Revealing the nonlinear response of a tunneling two-level system ensemble using coupled modes

Atomic sized two-level systems (TLSs) in amorphous dielectrics are known as a major source of loss in superconducting devices. In addition, individual TLSs are known to induce large frequency shifts due to strong coupling to the devices. However, in the presence of a broad ensemble of TLSs these shifts are symmetrically canceled out and not observed in a typical single-tone spectroscopy experiment. We introduce a two-tone spectroscopy on the normal modes of a pair of coupled superconducting coplanar waveguide resonators to reveal this effect. Together with an appropriate saturation model this enables us to extract the average single-photon Rabi frequency of dominant TLSs to be Ω0/2π≈79 kHz. At high photon numbers we observe an enhanced frequency shift due to nonlinear kinetic inductance when using the two-tone method and estimate the value of the nonlinear coefficient as K/2π≈-1×10-4 Hz/photon. Furthermore, the lifetime of each resonance can be controlled (increased) by pumping of the other mode as demonstrated both experimentally and theoretically.