Phase-dependent microwave response of a graphene Josephson junction
R. Haller, Gergő Fülöp, David I. Indolese, Joost Ridderbos, R. Kraft, L. Y. Cheung, Jann Hinnerk Ungerer, Kenji Watanabe, Takashi Taniguchi, D. Beckmann, R. Danneau, Pauli Virtanen, Christian Schönenberger
Gate-tunable Josephson junctions embedded in a microwave environment provide a promising platform to in situ engineer and optimize novel superconducting quantum circuits. The key quantity for the circuit design is the phase-dependent complex admittance of the junction, which can be probed by sensing a radio frequency SQUID with a tank circuit. Here, we investigate a graphene-based Josephson junction as a prototype gate-tunable element enclosed in a SQUID loop that is inductively coupled to a superconducting resonator operating at 3 GHz. With a concise circuit model that describes the dispersive and dissipative response of the coupled system, we extract the phase-dependent junction admittance corrected for self-screening of the SQUID loop. We decompose the admittance into the current-phase relation and the phase-dependent loss, and as these quantities are dictated by the spectrum and population dynamics of the supercurrent-carrying Andreev bound states, we gain insight to the underlying microscopic transport mechanisms in the junction. We theoretically reproduce the experimental results by considering a short, diffusive junction model that takes into account the interaction between the Andreev spectrum and the electromagnetic environment, from which we estimate lifetimes on the order of $\ensuremath{\sim}10$ ps for nonequilibrium populations.
Gate-tunable Josephson junctions embedded in a microwave environment provide a promising platform to in situ engineer and optimize novel superconducting quantum circuits. The key quantity for the circuit design is the phase-dependent complex admittance of the junction, which can be probed by sensing a radio frequency SQUID with a tank circuit. Here, we investigate a graphene-based Josephson junction as a prototype gate-tunable element enclosed in a SQUID loop that is inductively coupled to a superconducting resonator operating at 3 GHz. With a concise circuit model that describes the dispersive and dissipative response of the coupled system, we extract the phase-dependent junction admittance corrected for self-screening of the SQUID loop. We decompose the admittance into the current-phase relation and the phase-dependent loss, and as these quantities are dictated by the spectrum and population dynamics of the supercurrent-carrying Andreev bound states, we gain insight to the underlying microscopic transport mechanisms in the junction. We theoretically reproduce the experimental results by considering a short, diffusive junction model that takes into account the interaction between the Andreev spectrum and the electromagnetic environment, from which we estimate lifetimes on the order of \ensuremath∼10 ps for nonequilibrium populations.
With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of µeV). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipation-free nonlinearity. The magnetic control is not an industry standard for devices and starts already to be an issue in large scale circuits. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable nonlinear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires, a two dimensional electron gas, carbon nanotubes and graphene. However, given the challenge of balancing nonlinearity, dissipation, participation, and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. The work presented in this PhD thesis demonstrates the design, fabrication and performances of a parametric amplifier leveraging a graphene Josephson junction.The graphene is encapsulated in between hBN flakes in order to improve its quality. Using such high quality junctions, we demonstrate amplification with 20 dB gain which is the milestone for overcoming noise of the classical amplifiers in the rest of the amplification chain. The Josephson parametric amplifier being based on a resonant structure (around 6 GHz) suffers from the gain bandwidth product limiting the amplification to a few MegaHertz frequency range. The use of a side gate to electrically tune the graphene gives control of the Josephson junction inductance and thus the resonant frequency of the amplifier. We demonstrate a near 1 GHz tunability of the amplification frequency with the use of a side gate which is as good as the tunability offered by using a magnetic flux on a SQUID for similar amplifier designs. Moreover, graphene has shown to exhibit nonlinear loss under a strong microwave irradiation arising because of dynamics in the Andreev states. Dissipation is known to add intrinsic noise on quantum amplifiers and could be a problem for quantum limited parametric amplification. We demonstrate that despite the presence of nonlinear loss, graphene based Josephson parametric amplifiers can reach near quantum limited amplification. A two photon loss model was used to describe the behaviour of the device but we show that a more complex model is required in order to take into account the nonlinear dissipation and the non-sinusoidal current phase relation. We also studied the dynamic range and showed that the graphene based Josephson parametric amplifier can reach a 1 dB compression point of -123 dBm which is as good as single tunnel junctions based parametric amplifiers. Our results expand the toolset for electrically tunable superconducting quantum circuits and offer new opportunities for the development of quantum technologies such as quantum computing, quantum sensing and fundamental science.
