Broadband Kinetic-Inductance Parametric Amplifiers with Impedance Engineering

TL;DR

This work tackles the challenge of creating broadband, quantum-limited parametric amplifiers that combine high dynamic range with wide bandwidth and resilience to magnetic fields. The authors implement a kinetic-inductance PA (KIMPA) based on NbTiN nanowires and a three-stage impedance-transformer network to raise the nonlinear-resonator impedance $Z_{NR}$ while reducing the shunt capacitance. They demonstrate 450-MHz bandwidth with 17-dB gain and an added-noise level of about $0.5$–$1.3$ quanta, alongside an output saturation power near $-68$ dBm, significantly higher than typical JJ-based devices. The results open new possibilities for three-wave-mixing building blocks and suggest directions for on-chip integration and operation under higher temperature or magnetic-field conditions, advancing practical deployment of broadband quantum-limited amplifiers in quantum information systems.

Abstract

Broadband quantum-limited parametric amplifiers (PAs) are essential components in quantum information science and technology. Impedance-engineered resonator-based PAs and traveling-wave PAs are the primary approaches to overcome the gain-bandwidth constraint. While the former PAs are simpler to fabricate, the target characteristic impedance Z_\text{NR} of the nonlinear resonator has been restricted to be below 10 Ω, requiring large capacitance. Moreover, these PAs have only been implemented with aluminum-based Josephson junctions (JJs), hindering their operation at high temperatures or strong magnetic fields. To address these issues, we propose a three-stage impedance-transformer scheme, showcased with a 20-nm-thick, 250-nm-wide high-kinetic-inductance niobium-titanium-nitride (NbTiN) film. Our scheme enables Z_\text{NR} up to several tens of ohms--a tenfold improvement over conventional designs, achieved through an additional quarter-wavelength transmission line with the characteristic impedance of 180 Ω. Our kinetic-inductance impedance-engineered parametric amplifiers (KIMPA), featuring a 330-fF shunt capacitor, demonstrate a phase-preserving amplification with a 450-MHz bandwidth at 17-dB gain, and an added noise ranging from 0.5-1.3 quanta near the center frequency of 8.4 GHz. Due to the high critical current of the NbTiN nanowire, the KIMPA also achieves a saturation power of up to -68\pm3 dBm, approximately 30-dB higher than that of JJ-based PAs. This scheme also opens new possibilities for other three-wave-mixing building blocks.

Figures (13)

