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IEEE Journal of Quantum Electronics

Third-order susceptibility of alkali metal vapors

H. Eicher

Published Apr 1, 1975• 60 citations
Publisher

Abstract

This paper presents calculations of the third-order susceptibility in the alkali metal vapors involving spin-orbit coupling in the energy spectrum of the alkali atoms and some power transfer between the atoms in the ensemble and their surroundings, including the radiation field. The results are plotted as a function of wavelength in the vicinity of the neodymium and iodine laser lines, and their second, third, and fourth harmonics for each of the alkalies; i.e., 10 520 Å\lambda, 2\lambda, 3\lambda, 4\lambda)\lambda, 2\lambda, 3\lambda, 4\lambda) < 13 230 Å, respectively.

DOI
10.1109/jqe.1975.1068583

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Journal of Experimental and Theoretical Physics Letters•Mar 1, 2015•19 citations
This paper presents calculations of the third-order susceptibility in the alkali metal vapors involving spin-orbit coupling in the energy spectrum of the alkali atoms and some power transfer between the atoms in the ensemble and their surroundings, including the radiation field. The results are plotted as a function of wavelength in the vicinity of the neodymium and iodine laser lines, and their second, third, and fourth harmonics for each of the alkalies; i.e., 10 520 Å\lambda, 2\lambda, 3\lambda, 4\lambda)\lambda, 2\lambda, 3\lambda, 4\lambda) < 13 230 Å, respectively.
A method is suggested for the calculation of the nonlinear susceptibility corresponding to the generation of second and third optical harmonics in atomic gases. The method is based on the use of the Green's function of an atomic optical electron in the computation of the composite matrix elements. The results are given of a numerical calculation of χ(–3ω;ω,ω,ω) and χ(–2ω;0,ω,ω) for hydrogen, alkali atoms, and inert gases at the frequencies of ruby and neodymium laser radiations and their second harmonics. A two-photon resonance in the generation of the third harmonics is considered.
Starting with well known formulae for nth-order atomic susceptibilities, irreducible spherical tensor techniques and Racah algebra are used to put these in a form suitable for the treatment of complex nonlinear processes, e.g. where fine and hyperfine interactions can be included and the interacting fields can have quite general polarizations. By way of illustration the susceptibilities are calculated in detail for third harmonic generation and Raman scattering in alkali vapours, taking into account the effect of spin-orbit coupling.
The van der Waals coefficients, from C11{C}_{11}C11​ through to C16{C}_{16}C16​ resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the Cn∕rn{C}_{n}∕{r}^{n}Cn​∕rn potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to C10∕r10{C}_{10}∕{r}^{10}C10​∕r10 results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than 20a020{a}_{0}20a0​. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive (C11,C13,C15)({C}_{11},{C}_{13},{C}_{15})(C11​,C13​,C15​) and attractive (C12,C14,C16)({C}_{12},{C}_{14},{C}_{16})(C12​,C14​,C16​) dispersion forces.
In this paper we calculate the effect of spin-exchange collisions in alkali-metal vapors. In the framework of the high-energy approximation, we evaluate the spin-exchange cross sections related to the line broadening and to the frequency shift of the ground state hyperfine transition. We do the calculation for the four isotopes, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 87Rb^{87}\mathrm{Rb}87Rb, and 133Cs^{133}\mathrm{Cs}133Cs. The results are used in particular to evaluate the spin-exchange frequency shift in Rb vapor cell frequency standards used in many applications. It turns out that, due to possible fluctuations in the atomic density, spin exchange may affect significantly the medium and long term frequency stability of the frequency standard.
It has been shown that the D 1 line of atomic vapors of alkali metals excited by π-polarized radiation in a strong transverse magnetic field includes specific “guiding” (indicating) atomic transitions between the magnetic sublevels of the hyperfine structure. The dependence of the frequency shift of the guiding transitions on the magnetic field, as well as on their dipole moments, is asymptotic for all other transitions. An experiment with a nanocell with Rb vapor with a thickness of half the wavelength (λ/2 method) for ensuring a sub-Doppler spectral resolution has completely confirmed the presence of guiding transitions. Two groups of six transitions for 85 Rb and two groups of four transitions for 87 Rb have been detected in the absorption spectra in magnetic fields above 4 kG. A guiding transition has been identified in each of four groups. Four transitions forbidden at B = 0 have been also detected; with an increase in the magnetic field, their probabilities also approach the probabilities of the guiding transitions.