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Physical Review

Cross Relaxation and Concentration Effects in Ruby

Roy W. Roberts, James H. Burgess, Harold D. Tenney

Published Feb 15, 1961• 8 citations
Publisher

Abstract

Cross relaxation effects in ruby maser crystals are treated by introduction of a cross relaxation probability in the rate equations. Detailed solutions have been obtained for several specific processes and compared to recent experiments. It is shown that cross relaxation can improve maser performance even in the absence of impurity doping. Pulse experiments at 0.06 and 0.14% chromium ion concentrations in a ruby traveling wave maser are interpreted in terms of a five-spin process in addition to a four-spin process.

DOI
10.1103/physrev.121.997

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We have found that the amplitudes of the optical FID, two-pulse photon echoes and stimulated photon echoes in ruby measured as a function of applied magnetic field exhibit sharp increases at the magnetic fields where two Zeeman splittings in the ground state 4 A 2 or in the excited state \bar E ( 2 E ) are harmonically related. The phenomena are confirmed to be inherent in the Stark (or frequency) switching experiment where the sample is subjected to the cw irradiation, and the origin of the sharp increases be the change of the steady state population in 4 A 2 of the nonresonant Cr ions caused by a combined action of the cw optical pumping and the spin-spin cross relaxation. The mechanism involved is successfully explained by the analysis based on the rate equations.

Journal of the Physical Society of Japan•Dec 1, 1980•3 citations
Cross relaxation effects in ruby maser crystals are treated by introduction of a cross relaxation probability in the rate equations. Detailed solutions have been obtained for several specific processes and compared to recent experiments. It is shown that cross relaxation can improve maser performance even in the absence of impurity doping. Pulse experiments at 0.06 and 0.14% chromium ion concentrations in a ruby traveling wave maser are interpreted in terms of a five-spin process in addition to a four-spin process.
The reversals of maser behaviour which occur in ruby at low fields on cooling from 80° to 4 oK are explained in terms of cross-relaxation transitions (resonant interchanges of energy between neighbouring paramagnetic ions). For an angle of 29° between the magnetic field and the crystal axis a cross-relaxation process has been demonstrated which involves groups of three ions and has a transition probability of 700± 100 per second in 0·013% ruby. The profile of the cross-relaxation resonance has a half-width of 190±30 Mcts at half-intensity, and has an approximately Gaussian shape. It should be possible to obtain useful low-field L-band maser action at 4 oK by pumping V41 with the magnetic field nearly perpendicular to the crystal axis, and also at 80 oK using a concentration ten times higher, i.e. 0·13%
Cross relaxation between adjacent intervals may be used to secure an advantage in maser operation comparable to that obtained by ``push-pull'' pumping. Equations for the rate of change of populations in a scheme of four levels (A,B,C,D) when AC is pumped and cross relaxation takes place between BC, CD have been formulated, and the steady-state condition corresponding to various assumptions regarding lattice relaxation times is discussed. In an experimental investigation of maser operation based on this scheme and using ruby as the active material, an inversion of 0.9:1 was obtained at a signal frequency of 14.5 kMc when pumping at 24.5 kMc.
The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.
We have found that the amplitudes of the optical FID, two-pulse photon echoes and stimulated photon echoes in ruby measured as a function of applied magnetic field exhibit sharp increases at the magnetic fields where two Zeeman splittings in the ground state 4 A 2 or in the excited state \bar E ( 2 E ) are harmonically related. The phenomena are confirmed to be inherent in the Stark (or frequency) switching experiment where the sample is subjected to the cw irradiation, and the origin of the sharp increases be the change of the steady state population in 4 A 2 of the nonresonant Cr ions caused by a combined action of the cw optical pumping and the spin-spin cross relaxation. The mechanism involved is successfully explained by the analysis based on the rate equations.