NEXT-GENERATION SUPERCONDUCTING METAMATERIALS: CHARACTERIZATION OF SUPERCONDUCTING RESONATORS AND STUDY OF STRONGLY COUPLED SUPERCONDUCTING QUANTUM INTERFERENCE META-ATOMS

Abstract

Metamaterials are artificial structures consisting of sub-wavelength ‘atoms’ with engineered electromagnetic properties that create exotic light-matter interactions through the effective medium approximation. Since the early 2000s, superconductors have been incorporated into a variety of structures to achieve tunable, low-loss, and nonlinear metamaterials, and have enabled applications such as negative index of refraction, near zero permittivity, and parametric amplification. We have designed, fabricated and characterized two types of superconducting metamaterials based on the quantum three-junction flux qubits and classical radio frequency superconducting quantum interference devices (rf SQUIDs). The coplanar waveguide resonators hosting the qubit meta-atoms exhibit anomalous reduction in loss in microwave transmission measurements at low rf excitation levels upon decreasing temperature below 40 mK. In contrast, the well-known standard tunneling model (STM) of the two-level system (TLS), believed to be the dominant source of loss at low temperatures, predicts a loss increasing then saturating with lowering temperatures. This anomalous loss reduction is attributed to the discrete nature of an ensemble of TLSs in the resonator. As temperature decreases, the individual TLS response bandwidth reduces with their coherence rate Γ2 ∼ T, creating less overlap between neighboring TLSs in the energy spectrum. This effective reduction in the density of states around the probe frequency is responsible for the observed lower loss at low rf excitation levels and low temperatures as compared to the STM prediction. We also incorporate the discrete TLS ansatz with the generalized tunneling model proposed by Faoro and Ioffe [PRL 2012, 109, 157005 and PRB 2015, 91, 014201] to fit the experimental data over a wide range of temperatures and rf excitation powers. The resulting goodness of fit is better than all common alternative explanations for the observed phenomenon. Metamaterials made of large arrays of hysteretic (βrf= Lgeo/LJJ > 1) classical rf SQUIDs are also designed and characterized in microwave transmission measurements, where we observed the SQUID self-resonances tuning with applied dc and rf magnetic flux, as well as temperature. The resonance features are tuned with dc flux in integers of the flux quantum, as expected. Due to the phenomenon of multistability present in the large system, the resonance bands can cross those from adjacent dc flux periodicities resulting in hysteresis in dc flux sweeps, which is observed in the experiment. Furthermore, we developed a new three-dimensional architecture of rf SQUID metamaterials where the nearest-neighbor SQUID loops overlap. The resulting capacitive coupling dramatically changes the response by introducing many more resonance bands that spread over a broad range of frequencies, the upper limit of which is much higher than the single-layer counterparts. A resistively and capacitively shunted junction (RCSJ) model with additional capacitive coupling between SQUIDs is proposed and successfully attributes the high frequency bands to the displacement current loops formed between the overlapping wiring of neighboring SQUIDs. The capacitively-coupled rf SQUID metamaterial is relevant to the design of single-flux-quantum-based superconducting digital electronic circuits, which has adopted three-dimensional wiring to reduce the circuit footprint.