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.
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%
Direct relaxation within the optically excited
E(2E) level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the
c axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a ${cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{G}}^{\ensuremath{-}5}$${\mathrm{s}}^{\ensuremath{-}1}$ is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations ${N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. In stationary experiments, a nonlinear increase with
N∗ is observed of the equilibrium population of the upper Zeeman level of
E to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and
Cr3+ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the
E direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the practical frequency range of 2-15 ${\mathrm{cm}}^{\ensuremath{-}1}$.
摘要 本文计算了在低温、低浓度下红宝石基态自旋-晶格弛豫的直接过程。应用强场耦合表象中基态的二级微扰波函数,在θ=90°,脉冲饱和法测量条件下,计算了基态四能级之间的无辐射跃迁几率。然后,用求解粒子数方程的方法,计算1.4°K的自旋-晶格弛豫时间。计算结果与Pace等人的实验结果较好地符合。 Abstract The direct process of spin-lattice relaxation in the ground state of ruby of low concentration is calculated at low temperature. The nonradiative transition probabilities within the four ground sub-levels are calculated by aid of second-order wave functions obtained in the strong-field coupling scheme. Under the measured condition of impulse saturation at θ=90°, the spin-lattice relaxation time at 1.4°K is obtained by solving the rate equations. The calculated result conforms satisfactorily to the experimental data given by Pace et al. 作者及机构信息 黄武汉, 林福成, 楼祺洪 1. 中国科学院 Authors and contacts HUANG WU-HAN, LIN FU-CHENG, LAU CHIE-HUNG 1. 中国科学院 参考文献 [1] 施引文献
The relaxation times T1for the grouud state levels in ruby were measured in the temperature range 4.2 to 1.6°K for the various concentrations of theCr^{3+}ionsffrom 0.05 to 0.7 percent. The dependenceT_{1}(f)of the formT_{1}^{-1}(f) = T_{1}^{-1}(0) + T_{1}^{-1}(I)f ^{n}withn \simeq 2has been obtained for the different transitions. The measurements of relaxation times for\pm \frac{1}{2} \leftrightarrow \pm \frac{3}{2}transition at zero magnetic field were especially aimed at establishing a form of dependenceT_{1}(f)because of the absence of the cross relaxation effects in this case. The normal temperature dependenceT_{1} \propto T_{1}^{-1}has been obtained at all concentrations in comparison with anomalous dependences observed at high concentrations by some researchers.
The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a
Q-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the
4A2 ground state to the levels of the
E(2E) excited state. The change in
Mz is linearly proportional to
H except near the anticrossing points of the
4A2 spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the
4A2 wave functions. When
H has a small component perpendicular to the
z axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of
Mz was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.