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Physical Review A

Experimental Study of Zeeman Light Shifts in Weak Magnetic Fields

Claude N. Cohen-Tannoudji, J. Dupont-Roc

Published Feb 1, 1972• 265 citations
Publisher

Abstract

According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian ${\mathcal{H}}_{e}$ which depends on the polarization and spectral profile of the incident light. In order to check the structure of ${\mathcal{H}}_{e}$, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to ${\mathcal{H}}_{e}$. We have been able to obtain experimentally in the ground state of $^{199}\mathrm{Hg}$, $^{201}\mathrm{Hg}$, and $^{87}\mathrm{Rb}$, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of ${\mathcal{H}}_{e}$ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.

DOI
10.1103/physreva.5.968

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Soviet Physics Uspekhi•Apr 30, 1975•19 citations
According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian He{\mathcal{H}}_{e}He​ which depends on the polarization and spectral profile of the incident light. In order to check the structure of He{\mathcal{H}}_{e}He​, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to He{\mathcal{H}}_{e}He​. We have been able to obtain experimentally in the ground state of 199Hg^{199}\mathrm{Hg}199Hg, 201Hg^{201}\mathrm{Hg}201Hg, and 87Rb^{87}\mathrm{Rb}87Rb, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field H\ensuremath→0{\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}H\ensuremath→​0​ is added. We have checked that the effect of He{\mathcal{H}}_{e}He​ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.
The effect of a dc magnetic field on the rate at which a ground-level, Zeeman-degenerate atom is photoionized via a short-lived autoionizing level is calculated. We consider single-step as well as two-step photoionization; in the latter case we allow the light to be either resonant or far from resonance with an intermediate level. In all cases we find that the magnetic field may raise the fraction of the atoms available for photoionization and consequently increase the photoion fraction produced by a light pulse of given fluence. In the resonant case we find that if the magnetic-field Zeeman splitting of the ground and intermediate level is much larger than the rate at which population enters or leaves that level then the Zeeman-state populations are decoupled from one another and there exist simple conditions under which they obey rate equations. In the nonresonant case an additional condition for two-photon rate equations is that the optical Stark shift of the ground state be much smaller than the magnetic Zeeman splitting. These results apply specifically to excitation by lasers whose spectral widths are narrow compared to the homogeneous linewidths of the corresponding atomic transitions, but appear to be generalizable to the opposite limit, in which the laser spectral widths are much broader than the homogeneous linewidths.
This is a brief account of recent results obtained in Paris by the development of optical-pumping techniques, and especially on the thesis of Cagnac and the thesis of Cohen-Tannoudji. Cagnac has used the optical-pumping technique to achieve nuclear orientation in the ground state of the odd mercury isotopes and has made an extensive study of the longitudinal relaxation time. Barrat and Cohen-Tannoudji have developed the quantum-mechanical theory of the optical-pumping cycle of an atom and Cohen-Tannoudji in his thesis has confirmed the theoretical predictions experimentally by applying Dehmelt’s cross-beam technique to Hg199: If a collection of atoms is irradiated permanently by light which can be absorbed and re-emitted, this pumping cycle has different effects on the ground-state properties of the atoms; these effects are experimentally detectable by observing the magnetic resonance of the atomic ground state. A broadening of the magnetic-resonance line proportional to the light intensity occurs. It is due to the shortening of the lifetime of the ground-state Zeeman levels by light absorptions. Other effects are displacements of the Zeeman levels of the ground state caused by irradiation resulting in a change of the magnetic-resonance frequency. Theory predicts displacements of 2 different kinds: (1) Displacements caused by real transitions—During an up-and-down transition of an atom, coherence is partly conserved. As a result, a certain amount of the g factor of the excited state is mixed with the g factor of the ground state. (2) Displacements caused by virtual transitions—These displacements are related to the dispersion of light. All these effects, predicted by the theory, have been qualitatively and quantitatively confirmed by Cohen’s experiments.
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 report a different type of optical Stern-Gerlach effect, where a magnetic-field gradient is replaced with a light-intensity gradient and a paramagnetic atom is deflected according to its magnetic quantum number. The laser light is detuned between the D1D1D1 and D2D2D2 frequencies, with the size of the detuning from the D2D2D2 resonance being twice that from the D1D1D1 resonance, and it is circularly polarized to produce an ac Stark shift that takes the form of a pure Zeeman shift. Slow rubidium atoms are extracted from a magneto-optical trap and then spin polarized. The atoms traversing the laser-intensity gradient on one side of the Gaussian beam profile show deflections that depend on the atomic spin state and the laser polarization. When the laser-beam axis is aligned with the slit that defines the atomic beam, we observe focusing and defocusing of the atomic beam.
Cs and Rb atomic vapors have been optically pumped in their ground states. The optical/rf-field configuration used allowed for the optical detection of magnetic resonance spectra with subkilohertz resolution by a pump–probe beam technique, in which the free-precessional motion of spins is recorded in the time domain. A six-level system serves as a model to describe the dependence of the observed spectra on the optical frequencies involved. With an intense laser beam applied during the free-precession period, Zeeman light-shift effects are observed. The spatial electric-field distribution of the laser beams and particle diffusion have to be taken into account to let us explain the observed magnetic resonance line shapes adequately.
The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.