent control over the density and temperature of the plasma through the excitation process. Characteristic of these systems is an inhomogeneous density profile, inherited from the density distribution of the laser-cooled neutral atom sample. Most work has dealt with unconfined plasmas in vacuum, which expand outward at velocities of order 100 m/s, governed by electron pressure, and with lifetimes of order 100 μs, limited by stray electric fields. Using detection of charged particles and optical detection techniques, a wide variety of properties and phenomena have been observed, including expansion dynamics, collective excitations in both the electrons and ions, and collisional properties. Through three-body recombination collisions, the plasmas rapidly form Rydberg atoms, and clouds of cold Rydberg atoms have been observed to spontaneously avalanche ionize to form plasmas. Of particular interest is the possibility of the formation of strongly coupled plasmas, where Coulomb forces dominate thermal motion and correlations become important. The strongest impediment to strong coupling is disorder-induced heating, a process in which Coulomb energy from an initially disordered sample is converted into thermal energy. This restricts electrons to a weakly coupled regime and leaves the ions barely within the strongly coupled regime. This review will give an overview of the field of ultracold neutral plasmas, from its inception in 1999 to current work, including efforts to increase strong coupling and effects on plasma properties due to strong coupling.
Using high-resolution laser-induced fluorescence spectroscopy, ion dynamics in\nan expanding ultracold neutral plasma (UNP) have been studied in unprecedented\ndetail. The evolution of the ion temperature is of great interest because the ions in\nan ultracold neutral plasma are strongly coupled, meaning their Coulomb interaction\nenergy exceeds the thermal energy. This leads to novel plasma properties that are\nhard to describe theoretically. Understanding all the factors that contribute to ion\ntemperature evolution is critical for designing schemes to cool the ions and achieve\neven stronger Coulomb coupling.\nThis work has also observed several phenomena that have not previously been\nstudied in ultracold plasmas. Ion adiabatic cooling has been observed in a UNP for\nthe first time, resulting in ion temperatures as low as 100mK and up to a tripling of\nthe Coulomb coupling parameter. The importance of electron-ion energy transfer is\ndemonstrated with the first observations of electron-ion collisional heating. Inclusion\nof this effect into existing numerical models provides better agreement with experimental\nresults. Results of molecular dynamics simulations of equilibrating plasmas\nhave been compared to early time experimental data, which provides a new method\nof density determination that is much less sensitive to experimental systematics and\nis accurate to within 10%. This improved certainty in the density allows accurate\ncomparison between data and a theoretical model of the plasma dynamics. The\nagreement is excellent, but on a hydrodynamic time scale a small amount of extra\nheat (on order of 100mK), not ascribable to electron-ion collisions or other sources in\nthe model, is detected in the ion component. Potential sources are discussed within\nas well as proposals for further studies and improvements.
We report the results of simulations that explain many properties of ultracold neutral plasmas. We find that three-body recombination is important at very low temperatures since it is a heating mechanism for the electron gas and it preferentially removes the slow ions from the plasma. We also find that collisions between cold electrons and Rydberg atoms are an important source of electron heating and deexcitation of atoms formed in the plasma. Simulations show that the Coulomb coupling constant does not become larger than similar1/5 for the reported experiments.
Ultracold neutral plasmas (UNPs) are highly correlated, charged-particle systems studied in standard atomic-molecular optical physics laboratories. Advances in ultracold physics techniques have led to the development of magneto-optical traps that permit the localization of micro-Kelvin temperature atomic samples (10⁸ - 10¹⁰ cm -³ that can be photoionized with a defined excess laser energy. Magneto-optical trapping of molecules proves difficult, and to date, lags in reaching conditions attainable for atoms. Molecules possess additional degrees of freedom where energy can flow during laser trapping and cooling. Alternatively, elastic collisions with inert gases offer another route to low temperatures. Super-sonic expansions of target molecules seeded in a noble gas can reduced the translational temperature to values as low as 0.1 K. Here I report on the formation of a molecular ultracold plasma in a molecular beam of nitric oxide seeded in an inert gas. Our method does not directly form a plasma, but instead, I create a Rydberg gas that spontaneously evolves to a plasma. I have verified the transition to a collective plasma state by applying pulsed-fields to the field-free flight region, and observe a signal that persists well beyond classical field amplitudes required to ionize individual Rydberg states. Electric field screening is a collective effect occurring over a characteristic distance, quantified by the Debye length, λ_D. Molecular ultracold plasmas described here exhibit Debye lengths smaller than the overall size, λ_D<<σ. Plasmas of this nature offer an exotic environment for which to study fundamental phenomena. While plasmas are generally thought of as hot, UNPs exist at low enough temperatures that electrostatic interaction energy between particles is greater than their kinetic energy. At this point, charged particles begin to find themselves in local potential energy minima. Over the entire sample this translates to long-range order, or correlation. It is of great interest for researchers studying UNPs to maximize particle correlation, which requires UNPs to remain very cold, and dense through their lifetime.