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

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### abstract

• 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 ${\mathrm{\ensuremath{\Omega}}}_{0}/2\ensuremath{\pi}\ensuremath{\approx}79$ 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 $K/2\ensuremath{\pi}\ensuremath{\approx}\ensuremath{-}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ Hz/photon. Furthermore, the lifetime of each resonance can be controlled (increased) by pumping of the other mode as demonstrated both experimentally and theoretically.

### publication date

• June 26, 2017