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arXiv:0911.4221 · Physical Review B

Power-dependent internal loss in Josephson bifurcation amplifiers

道生 渡部, K. Inomata, Tsuyoshi Yamamoto, Jaw-Shen Tsai

Published Nov 3, 2009• 6 citations
arXivHTMLPDF

Abstract

We have studied nonlinear superconducting resonators: $\ensuremath{\lambda}/2$ coplanar-waveguide (CPW) resonators with Josephson junctions (JJs) placed in the middle and $\ensuremath{\lambda}/4$ CPW resonators terminated by JJs, which can be used for the qubit readout as ``bifurcation amplifiers.'' The nonlinearity of the resonators arises from the Josephson junctions, and because of the nonlinearity, the resonators with appropriate parameters are expected to show a hysteretic response to the frequency sweep, or ``bifurcation,'' when they are driven with a sufficiently large power. We designed and fabricated resonators whose resonant frequencies were around 10 GHz. We characterized the resonators at low temperatures, $T<0.05\text{ }\text{K}$, and confirmed that they indeed exhibited hysteresis. The sizes of the hysteresis, however, are sometimes considerably smaller than the predictions based on the loaded quality factor in the weak drive regime. When the discrepancy appears, it is mostly explained by taking into account the internal loss, which often increases in our resonators with increasing drive power in the relevant power range. As a possible origin of the power-dependent loss, the quasiparticle channel of conductance of the JJs is discussed.

DOI
10.1103/physrevb.80.174502

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Measuring the internal quality factor of coplanar waveguide superconducting resonators is an established method of determining small losses in superconducting devices. Often, resonator losses are attributed to two-level system (TLS) defects using a power dependent model for the quality factor. However, excess non-equilibrium quasiparticles can also limit the quality factor of superconducting resonators. Here, a two-temperature, power and temperature dependent model is used to evaluate resonator losses for titanium nitride and aluminum coplanar waveguide resonators with loss tangents of 10−5–10−6. This model enables a set of parameters to describe both the internal quality factor and fractional frequency shift of the resonator across a broad range of average cavity photon numbers, from 1 to 106, and temperatures between those limited by the experimental apparatus near 50 mK and thermal quasiparticle dominated. The presented model also offers potential insight into observing the temperature and power dependence of TLS–TLS interactions in these resonators.
Superconducting circuits incorporating Josephson elements represent a promising hardware platform for quantum technologies. Potential applications include scalable quantum computing, microwave quantum networks, and quantum-limited amplifiers. However, progress in Josephson junction–based quantum technologies is facing the ongoing challenge of minimizing loss channels. This is also true for parametric superconducting devices based on nonlinear Josephson resonators. In this work, we report on the fabrication and characterization of low-loss Josephson parametric devices operated in the GHz frequency range, showing record internal quality factors. Specifically, we achieve internal quality factors Q int significantly exceeding 10 5 for both Josephson parametric converters and Josephson parametric amplifiers in the single-photon regime by fitting the scattering data. We confirm the extracted Q int values by analyzing purity of squeezed vacuum states generated by these devices. These low-loss devices mark a significant step forward in realizing high-performance quantum circuits, enabling further advancements in superconducting quantum technologies.
Recent studies find that even drives far below the superconducting gap frequency may cause drive-induced quasiparticle generation (QPG) across Josephson junctions (JJs) of superconducting qubits (SCQs), posing a serious concern for fault-tolerant superconducting quantum computing (FTSQC). Nonetheless, quantitative experimental estimation on QPG rates has remained vague. Here, we investigate QPG using strongly driven SCQs, reaching qubit drive amplitudes up to $2π\times$300 GHz by applying intense drive fields through the readout resonators. The resonator nonlinear responses enable quantification of the energy loss at SCQs, including the contribution from QPG. Surprisingly, the estimated total energy loss rates are far lower than those expected by the Floquet-Markov formalism with QPG as the sole loss mechanism. Meanwhile, calculations that incorporate high-frequency cutoffs (HFCs) in the QPG conductance at approximately 17-20 GHz effectively explain the experimental observations. These results suggest limitations in either the QPG conductance model or the Markovian treatment of the QPG processes. Both possibilities possess crucial implications for handling QPG problems toward FTSQC and for a more deeper understanding of Josephson junctions.
The loss in superconducting microwave resonators at low-photon numbers and low temperatures is not well understood but has implications for achievable coherence times in superconducting qubits. We have fabricated single-layer resonators with a high quality factor by patterning a superconducting aluminum film on a sapphire substrate. Four resonator geometries were studied with resonant frequencies ranging from 5 to 7 GHz: a quasi-lumped element resonator, a coplanar strip waveguide resonator, and two hybrid designs that contain both a coplanar strip and a quasi-lumped element. Transmitted power measurements were taken at 30 mK as a function of frequency and probe power. We find that the resonator loss, expressed as the inverse of the internal quality factor, decreases slowly over four decades of photon number in a manner not merely explained by loss from a conventional uniform spatial distribution of two-level systems in an oxide layer on the superconducting surfaces of the resonator.
A Josephson tunnel junction which is rf driven near a dynamical bifurcation point can amplify quantum signals. However, the bifurcation point will exist robustly only if the electrodynamic environment of the junction meets certain criteria. We develop a general formalism for dealing with the nonlinear dynamics of a Josephson junction embedded in an arbitrary microwave circuit. We find sufficient conditions for the existence of the bifurcation regime: (a) the embedding impedance of the junction needs to present a resonance at a particular frequency ${\ensuremath{\omega}}_{R}$, with the quality factor QQQ of the resonance and the participation ratio ppp of the junction satisfying Qp⪢1Qp⪢1Qp⪢1, and (b) the drive frequency should be low frequency detuned away from ${\ensuremath{\omega}}_{R}$ by more than $\sqrt{3}{\ensuremath{\omega}}_{R}∕(2Q)$.
Superconducting boron-doped silicon is a promising material for integrated silicon quantum devices. In particular, its low electronic density and moderate disorder make it a suitable candidate for the fabrication of large inductances with low losses at microwave frequencies. We study experimentally the electrodynamics of superconducting silicon thin layers using coplanar waveguide resonators, focusing on the kinetic inductance, the internal losses, and the variation of these quantities with the resonator readout power. We report the observation in a doped semiconductor of microwave resonances with internal quality factors of a few thousand. As expected in the BCS framework, superconducting silicon presents a large sheet kinetic inductance in the 50--500-pH range, comparable to that of strongly disordered superconductors. The temperature dependence of the kinetic inductance is well described by the Mattis-Bardeen theory. However, we find an unexpectedly strong nonlinearity in the complex surface impedance that cannot be satisfactorily explained either by depairing or by quasiparticle heating.