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Journal of Physics B Atomic and Molecular Physics

Two-photon absorption: transitions induced in highly symmetric molecules by a magnetic field

Davıd L. Andrews

Published Sep 28, 1986• 1 citation
Publisher

Abstract

It has recently been shown that certain two-photon transitions can be indiced in atoms by applying a static magnetic field at the intersection of two crossed laser beams. The mechanism involves quantum mechanical interference between different excitation pathways. In this letter it is shown that a similar effect takes place in any highly symmetric molecule such as methane or sulphur hexafluoride belonging to a cubic symmetry group. However, in this case, the effect occurs through a non-linear magneto-optical interaction which is quite distinct from the interference mechanism.

DOI
10.1088/0022-3700/19/18/004

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It has recently been shown that certain two-photon transitions can be indiced in atoms by applying a static magnetic field at the intersection of two crossed laser beams. The mechanism involves quantum mechanical interference between different excitation pathways. In this letter it is shown that a similar effect takes place in any highly symmetric molecule such as methane or sulphur hexafluoride belonging to a cubic symmetry group. However, in this case, the effect occurs through a non-linear magneto-optical interaction which is quite distinct from the interference mechanism.
Quantum-mechanical interference is found in the two-photon excitation of an atomic 1S^{1}\mathrm{S}1S through the nonresonant sequence 11^{1}\mathrm{}^{1}11P\ensuremath{\leftarrow}1{\mathrm{}}^{1}1S, since the magnetic sublevels of the intermediate 1P^{1}\mathrm{P}1P state provide multiple pathways for absorption. Depending on the relative polarization of the two incident light beams, the interference can be either constructive or destructive. When the electric vectors of the light beams are linearly polarized and orthogonal, the interference is purely destructive and two-photon transitions are forbidden. Application of an external magnetic field, however, lifts the degeneracy of the intermediate state giving a two-photon absorption rate proportional to the square of the magnetic field strength. These effects are reported for the (7s)1{)}^{1})1S\ensuremath{\leftarrow}(5s2{\mathrm{s}}^{2}s2)1{)\mathrm{}}^{1})1S transition of atomic Sr excited by two dye lasers operating at different wavelengths.
When an atom is irradiated by two light beams whose sum frequency corresponds to an allowed two-photon transition between two 1S^{1}\mathrm{S}1S states, no radiation is absorbed if the electric vectors of the two beams are perpendicular to each other. Application of a magnetic field in a direction perpendicular to the plane defined by the two electric vectors permits two-photon absorption to take place. According to quantum theory the effect is interpreted as an interference phenomenon. That is, if no field is applied, the intermediate states are degenerate and the interference is destructive; when a magnetic field is applied, two different paths through intermediate states are possible, permitting population of the upper state. The effect is related to the Hanle effect and likewise provides the basis for an experimental method of determining Land\'e factors.
Two-photon transitions between atomic states of total electronic angular-momentum Ja=0{J}_{a}=0Ja​=0 and Jb=1{J}_{b}=1Jb​=1 are forbidden when the photons are of the same energy. This selection rule is analogous to the Landau-Yang theorem in particle physics that forbids decays of vector particle into two photons. It arises because it is impossible to construct a total angular-momentum ${J}_{2\ensuremath{\gamma}}=1$ quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with nonzero nuclear spin, the selection rule can be violated due to hyperfine interactions. Two distinct mechanisms responsible for the hyperfine-induced two-photon transitions are identified, and the hyperfine structure of the induced transitions is evaluated. The selection rule is also relaxed, even for zero-nuclear-spin atoms, by application of an external magnetic field. Once again, there are two similar mechanisms at play: Zeeman splitting of the intermediate-state sublevels, and off-diagonal mixing of states with different total electronic angular momentum in the final state. The present theoretical treatment is relevant to the ongoing experimental search for a possible Bose-Einstein-statistics violation using two-photon transitions in barium, where the hyperfine-induced transitions have been recently observed, and the magnetic-field-induced transitions are being considered both as a possible systematic effect, and as a way to calibrate the measurement.
Multiphoton nonlinear frequency mixing effects on coherent electromagnetically induced absorption spectra of 85Rb^{85}\mathrm{Rb}85Rb atoms using two orthogonal linear polarizations of strong-coupling and weak probe beams are investigated theoretically and experimentally with respect to an applied longitudinal magnetic field and coupling powers. Herein, we confirm that at least five-photon interactions in solving density matrix equations for the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85Rb^{85}\mathrm{Rb}85Rb atoms are required to explain experimentally observed coherent electromagnetically induced absorption spectra when a quantum axis is selected as the propagation direction of co-propagating coupling and probe laser beams. Distinct calculated spectral differences owing to variations in the magnetic field and coupling power between three- and five-photon interactions are confirmed. The obtained asymmetrical spectral shapes match very well with those calculated from five-photon interactions considering the off-resonant ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=2,3$ transitions. Genuine coherent spectral shapes are observed with a single laser combined with two acousto-optic modulators, wherein the spectral resolution is limited because of the decoherence rate between Zeeman sublevels in the ground state from transit-time relaxation.
A novel mechanism is proposed for optical bistability by utilizing the effect of interference which occurs when two levels are coupled by a one-photon resonance and by a two-photon resonance. The resulting bistability does not require atomic saturation, so the bistability can be observed at relatively low incident intensities, and the mechanism is essentially Doppler free, since it occurs by a two-photon process involving absorption of counterpropagating beams of the same frequency. A significant feature is that two-photon bistability can be controlled not only by the magnitude of the field of the one-photon resonance but also by its phase, and an oscillation or amplification of the field of the two-photon resonance can be observed under certain conditions by the mechanism of the parametric interaction of the field of the one-photon resonance and the field of the two-photon resonance through a nonlinear medium.
A theoretical study of the coherent interaction of multilevel atoms with a magneto-optical potential is presented. The potential is formed by counterpropagating linearly polarized laser beams whose polarization vectors intersect at an angle cphi and a static magnetic field applied parallel to the laser propagation direction. For a particular ratio of the light and magnetic field amplitudes, the light shift at positions of purely circularly polarized light is equal to the Zeeman splitting. In this case, for a three-level atom, one of the eigenvalues has a triangular spatial form. The diffraction of atoms from this triangular phase grating is an efficient beam splitter. The splitting is symmetric for cphi=90\ifmmode^\circ\else\textdegree\fi{} and asymmetric for cphi90\ifmmode^\circ\else\textdegree\fi{}. In addition we show that at well-defined positions in the light field, the atom undergoes nonadiabatic transitions and thus by using state-selective detection, one could observe an interference pattern produced by an array of double slits.