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Wave propagation of heat in solids, which is often called `second sound', hasattracted increasing attention to its various potential applications such as inthermal diodes and waveguides. It has been suggested that ferroelectrics arestrong candidates for thermal-wave media$^1$, and several reports on anincipient ferroelectric, strontium titanate (SrTiO$_3$), have shown a novelwave-like excitation in light-scattering spectra$^{2,3}$. Second sound has beenproposed as the most plausible origin for this excitation based on ratherindirect demonstrations$^{3,4}$. However, the lack of a direct demonstrationstill leaves controversy$^5$ on the existence of second sound in SrTiO$_3$.Here, we present a direct demonstration of an optically generated coherent heatwave, i.e, coherent second sound, in bulk single crystals of SrTiO$_3$. Thegenerated wave-excitation has a linear dispersion relation with the predictedvelocity of second sound in SrTiO$_3$, and is overdamped at high temperaturesor low frequencies, exhibiting apparently diffusive behaviour with the decayrates defined by the known values of the thermal diffusivity of SrTiO$_3$. Thiswork offers not only convincing evidence for the existence of second sound inSrTiO$_3$, but also a first demonstration of coherent generation andwave-control of gigahertz temperature fields in a 3D bulk material. Ashigh-quality SrTiO$_3$ is widely available, and it is also known as a mothermaterial of superconductors, the coherent excitation of temperature wave inthis material offers a pathway for potential novel wave-based applications inheat management such as construction of thermal waveguides and directionaldevices or heat-control of superconductivity.

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