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Journal of Physics B Atomic Molecular and Optical Physics

Magnetic-field-induced two-colour frequency mixing in atoms: fine-structure effects on a double-resonance coherent cross section

K V Khalev, Vitalii D Ovsiannikov, V V Chernushkin

Published May 9, 2002• 3 citations
Publisher

Abstract

The fine-structure splitting of resonance atomic levels causes essential effects on the amplitude of a two-colour frequency mixing in a magnetic field. The fine-structure effects are analysed in the scattering cross section, and particularly in the circular dichroism phenomena, such as the elliptical polarization of the generated wave, when both incident waves are linearly polarized, and the dependence of the cross section on the helicity of one of the incident waves when the other one is linearly polarized. Together with general analytic expressions for the amplitude, the numerical data are presented for three different double-resonant routes involving two dipole and one quadrupole interactions of atoms with a field. The results may be useful for the polarization control of the process in an atomic vapour and for the frequency-mixing spectroscopic studies of atomic structure.

DOI
10.1088/0953-4075/35/10/308

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The fine-structure splitting of resonance atomic levels causes essential effects on the amplitude of a two-colour frequency mixing in a magnetic field. The fine-structure effects are analysed in the scattering cross section, and particularly in the circular dichroism phenomena, such as the elliptical polarization of the generated wave, when both incident waves are linearly polarized, and the dependence of the cross section on the helicity of one of the incident waves when the other one is linearly polarized. Together with general analytic expressions for the amplitude, the numerical data are presented for three different double-resonant routes involving two dipole and one quadrupole interactions of atoms with a field. The results may be useful for the polarization control of the process in an atomic vapour and for the frequency-mixing spectroscopic studies of atomic structure.
Application of a steady magnetic field allows sum-frequency radiation generated via dipole-forbidden mixing of two-colour fields in an atomic medium to be emitted in the (otherwise forbidden) forward direction. As a result of resonance tuning at low-field strength (not exceeding 0.1 T) a fourth-order magnetic-dipole-induced amplitude for the sum-frequency process can be made comparable to the third-order field-free amplitude. We show that the interference between different terms of the field-dependent amplitude may cause the circular dichroism of the forward-scattering cross section for one of the two incident waves or the sum-frequency wave when the other two waves are linearly polarized. The dichroism effect is due to the dissipation processes determined by the resonant level width Γ and depends strongly both on Γ and the resonance detuning Δ. The effect may be used to control the frequency conversion process or to make possible a frequency mixing laser spectroscopy of excited atomic levels.
In a gas of free atoms interacting with a two-colour laser radiation, a DC electric field provides the necessary conditions for generation of sum-frequency radiation, together with a resonance enhancement of the frequency conversion process. The interference between the DC-field-induced and the dipole-forbidden three-photon amplitudes causes circular dichroism effects in the scattering of the sum-frequency photons at right angles to the incident laser beams. The DC-field-induced resonance effect is strongly dependent on the frequency detuning and the width of the resonant levels.
The relative contributions of the magnetic dipole interaction ( M 1) and the electric quadrupole interaction ( E 2) in the dipole-forbidden three-wave process of mixing two-colour radiation in free atoms may be determined from the dependence of the frequency-conversion efficiency on the incident-wave polarization. Analytical expressions are derived for the polarization dependence of amplitudes and cross sections of a double-resonant scattering of the sum- and difference-frequency photons. Numerical estimates are presented for the ratio of E 2 and M 1 three-photon amplitudes in ground-state indium and thallium atoms.
Steady electric and magnetic fields can stimulate frequency mixing of two laser waves in ensemble of free atoms. In addition to coherence conditions, the steady fields may induce additional resonance singularities essentially enhancing the cross section for scattering the sum-frequency wave. Interference between different components of the electric- and magnetic-field induced frequency summation amplitudes may cause significant effects on the efficiency of conversion. The dependence on the incident wave polarization and the atomic resonance structure is calculated analytically for the frequency mixing in atoms with a singlet structure of the ground and resonance states. Numerical estimates for the quantitative characteristics of the effect are presented for helium, alkali-earth and mercury atoms in their groundn1S0-state in the case of the two-photon resonance on excited singlet states with angular momentum 0, 1, and 2.
Polarization dependence of amplitude for resonant magnetic-field-induced coherent mixing of two collinear laser waves may be used for separating M1 and E2 contributions to n1 2P1/2(3/2) - n2 2P3/2(1/2) dipole-forbidden transition in atoms. The interference between E2 and Ml terms of the amplitude may cause linear polarization and circular dichroism effects. The dependencies of the two effects on the width and splitting of resonance levels, on resonance detuning, on relative directions of steady and alternating field vectors are determined. Numerical data are presented for frequency summation of two laser waves on Cs, Rb and K atoms.
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.