Concentration-Dependent Photon-Echo Decay in Ruby

A detailed experimental study is reported of the decay of circularly polarized photon echoes as a function of Cr concentration in samples ranging from 0.006 to 1.2 wt.% ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$ in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$. The decay is found to be independent of temperature in the liquid-helium range and generally depends on the pulse separation $\tau$ as $\exp (-K{\tau }^{\frac{1}{2}})$ with the decay constant $K$ proportional to the square root of the Cr concentration. The measured decay is independent of external magnetic field in the range 1.5-6 kG except at 1.06 kG, where modified decays are observed. A theoretical analysis is made of photon-echo decay in terms of spin flips of echo ions resulting from Cr-Cr magnetic interactions and yields good agreement with the observed decays. Spectral diffusion, modified for photon echoes, is shown not to be an important effect. However, anomalously slow decay is observed in some samples when the laser is tuned to the long-wavelength tail of the sample absorption line and the spectral-diffusion mechanism may apply here. The photon-echo-decay measurements are compared with spin-resonance and available spin-echo data in ruby. Also, it is inferred that resonant optical energy transfer is not an important photon-echo-decay mechanism even in the darkest sample studied.