• Figure 1: (a) Circuit diagram of our kinetic-inductance impedance-engineered parametric amplifier (KIMPA). The three-stage impedance transformer, consisting of two quarter-wavelength ($\lambda/4$) and one half-wavelength ($\lambda/2$) transmission lines, broadens the bandwidth of the nonlinear resonator (NR) consisting of a shunt capacitor and a modulated inductor $L(t)$. The resonance of NR is close to the resonance of the $\lambda/2$ line. (b) Equivalent time-independent circuit diagram. The amplification ABCD matrix describes the relationship of signal and idler currents, sent from the left and the right, respectively. The signal (blue) and the idler (lavender) segments undergo frequencies of $\omega_\mathrm{s}$ and $-\omega_\mathrm{i}$, respectively. (c) Schematic diagram of (a) on the right and the experimental setup on the left. The signal path incorporates a bias tee for the dc-current ($I_\mathrm{dc}$) injection and a diplexer for combining the signal and pump. The device is fabricated using two materials, NbTiN (red) and aluminum (gray). The nonlinear resonator has a characteristic impedance $Z_{\mathrm{NR}}$.
• Figure 2: (a) Optical images of the device. (b) Magnified image of the dotted rectangular zone in (a). The high-impedance $\lambda/4$ CPW has a center conductor (2 $\mu$m in width) made of NbTiN (red). All other electrodes and ground planes are covered with 120-nm-thick aluminum with low KI. There are high-density holes in the ground plane to trap stray vortices. The black arrow points at the location of the NbTiN nanowire. (c) Scanning-electron-microscope image showing a 250-nm-wide NbTiN nanowire inductor (red).
• Figure 3: Characterization of the KIMPA. (a) Amplitude and (b) phase of the reflection coefficient $S_{11}$ vs signal frequency $\omega_\mathrm{s}$ (blue) and the numerical simulation (orange). (c) Signal gain $G_\mathrm{s}$ vs signal frequency $\omega_\mathrm{s}$ detuned from half the pump frequency $\omega_\mathrm{p}$ by $\Delta\omega_\mathrm{s} = \omega_\mathrm{s} - \omega_\mathrm{p}/2$, at different pump powers $P_\mathrm{p}$. (d) $G_\mathrm{s}$ as a function of $\Delta \omega_\mathrm{s}$ and $P_\mathrm{p}$. (e) Bandwidth $\Delta \omega$ at 17-dB gain as a function of $\omega_\mathrm{p}$ and $I_\mathrm{dc}$. (f) Refined bandwidth map subject to a stability criterion $\delta P_\mathrm{p} = P_\mathrm{p}^{\mathrm{SC}}/P_\mathrm{p}$ > 0.5 dB to ensure reliable operation. Here, $P_\mathrm{p}^{\mathrm{SC}}$ is the maximum pump power before superconductivity breakdowns occur. The breakdown event rate increases further when $P_\mathrm{p}$ approaches $P_\mathrm{p}^{\mathrm{SC}}$. The black squares in (e) and (f) mark the operating point used in (c) and (d), chosen for the optimal balance between bandwidth and gain ripples.
• Figure 4: Saturation-power characterization of the KIMPA. (a) Color map showing the signal gain $G_\mathrm{s}$ as a function of $\Delta\omega_\mathrm{s}$ and the signal power $P_\mathrm{s}$. $G_\mathrm{s}$ shows an abrupt drop-off at high $P_\mathrm{s}$ rather than gradual compression on the right side, indicating the breakdown of superconductivity, where this power level is denoted as $P_\mathrm{s}^\mathrm{SC}$. $P_\mathrm{s}^\mathrm{SC}$ is sometimes smaller than the input 1-dB compression power, $P_{1\mathrm{dB}}^{\mathrm{in}}$, and thus we define $P_{1\mathrm{dB}}^{\mathrm{in}}$ = $P_\mathrm{s}^\mathrm{SC}$ in such cases. (b) Examples of gain compression curves for two different operating points, with red crosses indicating $P_{1\mathrm{dB}}^{\mathrm{in}}$. The data correspond to those on the dashed lines in (a). (c) $P_{1\mathrm{dB}}^{\mathrm{in}}$ as a function of $\Delta\omega_\mathrm{s}$. We mark red when $P_{1\mathrm{dB}}^{\mathrm{in}}$ = $P_\mathrm{s}^\mathrm{SC}$. (d) Scatter plot of $P_{1\mathrm{dB}}^{\mathrm{in}}$ versus the corresponding $G_\mathrm{s}$ in 0.5-dB increments, indicating variations in $P_{1\mathrm{dB}}^{\mathrm{in}}$ even at constant gain levels.
• Figure 5: (a) Model for calibrating the added noise $N_\mathrm{A}$. We consider loss components, $A_\mathrm{in}$ and $A_{23}$, the KIMPA gain $G_\mathrm{s}$ and the subsequent gain $G_{\mathrm{sys}}$ in the measurement chain. (b) Noise spectrum obtained with a spectrum analyzer. The peak difference with and without the pump represents the KIMPA gain. Similarly, the signal-to-noise-ratio (SNR) gain $G_{\mathrm{SNR}}$ is indicated by the noise-floor difference as displayed in the panel. (c) $G_{\mathrm{SNR}}$ (orange) and $G_\mathrm{s}$ (gray) as a function of the signal-frequency detuning $\Delta\omega_\mathrm{s}$. (d) Added noise $N_\mathrm{A}$ (red) as a function of $\Delta\omega_\mathrm{s}$. $N_\mathrm{A}$ is extracted using Eq. (\ref{['eq.added_noise']}). Error bars (blue) are determined by the fitting inaccuracy and the uncertainty in the microwave component difference between the qubit and KIMPA measurement chains (see Appendix \ref{['appen_sys_noise']}). The gray dashed line represents the quantum-limited noise of 0.5 quanta.