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Optics Letters

Photon-echo interferometry

A. M. Bacon, H. Z. Zhao, P. J. Laverty, L. J. Wang, John E. Thomas

Published May 15, 1994• 1 citation
Publisher

Abstract

Temporal interference between photon echoes of adjacent transitions in simple atoms is demonstrated, yielding suppression of the echo intensity by a factor of 10(4). The method provides a sensitive probe of perturbations that differentially affect the phase of the dipole moments for the adjacent transitions.
DOI
10.1364/ol.19.000746

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A method of high-resolution time-resolved optical spectroscopy using oscillations of the photon echo intensity in the presence of a perturbation, which splits the optical frequencies of the transitions of two or more ion subgroups, has been proposed and demonstrated. This method has been applied to systems in which the Zee-man effect is manifested. The transition frequencies of ions are switched by a pulsed magnetic field. Oscillations of the photon echo intensity were observed in LiLuF4:Er3+ and LiYF4:Er3+. The first minimum corresponding to the accumulated phase of the electric dipole moment π/2 is reached in the pulsed magnetic field with an amplitude of ∼2 G at a duration of 30 ns. The Zeeman splitting in this field is ∼10 MHz, which is much less than the laser spectral width (0.15 Å ∼ 9 GHz). The g factor of the 4 F 9/2(I) excited state of the Er3+ ion in the LiLuF4 matrix has been determined in zero magnetic field. The comparison with the g-factor value found from the measurement of the absorption spectrum in a magnetic field of 8 kG has been performed.

Journal of Experimental and Theoretical Physics Letters•Mar 1, 2012•13 citations
Effects of electric dipole reorienting collisions on photon echoes are investigated. In an extension of the author's earlier work, a general expression is derived, including terms from binary collisions, for the photonecho dipole moment amplitude. The explicit results are worked out for simple cases such as ${j}_{1}=\frac{1}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=0$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=1$, and ${j}_{1}=\frac{3}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$ transitions. While it is shown that echoes resulting from the above simple transitions will not be depolarized by atomic collisions, photon echoes induced by any other transitions are necessarily depolarized by collisions. In addition, it is possible to show that the general expression for the echo dipole moment can be written as a sum of multipole moments. Only the odd moments contribute to the echoes. The importance of this picture is that collision-induced relaxation of each moment is described by a single time constant---as in the model commonly used for Hanle-effect experiments. As a result, for an echo arising from a ${j}_{1}\ensuremath{\leftrightarrow}{j}_{2}$ transition (${j}_{1}\ensuremath{\ge}{j}_{2}$), there must be 12j1(j1+1)\frac{1}{2}{j}_{1}({j}_{1}+1)21​j1​(j1​+1) time constants to describe the collision damping of the echo intensity, j1{j}_{1}j1​ being an integer. The corresponding formula for the half-integer case is 12(j2+12)(j2+32)\frac{1}{2}({j}_{2}+\frac{1}{2})({j}_{2}+\frac{3}{2})21​(j2​+21​)(j2​+23​).
A method of high-resolution time-resolved optical spectroscopy using oscillations of the photon echo intensity in the presence of a perturbation, which splits the optical frequencies of the transitions of two or more ion subgroups, has been proposed and demonstrated. This method has been applied to systems in which the Zee-man effect is manifested. The transition frequencies of ions are switched by a pulsed magnetic field. Oscillations of the photon echo intensity were observed in LiLuF4:Er3+ and LiYF4:Er3+. The first minimum corresponding to the accumulated phase of the electric dipole moment π/2 is reached in the pulsed magnetic field with an amplitude of ∼2 G at a duration of 30 ns. The Zeeman splitting in this field is ∼10 MHz, which is much less than the laser spectral width (0.15 Å ∼ 9 GHz). The g factor of the 4 F 9/2(I) excited state of the Er3+ ion in the LiLuF4 matrix has been determined in zero magnetic field. The comparison with the g-factor value found from the measurement of the absorption spectrum in a magnetic field of 8 kG has been performed.