Understanding and mitigating loss channels due to two-level systems (TLS) is one of the main corner stones in the quest of realizing long photon lifetimes in superconducting quantumcircuits. Typically, the TLS to which a circuit couples are modelled as a large bath without any coherence. Here we demonstrate that the coherence of TLS has to be considered to accurately describe the ring-down dynamics of a coaxial quarter-waver resonator with an internal quality factor of 0.5×109 at the single-photon level. The transient analysis reveals an effective non-markovian dynamics of the combined TLS and cavity system, which we can accurately fit by introducing a comprehensive TLS model. The fit returns relaxation times around T1=0.8μs for a total of N≈2×108 TLS with power-law distributed coupling strengths. Despite the short-lived TLS excitations, we observe long-term effects on the cavity decay due to coherent elastic scattering between the resonator field and the TLS. The presented method is applicable to various systems and allows for a simple characterization of TLS properties.
The possibility to operate massive mechanical resonators in the quantum regime has become central in fundamental sciences, in particular to test the boundaries of quantum mechanics.Optomechanics, where photons (e.g. optical, microwave) are coupled to mechanical motion, provide the tools to control mechanical motion near the fundamental quantum limits. Reaching single-photon strong coupling would allow to prepare the mechanical resonator in non-Gaussian quantum states. Yet, this regime remains challenging to achieve with massive resonators due to the small optomechanical couplings. Here we demonstrate a novel approach where a massive mechanical resonator is magnetically coupled to a microwave cavity. By improving the coupling by one order of magnitude over current microwave optomechanical systems, we achieve single-photon strong cooperativity, an important intermediate step to reach single-photon strong coupling. Such strong interaction allows for cooling the mechanical resonator with on average a single photon in the microwave cavity. Beyond tests for quantum foundations, our approach is also well suited as a quantum sensor or a microwave to optical transducer.
Here we present the microwave characterization of microstrip resonators made from aluminum and niobium inside a 3D microwave waveguide. In the low temperature, low power limit internalquality factors of up to one million were reached. We found a good agreement to models predicting conductive losses and losses to two level systems for increasing temperature. The setup presented here is appealing for testing materials and structures, as it is free of wire bonds and offers a well controlled microwave environment. In combination with transmon qubits, these resonators serve as a building block for a novel circuit QED architecture inside a rectangular waveguide.