Light Shifts in the Alkali Atoms~

  • Mathur B
  • Tang H
  • HAPPKRt W
 et al. 
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Abstract

Quantitative formulas for computing the light shift due to virtual transitions in any alkali atom are pre-sented. The theoretically calculated light shifts for Rb87 are compared with experimentally measured light shifts, and good quantitative agreement is obtained. X. INTRODUCTION ~ NE of the interesting results of early optical-pumping experiments was the discovery of "light shifts. " It was found that in an optically pumped vapor certain ground-state transition frequencies underwent a shift which was proportional to the pumping light intensity. The first detailed experimental study of light shifts was carried out by Arditi and Carver. ' They showed that ordinary resonance lamps could cause light shifts as large as several hundred hertz in the 0-0 transition frequencies of rubidium and cesium. Al-though these shifts are very small compared to the reso-nance frequencies, which are typically several giga-hertz, they are, nevertheless, easily observable because of the extremely narrow linewidths which can be ob-tained in optical-pumping experiments. The first systematic, theoretical study of the optical-pumping cycle was made by Barrat and Cohen-Tan-noudji. ' They showed that optical pumping can shift the ground-state transition frequencies of an atom by two distinct processes involving, respectively, real and virtual absorption of light. Light shifts due to real ab-sorption of light occur when coherence from the atomic ground state can be transferred to the excited state upon absorption of a photon of pumping light. The excited-state coherence may then be passed on to the ground state, following spontaneous decay of the excited atom. Since the natural frequencies of the ground-state and excited-state coherences are not normally equal, a phase shift may occur in this coherence transfer cycle, and a shift in the effective ground-state transition frequency results. Light shifts due to real transitions are most pronounced when the resonant frequencies of the ground state diGer from those in the excited state by an amount on the order of the spontaneous decay rate of the excited state. Light shifts due to virtual transitions are simply the Stark shifts caused by the oscillating electric 6eld of the pumping light. In this paper we shall be concerned with light shifts due to virtual transitions in the alkali atoms. Much of the impetus for this work was a desire to understand 22, 329 (1961);22, 443 (1961). the effects of light shifts on the 0-0 hfs transition, which plays such an important role in various atomic-frequency standards. ' Shifts of the hfs transition fre-quencies are due almost exclusively to virtual transi-tions because of the large disparity between the hfs splittings of the ground state and those of the excited state. Thus, we shall not be concerned with shifts due to real transitions although such shifts are important for the Zeeman transitions. Recently, 4 it has been shown that one can consider-ably simplify the theory of light shifts due to virtual transitions by exploiting the rotational symmetry of the interaction of hght with atoms. Thus, even though the hyperfine structure of the alkali atoms is rather complex, the light shift due to virtual transitions can be described by a simple hght-shift operator which is added to the unperturbed ground-state Hamil-tonian of the atom. Each term in the light-shift operator produces a characteristic type of energy splitting of the ground-state sublevels of the atom (see Fig. 1). The c.m. light shift, represented by 88s in (1), is an equal downward (or upward) displacement of all of the ground-state sublevels. This type of shift was recently observed by Aleksandrov et ul. s in potassium vapor illuminated by hght from a Q-switched ruby laser. How-ever, none of the transition frequencies between ground-state sublevels is affected by the c.m. light shift, so that this term is not of interest in most optical-pump-ing work. The hfs light shift, which is represented by the term hbAI J in (1), is entirely equivalent to a shift in the magnetic-dipole coupling constant of the alkali-atom ground state. Thus, the hfs light shift will not aGect the frequencies of Zeeman transitions (AF=O transitions), but it will aGect the frequencies of hfs transitions (d, F=1 transitions). Both the hfs light shift and the c.m. light shift are scalar quantities which depend on the spectral pro6le of the light but not on its polarization. hen the light beam has some degree of circular polarization. , a Zeeman light shift can occur. The corre-sponding hght-shift operator — hH. p can be thought of 3 P. Pis'ma v Redakt-siyu 3, 85 (1966) LEnzlish trsnsl. : JETP Letters 3, 53 (1966)j. j.i

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Authors

  • B S Mathur

  • H Tang

  • W HAPPKRt

  • J P Barrat

  • C Cohen-Tannoudji

  • J Phys

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