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Journal de Physique Lettres

Observation of the interference between the magnetic and electric dipole amplitudes of the caesium 6S-7S transition in an electric field. measurement of the transition magnetic moment

Marie-Anne Bouchiat, Lionel Pottier

Published Jan 1, 1976• 26 citations
Publisher

Abstract

We report here the first observation and measurement of the transition magnetic moment for a strongly forbidden S-S transition of an alkali atom. By using single-photon excitation of the 6S1/2-7S1/2 caesium transition in a quasi-static electric field, we have detected an electronic polarization of the excited state, specific to an interference effect occurring in mixed electric magnetic dipole transitions. Our measurements, independent of the vapour density, indicate that the magnetic dipole amplitude M 1 has the same size as the electric dipole amplitude E1 , induced by an electric field, parallel to the light wave polarization, and equal to 2.62 ± 0.21 V/cm. We also obtain the relative sign of M 1 and E1. Using a theoretical value of E 1 and a well-defined phase convention, we deduce for the magnetic moment of the transition < 7S, 1/ 2 | μ z | 6S, 1/ 2 > = - (4.24 ± 0.34) 10-5 |μB|, in good agreement with a theoretical estimate. This result can also be expressed in terms of the oscillator strength in zero electric field f6S-7S = 4.05 × 10-15, or of the single-photon M1 decay rate Γ 7S-6S = 0.93 x 10-6 s-1.

