Coherence Time Enhancement of Interacting Two Level Systems in Aluminum Superconducting Resonators*

We investigate half-wavelength aluminum (Al) coplanar waveguide (CPW) resonators on sapphire substrates under microwave exciation in the superconducting state under conditions typical of superconducting quantum computing applications.  Measured temperature dependent and photon number dependent intrinsic quality factor Q_i(T)  and resonance frequency shift ? f(T) of these resonators are quantitively analized by applying the theoretical tunneling model of two level systems (TLS) along with the combination of equilibrium and non-equalibrium quasiparticles loss models. An unusual increase of intrinsic quality factor Q_i(T) with decreasing temperature is observed at ultra low power ( ~ one microwave photon) and low temperature (T).  This  behavior is attributed to the increase of TLS coherence time (T₂), which is propotial to 1/T at ultra-low temperatures and powers.

In addition, three junction flux qubits are also fabricated in locations that couple strongly to these resonators.  This transmission line will later host many flux qubits to study the collective behavior of a quantum metamaterial system.