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Physics Letters A

Forward scattering of resonant radiation as a function of applied magnetic field — theoretical study of the hyperfine lines of the sodium doublet

Suzanne Giraud-Cotton, V.Paul Kaftandjian, Lewis S. Klein

Published Apr 1, 1982• 29 citations
Publisher
DOI
10.1016/0375-9601(82)90539-4

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We present an experimental and theoretical analysis of the mechanical Hanle effect, i.e., the modification of the atomic trajectories following the interaction with laser fields in the Hanle configuration. The case of open transitions is examined. In our experiment a thermal sodium atomic beam is crossed perpendicularly by a single-mode linearly polarized laser beam. The laser field is tuned to resonance with an F g F e transition of the sodium D 1 line. A static magnetic field B is applied collinear to the laser light propagation direction. The atomic beam flux at the position corresponding to its maximum in the absence of laser light is studied as a function of the applied magnetic field. For the F g = F F e = F , F -1 transitions the atomic flux shows a sharp increase at B = 0, as a result of the coherent trapping of the population into the ground state. For the F g = 1 F e = 2 transition this effect is absent and no significant variation of the atomic flux with the magnetic field is observed. A theoretical description of the mechanical Hanle effect in open transitions is given and it is clarified why in our experiment the mechanical Hanle/CPT-resonances associated to different hyperfine transitions have different contrasts.

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The forward scattering of resonance radiation, with special reference to double resonance and level-crossing experiments

Alan Corney, B P Kibble, George William Series

Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jul 5, 1966•87 citations
The effects of magnetic optical activity in the sodium D1 line are investigated in detail both theoretically and experimentally. Particular consideration is given to the ultra-narrow Hanle-type features that are produced by the crossing of ground state Zeeman sub-levels and which although strongly exhibited by the F g =2 to F e =1, 2 doublet, are apparently absent from the F g =1 to F e =1,2 doublet. We demonstrate, quantitatively for the first time, that these features are principally a manifestation of Delta M=2 (quadrupole) coherences and are therefore not evidence for the existence of Delta M=4 (hexadecapole) coherences as originally proposed by Gawlik and co-workers (1987). Indeed the latter is shown to have little influence on these features even at light field intensities for which significant power broadening is observed. We also show explicitly that the width of these narrow crossing features is, for the typical vapour pressures used to give an optically thin sample, a function of the average time of transit through the light field. Using a simple phenomenological model we predict numerically both the absolute width of these coherence features and the rate at which they power broaden. Finally a brief consideration of the same coherence effects within the D2 line is presented.
We present an experimental and theoretical analysis of the mechanical Hanle effect, i.e., the modification of the atomic trajectories following the interaction with laser fields in the Hanle configuration. The case of open transitions is examined. In our experiment a thermal sodium atomic beam is crossed perpendicularly by a single-mode linearly polarized laser beam. The laser field is tuned to resonance with an F g F e transition of the sodium D 1 line. A static magnetic field B is applied collinear to the laser light propagation direction. The atomic beam flux at the position corresponding to its maximum in the absence of laser light is studied as a function of the applied magnetic field. For the F g = F F e = F , F -1 transitions the atomic flux shows a sharp increase at B = 0, as a result of the coherent trapping of the population into the ground state. For the F g = 1 F e = 2 transition this effect is absent and no significant variation of the atomic flux with the magnetic field is observed. A theoretical description of the mechanical Hanle effect in open transitions is given and it is clarified why in our experiment the mechanical Hanle/CPT-resonances associated to different hyperfine transitions have different contrasts.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.