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Physical Review Letters

Many-Body Effects in a Frozen Rydberg Gas

I. Mourachko, D. Comparat, F. De Tomasi, A. Fioretti, P. Nosbaum, V. M. Akulin, P. Pillet

Published Jan 12, 1998• 337 citations
Publisher

Abstract

We studied the properties of a cold ( $\ensuremath{\sim}100\ensuremath{\mu}\mathrm{K}$) and dense ( $\ensuremath{\sim}{10}^{8--10}{\mathrm{cm}}^{\ensuremath{-}3}$) atomic Rydberg Cs gas, and found that the observed widths and shapes of resonances in population transfers cannot be explained in the framework of a usual gas model. We propose a ``frozen Rydberg gas'' model, where the interplay between two-body and many-body phenomena affects in an unexpected way the width and the shape of spectral lines.

DOI
10.1103/physrevlett.80.253

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Physical Review A•Aug 28, 2020•0 citations
We studied the properties of a cold ( \ensuremath∼100\ensuremathμK\ensuremath{\sim}100\ensuremath{\mu}\mathrm{K}\ensuremath∼100\ensuremathμK) and dense ( \ensuremath∼108−−10cm\ensuremath−3\ensuremath{\sim}{10}^{8--10}{\mathrm{cm}}^{\ensuremath{-}3}\ensuremath∼108−−10cm\ensuremath−3) atomic Rydberg Cs gas, and found that the observed widths and shapes of resonances in population transfers cannot be explained in the framework of a usual gas model. We propose a ``frozen Rydberg gas'' model, where the interplay between two-body and many-body phenomena affects in an unexpected way the width and the shape of spectral lines.
Previous resonant dipole-dipole energy-transfer experiments of cold Rydberg gases [Anderson et al., Phys. Rev. Lett. 80, 249 (1998); Mourachko et al., Phys. Rev. Lett. 80, 253 (1998)] have been interpreted as providing evidence of many-body, as opposed to purely binary, effects. Here we separate two-body and many-body interactions by introducing an additional Rydberg state, which does not participate directly in the energy-transfer process, but is strongly coupled to one of the final states. We observe broadening of the energy-transfer resonances due to this added Rydberg state, which clearly demonstrates the many-body nature of the dipole-dipole interactions in such a system.
In a dense gas of 300 microK 85Rb atoms of n approximately 50 ionization occurs on a 100 ns time scale, far too fast to be explained by the motion of the atoms or photoionization by 300 K blackbody radiation. Rapid ionization is accompanied by spectral broadening, with the spectrum becoming continuous at n=88 at a density of 5x10(10)cm(-3). The atomic transitions broaden both smoothly and by the emergence of new features, which we attribute to multiple atom absorptions. We attribute the rapid ionization to a sequence of near resonant dipole-dipole transitions through virtual states in this intrinsically many-body system, culminating in the ionization of some of the atoms.
Spectral linewidth broadening in Rydberg gases, a phenomenon previously attributed to the many-body effect, was observed experimentally almost a decade ago. The observed linewidth was typically 80--100 times larger than the average interaction strength predicted from a binary interaction. The interpretation of such a phenomenon is usually based on the so-called diffusion model, where the linewidth broadening mostly originates from the diffusion of excitations. We present a model calculation to show that diffusion is not the main mechanism of the linewidth broadening. We find that the rare pair fluctuation at small separation is the dominant factor contributing to this broadening. Our results give a width of about 20--30 times larger than the average interaction strength. More importantly, by turning off the diffusion process, we do not observe an order-of-magnitude change in the spectral linewidth.
Using state-selective field ionization, the state distributions of Rydberg atoms in cold Rydberg gases are measured for various initially excited Rydberg levels, populations, and evolution times. We provide direct experimental evidence for lll-changing collisions that we previously observed indirectly [S. K. Dutta, D. Feldbaum, A. Walz-Flannigan, J. R. Guest, and G. Raithel, Phys. Rev. Lett. 86, 3993 (2001)]. We also observe nnn-mixing and find that its effects are largely in agreement with recent theoretical work on nnn-changing collisions between electrons and Rydberg atoms, thus enabling an estimation of the electron temperature. Unexpectedly large populations of atoms are found in states with principal quantum numbers much lower than that of the initially excited atoms. We explain this observation by collisions between high-lll Rydberg atoms, which are highly polar and can collide due to static electric-dipole forces between them.
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 $100\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. 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 $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ 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 nnn states of purely cold Rydberg samples, the initial ionization process which leads to electron trapping is one involving the interactions between Rydberg atoms.
We have observed the process $\mathrm{Rb}ns+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}ns+2h\ensuremath{\nu}\ensuremath{\rightarrow}\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{1/2}+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{3/2}$ from n=34n=34n=34 to n=40n=40n=40 in a frozen gas of Rb Rydberg atoms. It is resonant when the microwave frequency is halfway between the $ns\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}n{p}_{1/2}$ and $ns\ensuremath{\rightarrow}n{p}_{3/2}$ frequencies, which range from 57 to 106 GHz. The process cannot occur in isolated atoms, nor can it occur if the magnetic quantum numbers are unchanged, an implicit assumption of one-dimensional models. A Floquet-Forster model shows that the coupling between the initial and final states involves the absorption of two microwave photons and the dipole-dipole interaction, which leads to a coupling proportional to the product of the density, the microwave field squared, and n∗14{n}^{*14}n∗14, where n∗{n}^{*}n∗ is the effective quantum number of the np3/2n{p}_{3/2}np3/2​ state. We have experimentally verified these dependences. The observed resonances are asymmetric, with a low-frequency tail, which we attribute to the van der Waals shift of the final np1/2np3/2n{p}_{1/2}n{p}_{3/2}np1/2​np3/2​ state due to its dipole-dipole interaction with the nearby ns(n+1)sns(n+1)sns(n+1)s state. While the van der Waals shift is negligible for most of the atoms in the Rydberg gas, it is not for the pairs of close atoms which undergo this transition.