Coherent heat-wave generation in SrTiO$_3$ using stimulated light-scattering

Wave propagation of heat in solids, which is often called `second sound', has attracted increasing attention to its various potential applications such as in thermal diodes and waveguides. It has been suggested that ferroelectrics are strong candidates for thermal-wave media$^1$, and several reports on an incipient ferroelectric, strontium titanate (SrTiO$_3$), have shown a novel wave-like excitation in light-scattering spectra$^{2,3}$. Second sound has been proposed as the most plausible origin for this excitation based on rather indirect demonstrations$^{3,4}$. However, the lack of a direct demonstration still leaves controversy$^5$ on the existence of second sound in SrTiO$_3$. Here, we present a direct demonstration of an optically generated coherent heat wave, i.e, coherent second sound, in bulk single crystals of SrTiO$_3$. The generated wave-excitation has a linear dispersion relation with the predicted velocity of second sound in SrTiO$_3$, and is overdamped at high temperatures or low frequencies, exhibiting apparently diffusive behaviour with the decay rates defined by the known values of the thermal diffusivity of SrTiO$_3$. This work offers not only convincing evidence for the existence of second sound in SrTiO$_3$, but also a first demonstration of coherent generation and wave-control of gigahertz temperature fields in a 3D bulk material. As high-quality SrTiO$_3$ is widely available, and it is also known as a mother material of superconductors, the coherent excitation of temperature wave in this material offers a pathway for potential novel wave-based applications in heat management such as construction of thermal waveguides and directional devices or heat-control of superconductivity.