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.
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.
In the context of hybrid superconductor-semiconductor systems, Josephson junctions based on two-dimensional materials, such as graphene, offer promising opportunities because of their scalability and gate-tunable electronic properties. In this work, we investigate the inductive coupling between a quantum LC resonator and a superconducting loop embedding a short, ballistic, planar Josephson junction, with the graphene-based case as a representative example. Within a mean-field formalism, we analyze how the properties of the global system depend on the light-matter interaction coupling, the Fermi level of the two-dimensional material, and temperature. Our findings reveal that the current-phase relation can show features indicative of spontaneous time-reversal symmetry breaking. Furthermore, starting from the mean-field theory, we determine the low-energy spectrum of collective hybridized light-matter excitations.
Controlling the energy spectrum of quantum-coherent superconducting circuits, i.e., the energies of excited states, the circuit anharmonicity, and the states' charge dispersion, is essential for designing performant qubits. This control is usually achieved by adjusting the circuit's geometry. In situ control is traditionally obtained via an external magnetic field, in the case of tunnel Josephson junctions. More recently, semiconductor-weak-links-based Josephson junctions have emerged as an alternative building block with the advantage of tunability via the electric-field effect. Gate-tunable Josephson junctions have been succesfully integrated in superconducting circuits using, for instance, semiconducting nanowires or two-dimensional electron gases. In this Letter we demonstrate, in a graphene superconducting circuit, a large gate tunability of qubit properties: frequency, anharmonicity, and charge dispersion. We rationalize these features using a model considering the transmission of Cooper pairs through Andreev bound states. Noticeably, we show that the high transmission of Cooper pairs in such weak link strongly suppresses the charge dispersion. Our Letter illustrates the potential for graphene-based qubits as versatile building blocks in advanced quantum circuits.
Josephson junctions are the basis of superconducting qubits, amplifiers, and magnetometers. Historically, tunnel-style junctions have been most common. However, for some applications--those requiring a small, highly transparent, all-superconducting junction--nanobridge weak link junctions may be preferable. This thesis presents extensive characterization of aluminum nanobridge Josephson junctions. The junction behavior is simulated by numerically solving the Usadel equations. These simulations are then tested and confirmed via low- and microwave-frequency transport measurements. The data confirm that nanobridge junctions approach the ideal weak-link Josephson limit.Such a near-ideal junction can be used in a superconducting quantum interference device (SQUID) to form an ultra sensitive magnetometer. This thesis presents the first nanobridge-based dispersive SQUID magnetometer. The devices show near-zero dissipation, with bandwidth and sensitivity on par with the best reported results for any SQUID-based magnetometer. These magnetometers have several flexible modes of operation, allowing for optimization of sensitivity, bandwidth, or backaction. They also provide insight into the internal dynamics of dispersive measurement with nonlinear cavities, as the magnetometer backaction depends on the bias point and can readily be measured.Nanobridge junctions also provide a useful tool for diagnosing sources of decoherence in superconducting qubits. By replacing the usual tunnel junction with a nanobridge, the contribution of the junction to decoherence processes may be probed. In particular, the interaction of nanobridge junctions with quasiparticles provides information both about the junctions themselves and about quasiparticle generation and relaxation mechanisms. This thesis reports measurements of nonequilibrium quasiparticles trapping in phase-biased nanobridge junctions. By probing the quasiparticle-induced changes in resonant frequency of a high-Q nanoSQUID oscillator, one may measure the mean distribution of trapped quasiparticles and study its temperature dependence. These measurements also provide spectroscopy of the junctions' internal Andreev states and the dynamics of quasiparticle excitation and retrapping. The work presented here demonstrates the utility of nanobridge junctions as a tool for quantifying the population and distribution of quasiparticles in a superconducting circuit.