Measuring intrinsic relaxation rates in superconductors using nonlinear response

We study intrinsic relaxation rates in superconductors and how they can be measured using nonlinear terahertz response. We consider both s- and d-wave superconductors, with and without a phenomenological (energy-dependent) damping. Intrinsic relaxation rates of interest include the Higgs mode decay rate, the quasiparticle redistribution rate (1/T1), and the quasiparticle dephasing rate (1/T2). Using the Anderson pseudospin formalism, we show how these intrinsic relaxation rates are related to measurable quantities such as the time-dependent gap and the nonlinear current (third-harmonic generation). Hence, we show how intrinsic relaxation rates may be experimentally extracted and discuss what one may thereby learn about the underlying damping. We also discuss the effects of light polarization control, which offers a useful experimental knob, especially for d-wave superconductors, enabling selective excitation of modes in different irreducible representations (and readout of their corresponding relaxation rates).