DOI
10.1051/jphyslet:0197600370407900

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Polarization dependence of amplitude for resonant magnetic-field-induced coherent mixing of two collinear laser waves may be used for separating M 1 and E 2 contributions to n 1 2 P 1/2(3/2) – n 2 2 P 3/2(1/2) dipole-forbidden transition in atoms. In particular, the interference between E 2 and M 1 terms of the amplitude may cause linear polarization and circular dichroism effects. The dependencies of the two polarization effects on the width and splitting of resonance levels, on resonance detuning, on relative directions of steady and alternating field vectors are determined. A static electric field may induce essential changes to the cross section for the magnetic-field-induced mixing, modifying its dependence on the magnetic field and incident wave polarization vectors. Relations between the M 1/ E 2 amplitude ratio and quantitative characteristics of polarization asymmetry in cross section are determined. Numerical data are presented for coherent mixing of two laser waves on Cs, Rb and K atoms.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 27, 2005•3 citations
We report here the first observation and measurement of the transition magnetic moment for a strongly forbidden S-S transition of an alkali atom. By using single-photon excitation of the 6S1/2-7S1/2 caesium transition in a quasi-static electric field, we have detected an electronic polarization of the excited state, specific to an interference effect occurring in mixed electric magnetic dipole transitions. Our measurements, independent of the vapour density, indicate that the magnetic dipole amplitude M 1 has the same size as the electric dipole amplitude E1 , induced by an electric field, parallel to the light wave polarization, and equal to 2.62 ± 0.21 V/cm. We also obtain the relative sign of M 1 and E1. Using a theoretical value of E 1 and a well-defined phase convention, we deduce for the magnetic moment of the transition < 7S, 1/ 2 | μ z | 6S, 1/ 2 > = - (4.24 ± 0.34) 10-5 |μB|, in good agreement with a theoretical estimate. This result can also be expressed in terms of the oscillator strength in zero electric field f6S-7S = 4.05 × 10-15, or of the single-photon M1 decay rate Γ 7S-6S = 0.93 x 10-6 s-1.
We have observed the direct single-photon electric dipole excitation of the 7 2S1/2 state of cesium, by exciting the 6 2S1/2 ground state in an external d. c. electric field of 10 to 1 000 V/cm with a single-mode, c. w., tunable dye laser. The resonance was detected by monitoring the decay fluorescence from the excited state. We verified the selection rules obeyed by the hyperfine transitions which depend on the relative orientation of the linear polarization of the beam with respect to the field. When they are orthogonal, the line pattern reflects the existence of a spin-dependent part of the polarizability induced by spin-orbit effects, the size of which was measured with respect to that of the scalar part. Results in very weak fields show that the oscillator strength of the 6S-7S transition is smaller than 2 x 10-13.
We have developed a two-pathway Coherent Control technique for measurements of weak optical transition moments. We demonstrate this technique through a measurement of the transition moment of the highly-forbidden magnetic dipole transition between the 6s2S1/21/2 and 7s2S1/21/2 states in atomic Cesium. The experimental principle is based on a two-pathway excitation, using two phase-coherent laser fields, a fundamental field at 1079 nm and its second harmonic at 539.5 nm. The IR field induces a strong two-photon transition, while the 539.5 nm field drives a pair of weak one-photon transitions: a Stark-induced transition of controllable strength as well as the magnetic dipole transition. Observations of the interference between these transitions for different Stark-induced transition amplitudes, allow a measurement of the ratio of the magnetic dipole to the Stark-induced moment. The interference between the transitions is controlled by modulation of the phase-delay between the two optical fields. Our determination of the magnetic dipole moment is at the 0.4% level and in good agreement with previous measurements, and serves as a benchmark for our technique and apparatus. We anticipate that with further improvement of the apparatus detection sensitivity, the demonstrated scheme can be used for measurements of the very weak Parity Violation transition moment on the Cesium 6s2S1/21/2→7s2S1/21/2 transition.
Quantum-mechanical interference is found in the two-photon excitation of an atomic 1S^{1}\mathrm{S}1S through the nonresonant sequence 11^{1}\mathrm{}^{1}11P\ensuremath{\leftarrow}1{\mathrm{}}^{1}1S, since the magnetic sublevels of the intermediate 1P^{1}\mathrm{P}1P state provide multiple pathways for absorption. Depending on the relative polarization of the two incident light beams, the interference can be either constructive or destructive. When the electric vectors of the light beams are linearly polarized and orthogonal, the interference is purely destructive and two-photon transitions are forbidden. Application of an external magnetic field, however, lifts the degeneracy of the intermediate state giving a two-photon absorption rate proportional to the square of the magnetic field strength. These effects are reported for the (7s)1{)}^{1})1S\ensuremath{\leftarrow}(5s2{\mathrm{s}}^{2}s2)1{)\mathrm{}}^{1})1S transition of atomic Sr excited by two dye lasers operating at different wavelengths.
We have measured the magnetic dipole (M1) and electric quadrupole (E2) amplitudes in the D1 transition of rubidium atoms placed in a static electric field, ${\mathit{scrE}\ensuremath{\rightarrow}}_{\mathit{s}}$. The interference of the Stark induced M1 and E2 amplitudes with the normal E1 amplitude gives the atomic absorptivity a linear dependence on ${\mathit{scrE}\ensuremath{\rightarrow}}_{\mathit{s}}$ and on the atomic spin polarization. We find that the fractional change in absorptivity due to the Stark interference is aM1{\mathit{a}}_{\mathit{M}1}aM1​+aE2{\mathit{a}}_{\mathit{E}2}aE2​=(-2.37\ifmmode\pm\else\textpm\fi{}0.37\ifmmode\pm\else\textpm\fi{}0.28)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ (kV/cm${)}^{\mathrm{\ensuremath{-}}1}$.
Obtaining an accurate value of the electric dipole moment μ is essential in the fields of laser application technologies. A direct way of measuring the electric dipole moment μ is to observe the Rabi-oscillation which manifests itself in the coherent photo-excitation behavior of atoms. In the case of the elements which have large angular momenta, identifying the Rabi-oscillation in their excitation behavior becomes rather difficult. We proposed an accurate and straightforward method of determining the electric-dipole moment μ between multifold degenerate levels. The point is to remove the degeneracy by applying an external magnetic field with the aid of the Zeeman effect and, then, to realize a degeneration free coherent excitation. As a result, we can observe the Rabi-oscillations explicitly in the excitation vs. laser-fluence curves. The present method provides a reliable basis of experimental determination of μ. As an example, we applied the present method to a transition to 0–17,362 cm−1 level in uranium and obtained the value μ=0.86±0.06 (Debye).
Polarization dependence of amplitude for resonant magnetic-field-induced coherent mixing of two collinear laser waves may be used for separating M 1 and E 2 contributions to n 1 2 P 1/2(3/2) – n 2 2 P 3/2(1/2) dipole-forbidden transition in atoms. In particular, the interference between E 2 and M 1 terms of the amplitude may cause linear polarization and circular dichroism effects. The dependencies of the two polarization effects on the width and splitting of resonance levels, on resonance detuning, on relative directions of steady and alternating field vectors are determined. A static electric field may induce essential changes to the cross section for the magnetic-field-induced mixing, modifying its dependence on the magnetic field and incident wave polarization vectors. Relations between the M 1/ E 2 amplitude ratio and quantitative characteristics of polarization asymmetry in cross section are determined. Numerical data are presented for coherent mixing of two laser waves on Cs, Rb and K atoms.