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Applied Optics

Optical Detection of Magnetic Resonance in Alkali-Metal Vapor Using D_1 and D_2 Radiation Simultaneously

Takahiro Kubo

Published Jul 1, 1972• 6 citations
Publisher

Abstract

Change in polarization produced by circularly polarized D(1) + D(2) radiation and destroyed by the resonance can be observed by monitoring the intensity of the radiation transmitting the vapor. The polarization and intensity of the absorption signal (change in absorption of the radiation produced by the resonance) are calculated from the solutions of equations governing the rate at which the populations of Zeeman sublevels of the ground state change. The result shows that the polarization increases as the disorientation mixing in the excited state decreases, and that the signal intensity is nearly equal to that when the D(1) radiation was used alone. Signal representation derived by Bell and Bloom based on Bloch's equations is modified so as to be applied to the experiment using D(1) + D(2) radiation as well as to that using D(1) radiation alone. The calculated result from the representation shows that the amplitude of the modulation signal (rf light modulation at the resonance) for D(1) + D(2) radiation is also nearly equal to that for D(1) radiation alone.

DOI
10.1364/ao.11.001521

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Derivation of coherent-population-trapping resonance signals from density-matrix equations with all relevant sublevels of Cs atoms and confirmation of experimental results

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arXiv:2309.06761•Physical Review A•Aug 27, 2024•1 citation
Change in polarization produced by circularly polarized D(1) + D(2) radiation and destroyed by the resonance can be observed by monitoring the intensity of the radiation transmitting the vapor. The polarization and intensity of the absorption signal (change in absorption of the radiation produced by the resonance) are calculated from the solutions of equations governing the rate at which the populations of Zeeman sublevels of the ground state change. The result shows that the polarization increases as the disorientation mixing in the excited state decreases, and that the signal intensity is nearly equal to that when the D(1) radiation was used alone. Signal representation derived by Bell and Bloom based on Bloch's equations is modified so as to be applied to the experiment using D(1) + D(2) radiation as well as to that using D(1) radiation alone. The calculated result from the representation shows that the amplitude of the modulation signal (rf light modulation at the resonance) for D(1) + D(2) radiation is also nearly equal to that for D(1) radiation alone.
Optical orientation of Na atoms in a metal vapor with circularly polarized D1{D}_{1}D1​ resonance radiation results in a shift in the $2\mathrm{Na}\ensuremath{\leftrightarrow}\mathrm{Na}{}_{2}$ gas phase equilibrium in the direction that destroys dimers. Plane polarized D1{D}_{1}D1​ or D2{D}_{2}D2​ resonance radiation produces the opposite effect: an increase in equilibrium dimer density. The atom-dimer reaction can be controlled to favor either products or reactants by simply changing the polarization of the resonance light. Application of a radio-frequency field at the Na atomic Zeeman resonance frequency while optically pumping the atoms with circularly polarized D1{D}_{1}D1​ radiation also permits a magnetic resonance tuning control of either an increase or decrease in dimer density.
A variation of the usual method of atomic orientation of alkali metal vapors by optical pumping is proposed. This variation consists of employing a single circularly polarized D1{D}_{1}D1​ line as pumping radiation, instead of a mixture of the two DDD lines. Under these conditions, one magnetic substate of the ground state is transparent to the pumping radiation. It is shown that for a sufficiently intense light source and relatively weak relaxation, the entire population of the vapor will tend to be pumped into this single state, resulting in nearly one-hundred percent atomic orientation. The pumping process is analyzed in detail for sodium vapor illuminated with $3{P}_{\frac{1}{2}}\ensuremath{-}3{S}_{\frac{1}{2}}$ radiation, and the time dependence of the populations of the eight magnetic sublevels of the ground state is computed. It is shown that in the steady state, the light absorption by the vapor is linear rather than exponential with distance. A simple method of measuring relaxation times based on this observation is suggested. The conditions under which the imprisonment of resonance radiation limits the size of the oriented sample are discussed, and it is suggested that the proposed technique will allow the alignment of larger samples than is possible by the usual method of optical pumping.
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.
Abstract The absorption of a light wave interacting with optical transitions in the D1 line of an alkali metal atom subjected to microwave radiation that is in resonance with magnetic dipole transitions between hyperfine ground-state components, has been investigated. It is known that when scanning a longitudinal magnetic field (B || k, where k is the wavevector), one may observe a magneto-optical resonance due to the ground-state Hanle effect. In addition, the effect of double radio-optical resonance takes place because of the presence of the resonance microwave field. The joint influence of these effects on the formation of a narrow magneto-optical resonance in light wave absorption has been studied theoretically and experimentally. It has been shown analytically that the effects compete with each other and destructively act on the resonance formation. As a result, the amplitude of the resonance is small and its shape is complicated. However, in the presence of a buffer gas the pressure of which is such that the hyperfine splitting of the ground state remains spectrally unresolved, it becomes possible to observe a magneto-optical resonance with a relatively large amplitude. Experiments have been carried out with the use of a miniature glass cell (V ~ 0.1 cm3) filled with 87Rb vapor and a buffer gas argon (a pressure of about 95 Torr). In particular, the theoretically predicted resonance narrowing with increasing light field intensity has been experimentally observed. A configuration for magneto-optical resonance excitation suggested here may be applied in quantum magnetometry to measure weak permanent magnetic fields and resonance microwave fields using cells filled with alkali metal vapor.
The absorption of a light wave interacting with optical transitions in the D1line of an alkali metal atom subjected to microwave radiation that is in resonance with magnetic dipole transitions between hyperfine ground-state components, has been investigated. It is known that when scanning a longitudinal magnetic field (B||k, wherekis the wavevector), one may observe a magneto-optical resonance due to the ground-state Hanle effect. In addition, the effect of double radio-optical resonance takes place because of the presence of the resonance microwave field. The joint influence of these effects on the formation of a narrow magneto-optical resonance in light wave absorption has been studied theoretically and experimentally. It has been shown analytically that the effects compete with each other and destructively act on the resonance formation. As a result, the amplitude of the resonance is small and its shape is complicated. However, in the presence of a buffer gas the pressure of which is such that the hyperfine splitting of the ground state remains spectrally unresolved, it becomes possible to observe a magneto-optical resonance with a relatively large amplitude. Experiments have been carried out with the use of a miniature glass cell (V~ 0.1 cm3) filled with87Rb vapor and a buffer gas argon (a pressure of about 95 Torr). In particular, the theoretically predicted resonance narrowing with increasing light field intensity has been experimentally observed. A configuration for magneto-optical resonance excitation suggested here may be applied in quantum magnetometry to measure weak permanent magnetic fields and resonance microwave fields using cells filled with alkali metal vapor.
Coherent-population-trapping resonance in vapor cell is a quantum interference effect that appears in the two-photon transitions between the ground-state hyperfine levels of alkali-metal atoms and is often utilized in miniature and centimeter-scale clock devices. To quantitatively understand and predict the performance of this phenomenon, it is necessary to consider the transitions and relaxations between all hyperfine Zeeman sublevels involved in the different excitation processes of the atom. In this paper, we constructed a computational multilevel atomic model of the Liouville density-matrix equation for 32 Zeeman sublevels involved in the D1{D}_{1}D1​ line of 133Cs^{133}\mathrm{Cs}133Cs irradiated by two frequencies with circularly polarized components and then simulated the amplitude and shape of the resonance spectrum of the transmitted light through centimeter-scale Cs-vapor cells. We show that the numerical solutions of the equation and analytical investigations adequately explain a variety of the characteristics observed in the experiment.