Nonlinear Co-simulation for Designing Kinetic Inductance Parametric Amplifiers

TL;DR

The paper tackles accurate modeling of kinetic inductance parametric amplifiers (KIPAs) by marrying linear EM analysis of kinetic inductance with nonlinear circuit co-simulation to capture Kerr nonlinearity and parametric gain. Using a NbN nanowire-based KIPA, the authors validate the framework against experiments, reproducing linear resonance, temperature-dependent frequency shifts, and phase-sensitive degenerate amplification. The method demonstrates bifurcation behavior, large parametric gains, and broad tunability through multi-tone pumping, with reasonable agreement in gain-bandwidth compared to measurements. This co-simulation approach provides a practical, scalable tool for designing superconducting kinetic-inductance devices, with potential extensions to traveling-wave architectures and squeezing applications, facilitated by EM-derived S-parameters feeding nonlinear HB simulations. $L_k = L_{k0}igl[1 + igl(I/I_*igr)^2igr]$ encapsulates the Kerr nonlinearity central to the device physics, and the workflow supports systematic parameter sweeps to optimize performance.

Abstract

Kinetic inductance parametric amplifiers (KIPAs) have been widely studied for small-signal detection in superconducting quantum circuits. In this work, we demonstrate the modeling of a niobium nitride nanowire based KIPA using electromagnetic (EM) and circuit co-simulation, and compare the outcomes with experimental results. EM analysis is first performed on the device layout, taking into account the linear part of the kinetic inductance. The results are then integrated into a harmonic balance circuit simulator, in which the current-dependent inductance is modeled by representing the nanowire as a nonlinear inductor. Both linear and nonlinear responses of the device, including temperature-dependent resonance spectra and parametric gain, are extracted and show good agreement with experiments. We further show that when the KIPA operates as a degenerate amplifier, its phase-sensitive behavior can be accurately reproduced by the simulation. Our technique can serve as a valuable enabler for the simulation and design of quantum parametric amplifiers and superconducting kinetic inductance devices.

Figures (7)

• Figure 1: Device schematics. (a) The layout of the KIPA device, featuring a LC resonator coupled to a coplanar waveguide via a pair of interdigital capacitor. A zoom-in view of the nanowire is also shown. Each component is color coded to correspond with the circuit diagram. (b) A simplified circuit diagram representing the device. The nanowire can be viewed as a nonlinear inductor.
• Figure 2: EM analysis results. (a) Simulated resonance frequency as a function of temperature. The dots represent simulated temperatures and they are connected to guide visualization. The orange and red cross marks correspond to the measured resonance frequency at 10 mK and 3 K, respectively. (b) (c) Simulated and measured resonance spectra at the two different temperatures. The resonance linewidth and extinction match well between the two. This suggests that the simulation accurately captures the external coupling rate. The intrinsic loss is reproduced by artificially set the material loss to match with experiments.
• Figure 3: Setting up EM and circuit co-simulation. (a) EM simulation is first performed by replacing the nanowire with a component model of a linear inductor in the device layout (drawing not to scale). (b) The S-parameter is extracted with a method of moments (MoM) solver. (c) The linear response is then incorporated into circuit simulation where the nanowire is represented by a nonlinear inductor instead. A two-tone pump scheme is used for generating parametric gain. (d) Nonlinear simulation is performed with a harmonic balance (HB) solver. Parameters including signal frequency, pump power, and pump frequency, etc. are swept to extract the KIPA response.
• Figure 4: KIPA response under different signal power. The simulated $S_{11}$ of the device under varying signal power (no pump applied) is shown and artificially offset by 1 dB for visibility. The resonance undergoes bifurcation when the signal power is increased over -97 dBm.
• Figure 5: Simulated gain spectra at varying pump power and comparison with experiments. The frequencies of two pumps are fixed at 7.3716 GHz$\pm$133.5 MHz. (a) Two-dimensional sweep of parametric gain by varying the pump power and signal frequency in the simulation. The green, blue, and purple lines correspond to the pump powers used in the experiments. (b),(c),(d) Comparison between simulated and measured gain spectra at three different pump power. As the pump power is increased from -87.29 dBm to -86.89 dBm, the peak gain is increased while the 3-dB gain bandwidth is reduced.