Josephson traveling-wave parametric amplifier based on low-intrinsic-loss coplanar lumped-element waveguide

TL;DR

The paper presents a low-loss CP-JTWPA built from a coplanar lumped-element transmission line with open-stub shunts and expanded Manhattan junctions, achieving insertion loss < 1 dB up to 12 GHz. It introduces windowed impedance modulation to achieve phase-matched, ripple-suppressed gain, demonstrating boxcar, Hann, and Tukey window schemes. The Tukey-window device delivers 20–23 dB gain over a 5 GHz band under ideal matching and 17–20 dB under practical impedance mismatches, with added noise around 0.63–0.68 quanta and saturation at −99 dBm, approaching quantum-limited performance. These results represent a significant advance toward practical, broadband, low-noise JTWPAs suitable for scalable superconducting quantum information processing and wideband microwave quantum optics.

Abstract

We present a Josephson traveling-wave parametric amplifier (JTWPA) based on a low-loss coplanar lumped-element waveguide architecture. By employing open-stub capacitors and Manhattan-pattern junctions, our device achieves an insertion loss below 1~dB up to 12~GHz. We introduce windowed sinusoidal modulation for phase matching, demonstrating that a smooth transition in the impedance-modulation strength effectively suppresses intrinsic gain ripples. Using Tukey-windowed modulation with 8\% impedance variation, we achieve 20\text{--}23-dB~gain over 5-GHz bandwidth under ideal matching conditions. In a more practical circuit having impedance mismatches, the device maintains 17\text{--}20-dB gain over 4.8-GHz bandwidth with an added noise of 0.18~quanta above standard quantum limit at 20-dB gain and $-99$-dBm saturation power, while featuring zero to negative backward gain below the band-gap frequency.

Figures (13)

• Figure 1: Overview of the CP-JTWPA architecture and its transmission characteristics. (a) Double-spiral layout of the CP-JTWPA chip fabricated on a silicon substrate (darker regions) with aluminum thin films (brighter regions), implementing a nonlinear transmission line over a 5$\times$5-mm$^2$ area. (b) Unit cell structure of length 20 µ$\mathrm{m}$ showing the Josephson junction (red), open-stub capacitors (blue: centerline, green: ground), and airbridges (yellow) constructed across every single open stub and across the ground planes every five unit cells along the transmission line. (c) Lumped-element circuit model of a unit cell including junction inductance and capacitance ($L_\mathrm{J}$, $C_\mathrm{J}$), open-stub capacitance ($C_\mathrm{g}$), and two extra series inductors ($L_\mathrm{s}/2$) accounting for geometric inductance, with cross-stub and cross-ground airbridges (yellow) forming the ground current path. (d) 3D visualization of the unit-cell geometry with airbridge structures, where aluminum bandages connecting the junctions to the open stubs were fabricated in the same step as the airbridges. (e) SEM image of a Manhattan-type Josephson junction of approximately 1-µ m$^2$ area, formed by double-angled evaporations and liftoff with electrodes of 1-µ m width, wider than that typically used in transmon qubits to achieve sufficiently high critical current. (f) Device B baseline transmission at 12 mK compared to a 50-$\Omega$ SMA F--F adapter, measured at roughly $-125$-dBm power and 6 GHz using two microwave switches. The two paths between switches were verified at room temperature to have transmission difference of $<$0.1 $\mathrm{dB}$. At low temperature, besides the band gap which appears at the designed frequency (8.13 GHz), the typical insertion loss is less than 1 dB over the 4--12 GHz range including the sample package.
• Figure 2: Comparison of impedance-modulation profiles and their transmission characteristics for boxcar (left panels) and Hann (right panels) windows. (a,b) Example impedance-modulation profiles showing the JTWPA sections embedded between 50-$\Omega$ transmission lines. Simulation parameters are provided in Appendix \ref{['sec:appendix_numerical_analysis_1dTL']}. For visual clarity, the modulation patterns are shown with a reduced frequency compared to those used in the example. (c,d) Transmission ($|S_{21}|^2$) and reflection ($|S_{11}|^2$) characteristics with 1.5% impedance-modulation amplitude, calculated using both the analytical coupled-mode analysis (CMA) and numerical ABCD-matrix method (ABCD). (e,f) ABCD-matrix simulations at 7.7% impedance-modulation amplitude (achieved through 16% capacitance modulation), showing that the transmission ripples in the boxcar case and their suppression in the Hann case persist similarly to the weak-modulation case.
• Figure 3: Comparison of transmission characteristics between device A (boxcar window, top) and device B (Hann window, bottom). Left panels [(a) and (b)] show both measured and simulated data from 4--12 GHz: measured and simulated normalized forward transmission $|S_{21}|^2$ without pump (transmission), measured and simulated normalized forward transmission $|S_{21}|^2$ with pump (gain), and simulated reflection $|S_{11}|^2$ (reflection). All simulations were performed assuming lossless transmission lines. Right panels [(c) and (d)] present enlarged views of the high-gain regions marked by red dotted-line boxes. Base transmission and reflection magnitudes are calculated using ABCD-matrix methods, while gain profiles are obtained through harmonic-balance simulations. The band gap appears at 7.90 GHz and 8.13 GHz for devices A and B, respectively.
• Figure 4: Characterization of device C implementing a windowed periodic impedance modulation with a Tukey window with equal length in taper and maximum-amplitude region ($\alpha = 0.5$). (a) The impedance modulation profile along the signal path. The modulation amplitude increases smoothly from zero at the input to 8% in the central uniform section, then decreases symmetrically to zero at the output. (b) Measured and simulated scattering parameters with 10-dB attenuators at both ports providing 50-$\Omega$ impedance matching. (c) Measured forward and backward scattering parameters without output attenuation (see Appendix \ref{['sec:appendix_sysAttCal']} for the corresponding microwave network), representing a more realistic microwave environment with typical circuit impedance mismatches present in applications. The noise measurement was performed at 5.563 GHz (arrow) under this configuration.
• Figure 5: Noise performance of the Tukey CP-JTWPA measured at 5.563 GHz. (a) Added noise versus gain. The added noise increases from $<$0.5 quanta at gain below 5 dB to 0.68 quanta at 21-dB gain, closely following the trend given by the SQL, before rising significantly at higher gain. (b) System noise temperature referred to the CP-JTWPA input. With the JTWPA off (orange), the system exhibits a baseline noise of approximately 7.0 K (26.2 quanta). When the JTWPA is activated (blue), the noise rapidly decreases to below 1.06 K (3.96 quanta) within the first 10 dB of gain, then gradually approaches 382 mK (1.43 quanta) at 21-dB gain, before increasing at higher gain. Shaded regions represent statistical measurement uncertainties, with the added noise varying by $\pm$0.31 quanta at high gain. The system noise uncertainty ranges from $\pm$1.72 K ($\pm$ 6.42 quanta) in the off state to $\pm$90 mK ($\pm$0.34 quanta) at high gain.