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

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.

Interference ofE2 andM1n12P–n22P transition amplitudes in steady-field-induced coherent mixing of two resonant waves on atoms

“…where Ĵ and Ŝ are the operators of the total and spin momenta, correspondingly. Using explicit expressions of operators ( 7), ( 8), ( 9) in ( 3), (4), after integration in angular variables with the use of general methods of the quantum theory of angular momentum [26], we obtain (see [25])…”

“…After averaging in M 0 expressions (10) and ( 11) only terms with p = 0 remain, and equation ( 14) may be presented as follows [25],…”

“…Integrating in angular variables the matrix elements ( 22) and ( 23) with explicit expressions for operators (7), ( 9), (24), (25) and with the use of the general methods of quantum theory of angular momentum, we obtain U (5) 1 ≈…”

“…, being in resonance with one of the two incident waves. This scheme with account of only E2 interaction between atom and wave has been considered in [25] as a case of DQD (dipolequadrupole-dipole) route in the double-resonant frequency summation. The M1 contribution on this route becomes significant in heavy alkali atoms, in which the spin-orbit interaction is rather strong to mix states |n 1 LJ and |n 2 LJ with different principal quantum numbers, n 1 = n 2 .…”

<title>Precision determination of E2/M1 amplitude ratio in atoms from polarization dependence of a two-color frequency mixing</title>

“…The frequency mixing process is characterized by the three-photon amplitude where the electric quadrupole and magnetic dipole parts can be separated from one another: U = U(Mi) + U2 (1) U(M1) corresponds to the magnetic dipole interaction of atom with the field of the first wave, described by the Harniltonian m((J+S)Eni><eiJ), (2) with J and S, the atomic total momentum and spini operator; U(E2) corresponds to the electric quadrupole interaction, with the Harniltonian…”