Hybridized-Mode Parametric Amplifier in Kinetic-Inductance Circuits

TL;DR

The paper addresses limitations of Josephson-junction–based amplifiers—magnetic sensitivity and limited power handling—by implementing a two-mode parametric amplifier using kinetic inductance in NbTiN and NbN films. It develops a two-mode four-wave mixing model for coupled Kerr resonators and validates it against experiments that deliver up to ~40 dB gain and a gain-bandwidth product as high as 6.9 MHz. NbN devices, with larger Kerr nonlinearity, exhibit improved GBP, confirming the advantage of high kinetic-inductance materials. The work demonstrates magnetically robust, broadband, high-power amplification with potential for scalable readout in superconducting qubits and other microwave-quantum platforms.

Abstract

Parametric amplification is essential for quantum measurement, enabling the amplification of weak microwave signals with minimal added noise. While Josephson-junction-based amplifiers have become standard in superconducting quantum circuits, their magnetic sensitivity, limited saturation power, and sub-kelvin operating requirements motivate the development of alternative nonlinear platforms. Here we demonstrate a two-mode kinetic-inductance parametric amplifier based on a pair of capacitively coupled Kerr-nonlinear resonators fabricated from NbTiN and NbN thin films. The distributed Kerr nonlinearity of these materials enables nondegenerate four-wave-mixing amplification with gains approaching 40 dB, gain-bandwidth products up to 6.9 MHz, and 1-dB compression powers two to three orders of magnitude higher than those of state-of-the-art Josephson amplifiers. A coupled-mode theoretical model accurately captures the pump-induced modification of the hybridized modes and quantitatively reproduces the observed signal and idler responses. The NbN device exhibits a significantly larger Kerr coefficient and superior gain-bandwidth performance, highlighting the advantages of high-kinetic-inductance materials. Our results establish coupled kinetic-inductance resonators as a robust platform for broadband, high-power, and magnetically resilient quantum-limited amplification, offering a scalable route for advanced readout in superconducting qubits, spin ensembles, quantum dots, and other microwave-quantum technologies.

Figures (4)

• Figure 1: (a) Schematic of the coupled–resonator system used for two-mode amplification. The device consists of two Kerr-nonlinear ($\chi^{(3)}$) resonators with bare frequencies $\omega_{1,2}$, coupled coherently at rate $g$. Each resonator exchanges energy with a common transmission line through an external damping channel $\kappa_{e,j}$ and experiences intrinsic dissipation $\kappa_{i,j}$. The intrinsic Kerr nonlinearity provides the effective $\chi^{(3)}$ response required for four-wave mixing, enabling the generation of signal and idler fields under pump drive. (b) False-color optical image of the implementation of the actual coupled kinetic-inductance amplifier. The green area shows the coplanar transmission line, and the yellow color areas exhibit the ground plane. Two Kerr-nonlinear LC resonators, realized using NbTiN or NbN nanowire inductors and U-shaped shunt capacitors, are capacitively coupled at rate $g$ and driven through an interdigitated capacitor fed by a coplanar transmission line. The kinetic-inductance nonlinearity of the thin films provides the $\chi^{(3)}$ response needed for four-wave-mixing amplification. (c) Zoomed-in image of coupled resonators.
• Figure 2: (a) Reflection spectrum of the NbTiN device showing two hybridized modes at $\omega_{-}/2\pi = 10.178~\text{GHz}$ and $\omega_{+}/2\pi = 10.577~\text{GHz}$, corresponding to a mode splitting of $(2g)/2\pi \simeq 434~\text{MHz}$. The asymmetric coupling of the bare resonators results in different external linewidths for the two hybridized modes. (b) Self-Kerr shift of the hybridized modes extracted from the resonance frequency shift $\Delta \omega$ versus intracavity photon number $n$. The slopes yield Kerr coefficients of $K/2\pi \approx 0.01~\text{Hz}$ for NbTiN and $K/2\pi \approx 0.21~\text{Hz}$ for NbN using 1 $\mu$m-wide nanowires, with the larger Kerr in NbN reflecting its higher kinetic-inductance participation.
• Figure 3: (a) Signal and idler gain versus detuning for the NbTiN device at several pump powers. Maximum gain approaches $40~\mathrm{dB}$ at a pump power of $-23~\mathrm{dBm}$, with solid curves showing fits to the theoretical model. (b) Gain–bandwidth product (GBP) as a function of gain for NbTiN and NbN devices. The NbTiN device reaches $\mathrm{GBP} = 3.3~\mathrm{MHz}$, while NbN reaches $\mathrm{GBP} = 6.9~\mathrm{MHz}$, consistent with its larger Kerr nonlinearity. Power-saturation characteristics for NbTiN (c) and NbN (d). The 1-dB compression points occur near $P_{\mathrm{in}} \approx -91~\mathrm{dBm}$ (NbTiN) and $-83~\mathrm{dBm}$ (NbN) at $20~\mathrm{dB}$ gain, demonstrating saturation powers two to three orders of magnitude higher than typical Josephson-junction-based amplifiers.
• Figure 4: (a) Frequency response measured in reflection for the coupled NbN resonators. (b) Kerr shift of the $\omega_{-}$ mode obtained by driving the resonator with a strong signal tone. (c) Two-mode amplification observed when the device is driven with a pump tone placed midway between the hybridized modes. Dotted curves show measured data fitted using Eq. \ref{['EqGain']}.