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Physical Review

Microwave Technique for Determining the Fine Structure of the Helium Atom

Willis E. Lamb

Published Jan 15, 1957• 52 citations
Publisher

Abstract

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 $(1snp)^{3}P_{J}(J=0, 1, 2)$ 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.

DOI
10.1103/physrev.105.559

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Optics and Spectroscopy•Feb 1, 2001•1 citation
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.
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.
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.
We have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains concerning their widths.
We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2){D}_{5/2}\ensuremath{\rightarrow}n{F}_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the DDD Rydberg state using a two-step laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier sideband spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\ensuremath{\gtrsim}3\ensuremath{\pi}$. Furthermore, we investigate the Zeeman effect of the clearly resolved nFJn{F}_{J}nFJ​ fine-structure levels in fields up to 120 mG, where the transition into nF7/2n{F}_{7/2}nF7/2​ displays a thee-peak Zeeman pattern, while nF5/2n{F}_{5/2}nF5/2​ shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of dc magnetic fields in experimental chambers for cold atoms.
The 23S12^{3}S_{1}23S1​ (metastable) and 23P1,22^{3}P_{1,2}23P1,2​ excited-state atoms of He4{\mathrm{He}}^{4}He4 are aligned by an unpolarized beam of resonance radiation. The alignment is detected by the depolarization of the resonance fluorescence at 1\ensuremath{\mu}, which occurs when either the 23S12^{3}S_{1}23S1​ level or the 22P1,22^{2}P_{1,2}22P1,2​ levels are saturated by a rf magnetic field at the Zeeman frequency. The observed signals are several orders of magnitude larger than the corresponding signals observed by monitoring intensity changes in the transmitted beam. Considerably smaller signals are observed even in the absence of the pumping beam. Expressions for the intensity of the $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ components of the scattered radiation are derived in terms of the alignment and density of the metastable atoms. The alignment of the 23S1(F=32)2^{3}S_{1} (F=\frac{3}{2})23S1​(F=23​) and the 23P2(F=52)2^{3}P_{2} (F=\frac{5}{2})23P2​(F=25​) levels of He3{\mathrm{He}}^{3}He3 is also observed. The excited-state linewidth as a function of pressure leads to a radiative decay time of $\ensuremath{\tau}\ensuremath{\approx}0.96\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ sec and a mixing cross section of 53\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2. The alignment of the 33P3^{3}P33P level of He4{\mathrm{He}}^{4}He4 is also observed by monitoring polarization changes of the 3889 \AA{} line.
Experimental results of studying the spectrum of the microwave 37 P -37 S transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system.