Parametric amplification in a Kerr Oscillator based on Ne FIB Nanobridges

Abstract

Superconducting circuits play a crucial role in the advancement of quantum computing and quantum sensing. Typically such circuits require the presence of a non-linear element, where the engineered anharmonicity (Kerr factor) and resonant linewidth determine the potential applications of the circuit. In this work we have fabricated Nb-based CPW resonators embedded with a DC SQUID incorporating Nb nanobridges as the weak links. We use two-tone spectroscopy to study the non-linear behaviour of the device at 15 mK up to a field of 2.48 mT. Under the application of a blue-detuned pump, the device shows a decrease in the resonant frequency which is used to estimate the Kerr factor. We further apply a red-detuned pump to go beyond the bifurcation threshold and observe the appearance of an additional idler mode with net gain. The gain of the device was maximized by further decreasing the pump frequency, showing a maximum amplification of 15 dB. Finally, we show agreement between the Kerr non-linear oscillator model and the measured transmission spectrum, and highlight further design modifications to improve the gain and bandwidth of such devices.

The paper investigates four-wave-mixing parametric amplification in a Nb nanobridge SQUID resonator, motivated by alternatives to Al devices for magnetic-field-exposed microwave applications. The device is a $\lambda/4$ CPW resonator terminated by a DC SQUID whose weak links are patterned using Ne focused-ion-beam lithography. Measurements at $15\,\mathrm{mK}$ characterize a resonance near $5.627\,\mathrm{GHz}$, with low-power internal and external quality factors of $7.4\times10^4$ and $4.5\times10^4$. Blue-detuned pump–probe spectroscopy measures the pump-induced resonance shift. Iterative fitting to the steady-state photon-number equation and linearized signal–idler response of a Kerr oscillator gives a zero-field Kerr factor of $-2.14\,\mathrm{mHz/photon}$, close to a circuit estimate of $-2.13\,\mathrm{mHz/photon}$. The Kerr response persists in perpendicular fields up to $2.48\,\mathrm{mT}$. Red-detuned pumping produces a signal–idler response, with separate spectrum-analyzer measurements verifying $\omega_s+\omega_i=2\omega_p$. Sweeping the pump frequency along the high-photon-number branch yields a maximum transmission gain of $15\,\mathrm{dB}$ relative to the measured baseline, with approximately $300\,\mathrm{kHz}$ bandwidth. A standard driven-Kerr input–output model reproduces the principal spectral features and branch switching. The field-dependent measurements establish nonlinear response rather than amplifier performance at the maximum field. Above $2.48\,\mathrm{mT}$, pump-dependent frequency jumps are attributed to vortex motion. Added noise and dynamic range remain unmeasured; stronger overcoupling and lower resonator quality factor are proposed to improve gain and bandwidth.