  Two-level system (TLS) loss is typically limiting the coherence of
superconducting quantum circuits. The loss induced by TLS defects is nonlinear,
resulting in quality factors with a strong dependence on the circulating
microwave power. We observe frequency mixing due to this nonlinearity by
applying a two-tone drive to a coplanar waveguide resonator and measuring the
intermodulation products using a multifrequency lock-in technique. This
intermodulation spectroscopy method provides an efficient approach to
characterizing TLS loss in superconducting circuits. Using harmonic balance
reconstruction, we recover the nonlinear parameters of the device-TLS
interaction, which are in good agreement with the standard tunnelling model for
TLSs.
