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Physical Review A

Frequency shifts and line broadenings in collisions between Rydberg and ground-state alkali-metal atoms

Douglas C. Thompson, E. Weinberger, Guoqing Xu, Boris Peter Stoicheff

Published Jan 1, 1987• 35 citations
Publisher

Abstract

The technique of Doppler-free two-photon spectroscopy was used to measure rates for line broadenings and frequency shifts of Rydberg levels with pressure. Measurements were made of spectra of $^{2}\mathrm{S}$ and $^{2}\mathrm{D}$ states (with n\ensuremath{\sim}10--40) for ${\mathrm{Rb}}^{\mathrm{*}\mathrm{*}}$+Rb and ${\mathrm{K}}^{\mathrm{*}\mathrm{*}}$+K, and of $^{2}\mathrm{S}$ states (with n=14--29) for ${\mathrm{K}}^{\mathrm{*}\mathrm{*}}$+Rb. Large oscillations are observed in both broadening and shift rates for n\ensuremath{\sim}20--30 in all series except for the $^{2}\mathrm{D}$ series in ${\mathrm{Rb}}^{\mathrm{*}\mathrm{*}}$+Rb. Overall rates for broadening and shift are compared with a theory based on the ``free-electron'' model. The observed oscillations are inconsistent with theories based on the resonance scattering of the Rydberg electron by the perturbing atom. A possible alternative mechanism related to interference in l-mixing collisions is suggested.

DOI
10.1103/physreva.35.690

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The technique of Doppler-free two-photon spectroscopy was used to measure rates for line broadenings and frequency shifts of Rydberg levels with pressure. Measurements were made of spectra of 2S^{2}\mathrm{S}2S and 2D^{2}\mathrm{D}2D states (with n\ensuremath{\sim}10--40) for Rb∗∗{\mathrm{Rb}}^{\mathrm{*}\mathrm{*}}Rb∗∗+Rb and K∗∗{\mathrm{K}}^{\mathrm{*}\mathrm{*}}K∗∗+K, and of 2S^{2}\mathrm{S}2S states (with n=14--29) for K∗∗{\mathrm{K}}^{\mathrm{*}\mathrm{*}}K∗∗+Rb. Large oscillations are observed in both broadening and shift rates for n\ensuremath{\sim}20--30 in all series except for the 2D^{2}\mathrm{D}2D series in Rb∗∗{\mathrm{Rb}}^{\mathrm{*}\mathrm{*}}Rb∗∗+Rb. Overall rates for broadening and shift are compared with a theory based on the ``free-electron'' model. The observed oscillations are inconsistent with theories based on the resonance scattering of the Rydberg electron by the perturbing atom. A possible alternative mechanism related to interference in l-mixing collisions is suggested.
A theory is developed that allows a qualitative explanation and quantitative calculation of the widths and shifts of the two-photon Doppler-free transitions from the ground states of alkali atoms to Rydberg n 2 S and n 2 D states. The widths and shifts result from collisions between Rydberg atoms and ground-state alkali atoms, either of the same or of other species. The collisions are represented by means of a pseudopotential that is a function of theoretically calculated free-electron elastic scattering resonant and nonresonant phase shifts, which depend upon the Rydberg electron momentum. The momentum, in turn, is correlated with the electronic position within the Rydberg atom. This theory assumes classical straight-line trajectories and takes into consideration the multicollisional nature of the Rydberg-electron-perturbing-atom interaction within the Rydberg atom. Impact theory calculations of the linewidths and shifts for K**( n S)-K, K**( n S)-Rb, Rb**( n S)-Rb, Rb**( n S)-K, K**( n D)-K, K**( n D)-Rb, Rb**( n D)-Rb and Rb**( n D)-K show substantial agreement with experiment for 10⩽ n ⩽40.
Broadening and shift rates for Rb 2S^{2}\mathrm{S}2S and 2D^{2}\mathrm{D}2D Rydberg states with principal quantum number n\ensuremath{\sim}10--50 have been measured for Ne, Kr, and H2{\mathrm{H}}_{2}H2​ perturbers, using the technique of Doppler-free two-photon spectroscopy. From the shift rates at high n, we derived electron scattering lengths of (0.24\ifmmode\pm\else\textpm\fi{}0.01)a0{a}_{0}a0​ for Ne, (-4.0\ifmmode\pm\else\textpm\fi{}0.3)a0{a}_{0}a0​ for Kr, and (1.64\ifmmode\pm\else\textpm\fi{}0.07)a0{a}_{0}a0​ for H2{\mathrm{H}}_{2}H2​. For Ne and Kr, these are in good agreement with other experimental values. Also, the n dependence of broadening and shift rates follows theoretical predictions for Ne and Kr, but not for H2{\mathrm{H}}_{2}H2​.
Self-broadenings and frequency shifts of n2S{n}^{2}Sn2S and n2D{n}^{2}Dn2D Rydberg levels (up to $n\ensuremath{\sim}70$) have been measured for rubidium in the pressure range of 3 to 100 mTorr, and the general dependence on principal quantum number nnn has been established for this low-pressure regime. A closer examination has revealed large (almost evenly spaced) oscillations in the dependence of linewidth on principal quantum number for the 2S^{2}S2S levels in the region of largest linewidth ($n\ensuremath{\sim}20 \mathrm{to} 30$).
The theory of impact broadening of the isolated spectral lines of the Rydberg atomic series perturbed by neutral particles is developed within the framework of the impulse approximation. The analysis of the broadening process is based on the consideration of the inelastic nl to n' transitions between highly excited states of the Rydberg atom. The role of the potential and resonance scattering of the quasifree electron by a perturbing particle in the impact broadening of the Rydberg nl levels is investigated. It is shown that the general expressions for the broadening cross sections presented in this paper contain the results of asymptotic Alekseev and Sobel'man theory (1965) as special cases. Both elastic and inelastic scattering contributions of the perturber by the parent core of Rydberg atom to the broadening cross sections are also considered within the framework of the 'shake' model. The results obtained are used for a quantitative explanation of experimental data on the broadening of Rydberg atomic levels perturbed by alkali-metal atoms. The energies and widths of the 3 P resonances on the quasidiscrete levels of the negative K - and Rb - ions are determined.
We apply two-photon resonant nondegenerate four-wave mixing with a resonant intermediate state for observing the broadening and the shifting of the barium Rydberg 6snd 1D2 series by collision with argon. The collision broadenings and the collision shifting cross sections are measured for n=1633. This technique is a purely optical means, and can achieve Doppler-free resolution of narrow spectral structures of Rydberg levels when the incident lasers have narrow bandwidths. Different from other experimental methods of studying the pressure dependence of the longitudinal relaxation rate of Rydberg states, our method is to investigate the pressure dependence of the transverse relaxation rate of the transition.
In this paper we present the results and discuss the applicability of an impact theory of lineshapes, developed by Henry and Herman for the pressure-induced broadening and shifting of transitions from the ground state to various Rydberg states of alkalis, to the situation in which the perturbing atoms are ground-state rare gas atoms. This theory, which has successfully described the collisional broadening of Rydberg states by alkali atoms, can without major alterations predict the widths and shifts of Doppler-free two-photon transitions to n S and n D states of Rb and Na, 6⩽ n ⩽30, perturbed by He, Ne, Ar, Kr and Xe. The results in all cases show reasonable agreement with experiment, with the transitions to Na**( n D) states being somewhat less satisfactory than the others.