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Physical Review A

Onset of a collisional modification of the Faraday effect in a high-density atomic gas

M. Kristensen, F.J. Blok, Martijn A. van Eijkelenborg, Gerard Nienhuis, J. P. Woerdman

Published Feb 1, 1995• 14 citations
Publisher

Abstract

We investigate, theoretically and experimentally, the onset of modified electronic precession due to quasimolecular behavior in dense atomic gases. The close connection between the angular coupling of collision pairs and a modification of the Faraday effect is pointed out. We have observed the onset of this quasimolecular modification of the atomic Faraday effect with high-resolution laser measurements of the absorption and Faraday spectra near the ${\mathit{D}}_{2}$ line of Rb atoms immersed in high-density buffer gases. The atomic Faraday effect itself is also affected by the presence of nuclear spin; this modifies the electronic precession through angular-momentum coupling. We describe how to separate the effect of nuclear spin from the effects due to quasimolecular behavior. In this way we establish the existence of angular coupling of the Rb valence electrons to neighboring buffer-gas atoms at densities above \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ in Xe buffer gas. In He buffer gas, quasimolecular modifications of the Faraday effect are approximately two times smaller than for Xe.

DOI
10.1103/physreva.51.1085

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Physical Review A•Dec 1, 1994•3 citations
We investigate, theoretically and experimentally, the onset of modified electronic precession due to quasimolecular behavior in dense atomic gases. The close connection between the angular coupling of collision pairs and a modification of the Faraday effect is pointed out. We have observed the onset of this quasimolecular modification of the atomic Faraday effect with high-resolution laser measurements of the absorption and Faraday spectra near the D2{\mathit{D}}_{2}D2​ line of Rb atoms immersed in high-density buffer gases. The atomic Faraday effect itself is also affected by the presence of nuclear spin; this modifies the electronic precession through angular-momentum coupling. We describe how to separate the effect of nuclear spin from the effects due to quasimolecular behavior. In this way we establish the existence of angular coupling of the Rb valence electrons to neighboring buffer-gas atoms at densities above \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}1019{10}^{19}1019 cm\ensuremath−3{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}cm\ensuremath−3 in Xe buffer gas. In He buffer gas, quasimolecular modifications of the Faraday effect are approximately two times smaller than for Xe.
We compare the Faraday spectrum with the dispersion spectrum near the D2{\mathit{D}}_{2}D2​ line of Rb atoms immersed in a high density Xe buffer gas. We observe deviations from the standard Becquerel relation, which relates the Faraday effect of an atomic gas to its dispersion. The deviations are due to coupling of the Rb valence electron to the Xe environment. The Rb D2{\mathit{D}}_{2}D2​ transition dipole moment becomes rotationally locked to the instantaneous collision axes at Xe densities of \ensuremath{\sim}1020{10}^{20}1020 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.
We have measured the D1{\mathit{D}}_{1}D1​ and D2{\mathit{D}}_{2}D2​ Faraday spectrum and absorption spectrum of Rb atoms immersed in high-density Xe buffer gas in the range nXe{\mathit{n}}_{\mathrm{Xe}}nXe​=0.8--4.5\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. We find that the shape of the Faraday spectrum obeys the Becquerel relation over this whole density range; however the relative strength of the Faraday effect compared to absorption changes rather abruptly near nXe{\mathit{n}}_{\mathrm{Xe}}nXe​=1\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. This is ascribed to the onset of a many-body nature (overlapping collisions) of the Rb:Xe line broadening; the number of perturbers within the Weisskopf sphere is unity at nXe{\mathit{n}}_{\mathrm{Xe}}nXe​\ensuremath{\sim}1\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. \textcopyright{} 1996 The American Physical Society.
When we rotate matter the nuclei follow the macroscopic motion. One may ask whether the atomic electrons also follow the rotation microscopically. If they do, a mechanical Faraday effect arises. We discuss the connection between the mechanical Faraday effect and the usual (i.e., magnetic) Faraday effect. As material medium we consider resonant atoms immersed in a high‐density buffer gas. The electronic wave functions of the resonant atoms are predicted to be rotationally coupled to the buffer gas as soon as nonimpact broadening becomes appreciable at line center. Preliminary experimental results for the case Rb+Xe indicate that this occurs for Xe pressures of a few atmospheres.
