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Physical Review A

Quantum interference in two-photon absorption: Polarization and magnetic field effects in the (7s )1 S←(5 s2 )1 S transition of atomic Sr

R. B. Stewart, Gerald J. Diebold

Published Sep 1, 1986• 7 citations
Publisher

Abstract

Quantum-mechanical interference is found in the two-photon excitation of an atomic $^{1}\mathrm{S}$ through the nonresonant sequence $^{1}\mathrm{}^{1}$P\ensuremath{\leftarrow}${\mathrm{}}^{1}$S, since the magnetic sublevels of the intermediate $^{1}\mathrm{P}$ 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${)}^{1}$S\ensuremath{\leftarrow}(5${\mathrm{s}}^{2}$${)\mathrm{}}^{1}$S transition of atomic Sr excited by two dye lasers operating at different wavelengths.

DOI
10.1103/physreva.34.2547

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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}(5{\mathrm{s}}^{2}$${)\mathrm{}}^{1}S 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.
The degree of linear polarization P L for two-photon absorption of alkali atoms in intermediate strength magnetic fields has been computationally investigated. Polarization spectra were obtained for n a s 2 S 1/2 to n b s 2 S 1/2 transitions with the photons in near resonance with intermediate 2 P j levels. Previous experiments and calculations in the absence of a magnetic held revealed a complete polarization reversal (P L approximately -100%) for frequencies near resonance between the 2 P 1/2 and 2 P 3/2 levels due to fine-structure coherence. Application of weak to intermediate strength fields induce additional depolarization features as a result of anomalous Zeeman splitting. The fine-structure depolarization feature disappears for strong fields (Paschen-Back regime), while the calculations predict that Zeeman depolarization persists though the transitions become forbidden. Magnetic-field-dependent polarization spectra can be measured in the laboratory with high precision and it should prove interesting to trace through the weak, intermediate, and strong field regimes.
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.
We report here the first observation and measurement of the transition magnetic moment for a strongly forbidden S-S transition of an alkali atom. By using single-photon excitation of the 6S1/2-7S1/2 caesium transition in a quasi-static electric field, we have detected an electronic polarization of the excited state, specific to an interference effect occurring in mixed electric magnetic dipole transitions. Our measurements, independent of the vapour density, indicate that the magnetic dipole amplitude M 1 has the same size as the electric dipole amplitude E1 , induced by an electric field, parallel to the light wave polarization, and equal to 2.62 ± 0.21 V/cm. We also obtain the relative sign of M 1 and E1. Using a theoretical value of E 1 and a well-defined phase convention, we deduce for the magnetic moment of the transition < 7S, 1/ 2 | μ z | 6S, 1/ 2 > = - (4.24 ± 0.34) 10-5 |μB|, in good agreement with a theoretical estimate. This result can also be expressed in terms of the oscillator strength in zero electric field f6S-7S = 4.05 × 10-15, or of the single-photon M1 decay rate Γ 7S-6S = 0.93 x 10-6 s-1.
Polarization dependence of amplitude for resonant magnetic-field-induced coherent mixing of two collinear laser waves may be used for separating M 1 and E 2 contributions to n 1 2 P 1/2(3/2) – n 2 2 P 3/2(1/2) dipole-forbidden transition in atoms. In particular, the interference between E 2 and M 1 terms of the amplitude may cause linear polarization and circular dichroism effects. The dependencies of the two polarization effects on the width and splitting of resonance levels, on resonance detuning, on relative directions of steady and alternating field vectors are determined. A static electric field may induce essential changes to the cross section for the magnetic-field-induced mixing, modifying its dependence on the magnetic field and incident wave polarization vectors. Relations between the M 1/ E 2 amplitude ratio and quantitative characteristics of polarization asymmetry in cross section are determined. Numerical data are presented for coherent mixing of two laser waves on Cs, Rb and K atoms.
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.