  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.