Cross sections for relaxation of circular and linear polarization of 62P326^{2}P_{\frac{3}{2}}62P23​​ cesium atoms, induced in collisions with ground-state He, Ne, Ar, and Xe, have been determined by Zeeman scanning techniques. A fluorescence cell containing low-pressure cesium vapor together with a buffer gas was irradiated with circularly or linearly polarized 8521-\AA{} Cs resonance radiation, producing excited and polarized Cs atoms which became depolarized in subsequent collisions with the buffer-gas atoms. The resulting depolarization of the cesium resonance fluorescence was monitored in relation to buffer-gas pressure (0-10 Torr) and to the strength of the ambient magnetic field (0-10 kG). At low fields at which the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$ is coupled to the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$, the measurements yielded depolarization cross sections Q(circ.)Q(\mathrm{circ}.)Q(circ.) and Q(lin.)Q(\mathrm{lin}.)Q(lin.), which agree within experimental error with theoretical values calculated for spin-coupled conditions. At kilogauss fields with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ decoupled, the experiments produced cross sections for disorientation and disalignment, which are also in satisfactory agreement with the appropriate theoretical predictions. The results indicate that the nuclear spin has a more pronounced effect on the collisional relaxation of the atomic dipole than of the quadrupole.
Spin relaxation of optically pumped Rb85{\mathrm{Rb}}^{85}Rb85 and Rb87{\mathrm{Rb}}^{87}Rb87 atoms colliding with light-noble-gas atoms is shown to be strongly influenced by an anomalous relaxation process which we attribute to the formation and destruction of bound and quasibound Van der Waals molecules. The anomalous relaxation rate has been measured and analyzed in Ne, complementing an earlier study in He. Relative rates of formation of complexes in two- and three-body collisions have been determined. The correlation time for the quasimolecular interaction in Rb-Ne has been found to be 6.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ ${p}^{\ensuremath{-}1}$ sec, where ppp is the Ne pressure in Torr. Nuclear-spin-independent cross sections for the relaxation of 〈Sz〉〈{S}_{z}〉〈Sz​〉 in sudden binary collisions of Rb atoms with noble-gas atoms have been measured to be (units of ${10}^{\ensuremath{-}24}$ cm2{\mathrm{cm}}^{2}cm2: $\ensuremath{\sigma}(\mathrm{Rb}\ensuremath{-}\mathrm{He})=3.1$ $\ensuremath{\sigma}(\mathrm{Rb}\ensuremath{-}\mathrm{Ne})=19$ $\ensuremath{\sigma}(\mathrm{Rb}\ensuremath{-}\mathrm{Ar})=630$ $\ensuremath{\sigma}(\mathrm{Rb}\ensuremath{-}{\mathrm{N}}_{2})=83$. Relaxation in sudden binary collisions is shown to follow the theoretically expected nuclear spin dynamics: two relaxation rates in the ratios 8:1 for Rb87{\mathrm{Rb}}^{87}Rb87 and 18:1 for Rb85{\mathrm{Rb}}^{85}Rb85 have been measured. Diffusion coefficients of Rb in the various buffer gases have been measured to be (units of cm2{\mathrm{cm}}^{2}cm2/ sec, at 305\ifmmode^\circ\else\textdegree\fi{}K): ${D}_{0}(\mathrm{Rb}\ensuremath{-}\mathrm{He})=0.42$, ${D}_{0}(\mathrm{Rb}\ensuremath{-}\mathrm{Ne})=0.235$, ${D}_{0}(\mathrm{Rb}\ensuremath{-}\mathrm{Ar})=0.16$, ${D}_{0}(\mathrm{Rb}\ensuremath{-}{\mathrm{N}}_{2})=0.16$. Nuclear-spin-independent cross sections for the relaxation of 〈Jz〉〈{J}_{z}〉〈Jz​〉 in the 52P125^{2}P_{\frac{1}{2}}52P21​​ state of Rb have been measured to be 3.4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2 for Rb-He, and 5.9 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2 for Rb-Ne. Anomalies, disagreements, and puzzles occurring in earlier measurements of ground-state relaxation in Rb are shown to be largely resolved when considered in the light of the new results.
Whereas mechanical rotation of a transparent solid induces rotation of the plane of linear polarization of a light beam, for a dilute vapor this mechanical Faraday effect must disappear. By studying the structure of the collision operator that is familiar in the unified theory of spectral line broadening, we demonstrate that a nonzero effect arises for a vapor of absorbing atoms embedded in a buffer gas. The size of the effect is easily compared with the magnetic Faraday effect, when the angular velocity is replaced with the Larmor precession frequency. Then, the mechanical effect is smaller by a factor of the order of the collision frequency multiplied with the duration of a collision. Furthermore, the mechanical effect is a linear combination of the frequency derivative of a (collision-broadened) dispersion curve and the derivative of an absorption curve.