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Journal of Physics B Atomic Molecular and Optical Physics

DC-field-induced resonance and polarization effects in two-colour frequency mixing in atoms

Nikolai L. Manakov, Vitalii D Ovsiannikov, Nikolai L. Manakov

Published May 16, 2000• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/33/11/306

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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.
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.
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.
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.
A resonance, induced by a DC field in a two-photon transition of an atom between states with opposite parity, results in a number of new effects related to the polarization of photons. These effects are caused by the interference of the non-resonant second-order dipole-forbidden amplitude and of a resonant part of the DC field-induced third-order amplitude. The linear and circular dichroism for the cross section of the process is revealed and analysed in detail for a two-photon excitation of the state from the ground state with a resonance on an state, induced by a DC electric field. The numerical data for alkali atoms demonstrate that the effects have quantitative characteristics of sufficiently large magnitudes and may be observed in experiments.
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.
The circular dichroism (CD) effect is predicted in a specific case of a two-color ionization of atoms, due to interfering a dc field-induced resonance two-photon ionization by electromagnetic radiation with frequency (omega) and the one- photon ionization by the wave with frequency 2(omega) . The maximum degree of CD may be observed in the range of fields where the probability for the dc field-induced two-photon ionization becomes comparable with that of the single-photon process and exceeds essentially the field-free two-photon ionization probability. The effect is sensitive to the relative phase between the two ac field components. The atomic parameters for this effect in alkali atoms are calculated. The range of fields is determined, for which the dichroism becomes observable. The use of the effect to control the branching ratio and the relative phase of the two radiations is discussed.