We have studied 1/f noise in critical current I_c in h-BN encapsulated monolayer graphene contacted by NbTiN electrodes. The sample is close to diffusive limit and the switching supercurrent with hysteresis at Dirac point amounts to ≃ 5 nA. The low frequency noise in the superconducting state is measured by tracking the variation in magnitude and phase of a reflection carrier signal v_rf at 600–650 MHz. We find 1/f critical current fluctuations on the order of δI_c/ I_c≃ 10 ^{- 3} per unit band at 1 Hz. The noise power spectrum of critical current fluctuations SIc measured near the Dirac point at large, sub-critical rf-carrier amplitudes obeys the law SIc/Ic2=a/fβ where a≃ 4 × 10 ^{- 6} and β≃ 1 at f> 0.1 Hz. Our results point towards significant fluctuations in I_c originating from variation of the proximity induced gap in the graphene junction.

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We present the design, measurement, and analysis of a current sensor based on a process of Josephson parametric upconversion in a superconducting microwave cavity. When a coplanar waveguide is terminated with a nanobridge-constriction Josephson junction, we observe modulation sidebands from the cavity that enable highly sensitive frequency-multiplexed output of small currents for applications such as readout of transition-edge sensor arrays. We derive an analytical model to reproduce the measurements over a wide range of bias current, detuning, and input power. When the frequency of the cavity is tuned by more than 100 MHz with a dc current, our device achieves a minimum current sensitivity of 8.9pA/Hz. Extrapolating the results of our analytical model, we predict an improved device based on our platform, capable of achieving a sensitivity down to 50fA/Hz, or even lower if one can take advantage of parametric amplification in the Josephson cavity. Taking advantage of the Josephson architecture, our approach can provide higher sensitivity than kinetic inductance designs, and potentially enables detection of currents ultimately limited by quantum noise.

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This thesis investigates fundamental properties of Josephson junctions embedded in microwave circuits, and an application arising from this hybrid approach. We used the versatility of superconducting coplanar DC bias cavities to extract previously inaccessible information on phase coherent and subgap mechanisms of graphene Josephson junctions. Chapter 1 gives an introduction to the technology of Josephson field effect transistors, among which graphene junctions show promise for future improvements in quantum computation. Together with an overview of the Josephson effect in superconducting-semiconducting systems, we introduce the concept of coplanar DC bias cavities for probing Josephson junctions at gigahertz frequencies. In chapter 2, we describe the experimental methods developed for carrying out the subsequent measurements. We include details on fabrication, material properties and measurement setup. Results of graphene Josephson junctions embedded in DC bias microwave resonators are presented in chapters 3 and 4. By following the resonance frequency and losses of the circuit, we are able to extract the junctions’ Josephson inductance and subgap resistance. Studying the nonlinear power and bias current response reveals further information on the underlying loss mechanisms and current phase relation. We turn to an application of our hybrid bias cavity – Josephson junction devices to detect small, low-frequency currents in chapter 5. Our device is competitive with state-of-the-art techniques for microwave radiation detection and, with minor modifications, should be able to outperform existing technologies by orders of magnitude. Finally, we conclude the presented work in chapter 6 and provide an outlook on potential future research. @en

In this report, we present nanoelectromechanical resonators fabricated with thin exfoliated crystals of a high-T _c cuprate superconductor Bi ₂ Sr ₂ Ca ₁ Cu ₂ O. The mechanical readout is performed by capacitively coupling their motion to a coplanar waveguide microwave cavity fabricated with a superconducting alloy of molybdenum-rhenium. We demonstrate mechanical frequency tunability with external dc-bias voltage, and quality factors up to ∼36 600. Our spectroscopic and time-domain measurements show that mechanical dissipation in these systems is limited by the contact resistance arising from resistive outer layers. The temperature dependence of dissipation indicates the presence of tunneling states, further suggesting that their intrinsic performance could be as good as other two-dimensional atomic crystals such as graphene.

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Josephson junctions (JJ) are a fundamental component of microwave quantum circuits, such as tunable cavities, qubits, and parametric amplifiers. Recently developed encapsulated graphene JJs, with supercurrents extending over micron distance scales, have exciting potential applications as a new building block for quantum circuits. Despite this, the microwave performance of this technology has not been explored. Here, we demonstrate a microwave circuit based on a ballistic graphene JJ embedded in a superconducting cavity. We directly observe a gate-tunable Josephson inductance through the resonance frequency of the device and, using a detailed RF model, we extract this inductance quantitatively. We also observe the microwave losses of the device, and translate this into sub-gap resistances of the junction at μeV energy scales, not accessible in DC measurements. The microwave performance we observe here suggests that graphene Josephson junctions are a feasible platform for implementing coherent quantum circuits.

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