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Journal of Physics B Atomic Molecular and Optical Physics

Magnetoelectric Jones spectroscopy of alkali atoms

V V Chernushkin, Polina V. Mironova, Vitalii D Ovsiannikov

Published May 27, 2008• 4 citations
Publisher

Abstract

The Jones effect in a medium of free atoms exposed to static electric and magnetic fields is a useful tool for determining details of an atomic structure. For atoms in their nS ground states irradiated by a monochromatic wave in resonance with a single-photon transition to an n' D state, the bilinear Jones effect is not shaded by the quadratic Kerr and Cotton–Mouton effects, nor by the linear in magnetic field Faraday effect. The position and shape of the amplitude resonance may provide information on spectroscopic properties of atomic levels. We generalize equations for the Jones-effect amplitude to the case of a doublet structure of energy levels and calculate corresponding parameters for alkali atoms. General equations are derived for the amplitude dependence on the relative orientation of the static electric and magnetic fields and on the angle between the static field and the major axis of the wave polarization vector. These equations demonstrate explicitly that the three bilinear-in-static-fields optical birefringence effects—(i) the Jones birefringence (in parallel fields), (ii) the linear birefringence and (iii) the directional birefringence (the last two in perpendicular fields)—correspond to particular cases of the bilinear-in-static-fields correction to the amplitude of Rayleigh forward scattering.

DOI
10.1088/0953-4075/41/11/115401

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The Jones effect in a medium of free atoms exposed to static electric and magnetic fields is a useful tool for determining details of an atomic structure. For atoms in their nS ground states irradiated by a monochromatic wave in resonance with a single-photon transition to an n' D state, the bilinear Jones effect is not shaded by the quadratic Kerr and Cotton–Mouton effects, nor by the linear in magnetic field Faraday effect. The position and shape of the amplitude resonance may provide information on spectroscopic properties of atomic levels. We generalize equations for the Jones-effect amplitude to the case of a doublet structure of energy levels and calculate corresponding parameters for alkali atoms. General equations are derived for the amplitude dependence on the relative orientation of the static electric and magnetic fields and on the angle between the static field and the major axis of the wave polarization vector. These equations demonstrate explicitly that the three bilinear-in-static-fields optical birefringence effects—(i) the Jones birefringence (in parallel fields), (ii) the linear birefringence and (iii) the directional birefringence (the last two in perpendicular fields)—correspond to particular cases of the bilinear-in-static-fields correction to the amplitude of Rayleigh forward scattering.
Theoretical treatment of the magnetoelectric Jones birefringence and dichroism is developed through the bilinear in static electric and magnetic field dipole-forbidden corrections to the amplitude of Rayleigh scattering. In particular cases of orientation of the static fields relative the polarization and wave vectors of monochromatic radiation, the amplitude determines corrections to the refractive index of atomic gas responsible for (i) the Jones birefringence and dichroism, (ii) linear birefringence and dichroism and (iii) directional anisotropy for the monochromatic wave. The analytical equations and numerical data for the indicated corrections, calculated for alkali atoms, determine optimal conditions for observing the effects in vapours. For resonance on D state essential enhancement is discovered in the frequency dependence for the ratio of refractive index anisotropy of the Jones effect to the square-root product of corresponding anisotropy determining the Kerr and Cotton-Mouton effects.
Theoretical treatment of the magnetoelectric Jones birefringence and dichroism is developed through the bilinearity in static electric and magnetic field dipole-forbidden corrections to the amplitude of Rayleigh scattering. In particular cases of orientation of the static fields relative to the polarization and wave vectors of monochromatic radiation, the amplitude determines corrections to the refractive index of atomic gas responsible for (i) the Jones birefringence and dichroism, (ii) linear birefringence and dichroism and (iii) directional anisotropy for the monochromatic wave. The analytical equations and numerical data for the indicated corrections, calculated for alkaline-earth-like atoms, determine optimal conditions for observing the effects in vapours. For resonance on 1D2 state essential enhancement is discovered in the frequency dependence for the ratio of refractive index anisotropy of the Jones effect to the square-root product of corresponding anisotropies determining the Kerr and Cotton–Mouton effects.
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.
A static electric field may induce essential changes to the cross section for the magnetic-field-induced coherent frecuency mixing of two laser waves, modifying the cross-section dependence on the magnetic field and polarization vectors of incident waves, which depends on the ratio of M1/E2 contributions to n1 2P1/2 (3/2) - n2 2P3/2(1/2) radiation transition amplitude. Relations between the M1/E2 ratio and quantitative characteristics of polarization asymmetry in cross section are determined. Calculated numerical data are presented for coherent mixing of two laser waves on Cs, Rb and K atoms.
A theoretical analysis is made of the nonlinear (in respect of the radiation intensity) rotation of the plane of polarization occuring in an atomic medium subjected to a static magnetic field near one-photon (two-level atoms) and two-photon (three-level atoms) resonances. A study is also made of the influence of a strong monochromatic pump wave on the propagation of a weak nonmonochromatic wave. The wave functions and quasienergies are calculated for a three-level system in static magnetic and monochromatic electromagnetic fields near a two-photon resonance. It is shown that the Verdet constant and the refractive index of such a system depend on the magnitude and relative sign of the frequency detuning from resonance. Proximity to a two-photon resonance destroys the polarizability of a medium for either sign of the detuning.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.