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

Abstract

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 fourthorder 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 and depends strongly both on and the resonance detuning . The effect may be used to control the frequency conversion process or to make possible a frequency mixing laser spectroscopy of excited atomic levels.

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

“…The steady external field may be a magnetic field which also breaks the symmetry of the atom so that the sum-frequency photon may be emitted collinearly with the incident light beams (in the case of co-propagation or counter-propagation of the beams). The small magnitude of the atom-magnetic field interaction may be compensated for considerably by a significant resonance increase of the field-induced matrix element (Khalev and Ovsiannikov 2001).…”

“…In our previous analysis of the frequency mixing in atoms without fine-structure splitting of resonance levels (Khalev and Ovsiannikov 2001) a strong wave polarization dependence was discovered, particularly the circular dichroism. The results were applicable only to atoms with singlet states or to atoms with negligible splitting of multiplet levels.…”

“…and the expression for the amplitude U ( 4) is reduced to the case of an atom without fine structure (Khalev and Ovsiannikov 2001).…”

Interference betweenE2 andM1 amplitudes in two-colour frequency mixing in atoms

“…The polarization dependence of the frequency mixing amplitudes may also be useful in the effective control of the frequency conversion in atomic gases. A steady electric or magnetic field breaks down atomic symmetry and can provide the necessary conditions for the collinear coherent generation of a sum-or difference-frequency wave (Manakov and Ovsiannikov 2000, Khalev and Ovsiannikov 2001, Khalev et al 2002. Therefore, detailed studies of field-induced resonant processes of frequency mixing in different atomic media may provide new information on the internal atomic structure, the spin-orbit forces and matrix elements of radiation transitions.…”

<title>E2/M1 amplitude ratio from DC-field-induced two-color frequency mixing in atoms</title>

“…The atomic factors a' = R +2R+(4R -R); a1 = -[R1 +R + (R' +R)] ; a2 = 2R' +R -(R' -4R) (2) represent the linear combinations of the radial matrix elements Rf = (nLoJojrgfrInLoJi) for the dc-fieldinduced second-order dipole transition from the ground state to the first excited level.…”