High-resolution optical study of a point-contact-induced phonon hot spot in ruby

A phonon hot spot is generated in ruby at 1.5 K by a micrometer-sized whisker-film W-W point contact, and subsequently studied by means of high-resolution optical techniques. The phonon distribution in the immediate vicinity of the point contact is imaged directly with micrometer spatial resolution. The method used is to observe the ${\mathit{R}}_1$ luminescence following optical excitation of ${\mathrm{Cr}}^{3+}$ to E¯${(}^2$E), where advantage is taken of the temperature dependence of the frequency and width of the ${}_{}{}^4{}_{}{}^{}$ ${\mathit{A}}_2$-E¯${(}^2$E) optical transition. A model description of the propagating phonon distribution is presented in terms of classical heat conduction close to the point contact and of quasiballistic propagation further away. Results of numerical calculations of the space- and frequency-dependent phonon distribution agree well with experiment.