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We performed resonant microwave measurements on superconducting titanium (Ti)down to temperatures of 40~mK, well below its critical temperature$T_\mathrm{c} \approx 0.5$~K. Our wide frequency range 3.3-40~GHz contains thezero-temperature energy gap $2\Delta_0$ and allows us to probe the fullelectrodynamics of the superconducting state, including excitations across thegap and the low-frequency responses of superfluid condensate and thermalquasiparticles. The observed behavior follows the predictions of the BCS-basedMattis-Bardeen formalism, which implies that superconducting Ti is in the dirtylimit, in agreement with our determination of the scattering rate. We directlydetermine the temperature dependence of the energy gap, which is in accordancewith BCS predictions, and $2\Delta_0/k_\mathrm{B}T_\mathrm{c}\approx3.5$ with$\Delta_0 \approx$ 75~$\mu$eV. We also evaluate the penetration depth, and wecharacterize the behavior of superconducting Ti in external magnetic field.

Complete electrodynamics of a BCS superconductor with $\mu$eV energy scales: microwave spectroscopy on titanium at mK temperatures