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Physical Review

The Optical Detection of Radiofrequency Resonance

Francis Bitter

Published Sep 15, 1949• 88 citations
Publisher

Abstract

Calculations are made of the frequency, intensity, and polarization of the light emitted by an atom in a $^{2}P\ensuremath{-}^{2}S$ transition in a weak magnetic field having an oscillating component. Near resonance, or when the frequency of the oscillating component approaches the Larmor frequency of one of the two states involved in the radiation process, all of the quantities calculated are modified. Qualitatively similar results are to be expected for other transitions. Observations in very weak fields would be of particular interest because they would give information on nuclear spins as well as atomic $g$-factors. Under such conditions, the Zeemann components will in general not be resolvable. There will, however, be a change in the polarization of the edges of a spectral line at resonance. It is shown that very small changes in this polarization structure are theoretically detectable.

DOI
10.1103/physrev.76.833

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Physical Review•Jan 15, 1957•52 citations
Calculations are made of the frequency, intensity, and polarization of the light emitted by an atom in a 2P\ensuremath−2S^{2}P\ensuremath{-}^{2}S2P\ensuremath−2S transition in a weak magnetic field having an oscillating component. Near resonance, or when the frequency of the oscillating component approaches the Larmor frequency of one of the two states involved in the radiation process, all of the quantities calculated are modified. Qualitatively similar results are to be expected for other transitions. Observations in very weak fields would be of particular interest because they would give information on nuclear spins as well as atomic ggg-factors. Under such conditions, the Zeemann components will in general not be resolvable. There will, however, be a change in the polarization of the edges of a spectral line at resonance. It is shown that very small changes in this polarization structure are theoretically detectable.
Excitation of atoms in a vapor by polarized light produces unequal population of the magnetic sublevels of the excited state. The emitted optical resonance radiation is therefore partly polarized. The application of radiofrequency or microwave fields at a magnetic resonance frequency will induce transitions between sublevels of the excited state. The degree of polarization of the emitted optical resonance radiation is altered when the magnetic resonance condition is fulfilled. As suggested by Brossel and Kastler, this effect may be used to reveal the structure of the energy level. A detailed theory applicable to, and experiments on the 3P1^{3}P_{1}3P1​ state of all the isotopes of mercury are reported. The results obtained indicate that double resonance phenomena constitute a valuable new tool for investigating the structure of atomic energy levels. The mean life of the 3P1^{3}P_{1}3P1​ state is shown by observations on the resonance line widths to be 1.55\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ sec for all the isotopes. The ggg-factor of the 3P1^{3}P_{1}3P1​ state for isotopes with zero spin, measured in terms of the proton ggg-factor, is 1.4838\ifmmode\pm\else\textpm\fi{}0.0004.
A treatment of resonance fluorescence is given in which the properties of the incident and scattered light are expressed in terms of coherency matrices. Calculations are made for two successive scattering processes corresponding to the experiments described in an accompanying paper. For the first process the scattering atoms are subjected to a magnetic field consisting of parallel static and oscillating components. The fluorescent light is frequency-modulated and may also be polarization-modulated. This light excites fluorescence in a second cell in which the atoms are subjected to a static magnetic field. The equations show under what conditions the second fluorescence is intensity-modulated and describe the resonances in the amplitude of modulation which occur when the modulation frequency matches a Zeeman interval of the excited atoms.
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.
Theoretical and experimental study of influence of quadratic Zeeman effect on the structure of double radio-optical resonance is presented. A specific transition in 87 Rb atom is considered in the case of excitation with linearly polarized laser radiation and detection of the signal at the second harmonic of the AC magnetic field frequency. It is shown, that for small magnetic fields the magnetic resonance consists of a solitary line similarly to resonance in potassium [1]. However, for magnetic fields greater than 50 μT the line acquires two additional side-peaks without breaking its symmetry and changingposition of resonance center. The described scheme can be used in magnetometry.
Magnetic resonance at the F g = 1 ⇄ \rightleftarrows ⇄ F e = 1 transition of the D 1 line in 87Rb has been studied with pumping and detection by linearly polarized radiation and detection at the double frequency of the radiofrequency field. The intervals of allowed values of the static and alternating magnetic fields in which magnetic resonance has a single maximum have been found. The structure appearing beyond these intervals has been explained. It has been shown that the quadratic Zeeman shift is responsible for the three-peak structure of resonance; the radiofrequency shift results in the appearance of additional extrema in resonance, which can be used to determine the relaxation constant Γ2. The possibility of application in magnetometry has been discussed.
A new technique of microwave spectroscopy is proposed for application to excited states of short lifetime. If atoms are excited by electron bombardment, closely-spaced energy levels may be unequally populated. The radiation emitted in decay to lower states may have an angular distribution and polarization character correlated with the direction of bombardment. When such atoms are acted on by radio-frequency fields, transitions may occur between excited states which cause an observable change in the pattern of decay radiation. An analysis is made of the possibility of applying such a method to a determination of the finestructure patterns (1snp)3PJ(J=0,1,2)(1snp)^{3}P_{J}(J=0, 1, 2)(1snp)3PJ​(J=0,1,2) of the helium atom. After a review of previous optical spectroscopic work and theory of this fine structure, an old unsolved mystery concerning the polarization of collision light is discussed. The theory of the Zeeman effect is worked out in a form applicable to the microwave experiments. Expected transition frequencies and rf matrix elements, intensity changes and shape of resonance curves, Stark effect and singlet-triplet mixing are also considered. An estimate is made of the signal to be expected in the experiment described in the following paper.