Nonlinearity and Parametric Amplification of Superconducting Nanowire Resonators in Magnetic Field

Abstract: Nonlinear superconducting devices, typically based on Josephson Junction (JJ) nonlinearities, are the basis for superconducting quantum electronics, enabling, e.g., the formation of isolated two-level superconducting qubits and amplifiers. While emerging spin, hybrid spin/superconducting (including Majorana), and nano-magneto-optical quantum systems could benefit tremendously from superconducting nonlinearities, the presence of strong magnetic fields in these systems are incompatible with conventional JJ devices, which are highly sensitive to applied magnetic fields. One potential solution is the use of kinetic inductance (KI) nonlinearity. To date, only linear kinetic inductance (KI) devices have been shown to operate in high magnetic fields, while nonlinear KI device operation in high magnetic fields has received virtually no attention. Here, we study the nonlinearity of superconducting nanowire (NW) KI resonators and their performance as parametric amplifiers for in-plane magnetic fields. We study the Kerr coefficients of NW KI resonators made from 10 nm-thin NbTiN films with characteristic impedance up to 3 k$\Omega$, and demonstrate both nondegenerate and degenerate parametric amplification, at magnetic fields up to 2 T, for the first time. We find that narrow KI resonators of width 0.1 $\mu$m are robust, in terms of gain, dynamic range and noise, to magnetic fields up to $\sim$2 T, while wider KI resonators of width 1 $\mu$m suffer significant suppression in the gain around at fields well below 2 T. Around 8 dB deamplification is observed for coherent states for a 0.1 $\mu$m KI resonator, implying the capability of noise squeezing. These results open a new pathway to developing nonlinear quantum devices that operate in or generate high magnetic fields such as spin, hybrid spin/superconducting, and magneto-opto-mechanical devices.