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IEEE Journal of Quantum Electronics

Photon, spin, and Raman echoes

Sven R. Hartmann

Published Nov 1, 1968• 116 citations
Publisher

Abstract

The general technique of the excitation of a system into a linear superposition of states is reviewed. Recent results in ruby are presented together with a simple theory which predicts Raman echoes.
DOI
10.1109/jqe.1968.1075009

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Effects of Superhyperfine Interactions on Photon-Echo Behavior in Dilute Ruby

L. Q. Lambert

A detailed analysis of the photon-echo decay in dilute ruby is presented. The experimental results are in quantitative agreement with an echo-decay theory based on the magnetic interaction between the Cr electronic spin and neighboring Al nuclear magnetic moments. Specifically, the following photon-echo properties are explained by the Cr-Al interaction: (i) modulation of the echo as a function of pulse separation time, (ii) the rapid decay of the echo from the $^{4}A({m}_{s}=\frac{3}{2})$ to $^{2}E({m}_{s}=\frac{1}{2})$ transition, (iii) the dependence of the echo on the direction and magnitude of an external magnetic field, (iv) the echo behavior at the 2.06- and 4.12-kG level crossings, and (v) the photon-echo decay in low magnetic fields. In addition, the experiments presented here show that the Cr-Al magnetic interactions in the $^{2}E$ excited state are roughly the same as the corresponding interactions in the $^{4}A_{2}$ ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.

Physical review. B, Solid state•Mar 1, 1973•59 citations
There has been much recent interest in the use of optical photon echoes for information storage and processing. Unfortunately, existing optical echo memories require doped crystals at liquid He temperature. The proposed scheme uses an optically excited microwave spin echo to store optical temporal information in the Raman excited ground state coherences. The advantage is that microwave echoes are known to exist at room temperature with decay times approaching 1 s in certain materials. We show that these spin echoes can be excited and detected optically, thereby allowing storage densities that are comparable to the optical echo techniques. Briefly, a three level A system is used, which can be excited by two near resonant optical transitions or one near resonant microwave transition. The Raman interaction first stores temporal and phase information in an inhomogeneously broadened ground states coherence. A microwave π-pulse is used to time-reverse the coherences, thus generating spin echoes that can be detected optically by a Raman probe. Preliminary experimental results will also be reviewed.
The amplitude of the electron-spin or photon echo from an ensemble of isolated atoms (echo atoms) interacting with magnetic-nuclear neighbors is calculated as a function of the magnitude and the orientation of an applied magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ and the separation between the two excitation pulses, in the limit that the magnitude of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ is large compared to the effective local fields at the echo-atom sites due to the nuclear neighbors. The general problem is reduced to the equivalent problem of two-level echo atoms interacting with nuclear neighbors. The latter problem is readily solved and applied to both spin and photon echoes. Experimentally observed spin-echo behavior in ruby is compared to calculated spin-echo behavior using no adjustable parameters, and is found to be in good agreement even when the magnetic field is tilted away from the optic axis thereby causing the echoes to disappear. Calculated photon-echo behavior, in which it is assumed that the interaction constants in the excited state are simply related to those in the ground state, shows the same general features as those that have been observed in experiment. Several results are presented to show the wide range of photon-echo behavior for different values of the interaction constants. A simple theory is presented which explains most observed echo behavior in a straightforward way.
A detailed analysis of the photon-echo decay in dilute ruby is presented. The experimental results are in quantitative agreement with an echo-decay theory based on the magnetic interaction between the Cr electronic spin and neighboring Al nuclear magnetic moments. Specifically, the following photon-echo properties are explained by the Cr-Al interaction: (i) modulation of the echo as a function of pulse separation time, (ii) the rapid decay of the echo from the 4A(ms=32)^{4}A({m}_{s}=\frac{3}{2})4A(ms​=23​) to 2E(ms=12)^{2}E({m}_{s}=\frac{1}{2})2E(ms​=21​) transition, (iii) the dependence of the echo on the direction and magnitude of an external magnetic field, (iv) the echo behavior at the 2.06- and 4.12-kG level crossings, and (v) the photon-echo decay in low magnetic fields. In addition, the experiments presented here show that the Cr-Al magnetic interactions in the 2E^{2}E2E excited state are roughly the same as the corresponding interactions in the 4A2^{4}A_{2}4A2​ ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.