Strong kinetic-inductance Kerr nonlinearity with titanium nitride nanowires

Thin films of disordered superconductors such as titanium nitride (TiN) exhibit large kinetic inductance (KI), high critical temperature, and large quality factors at the single-photon level. KI nonlinearity can be exploited as an alternative to Josephson junctions for creating novel nonlinear quantum devices with the potential to operate at higher frequencies and at elevated temperatures. We study a means of magnifying KI nonlinearity by confining the current density of resonant electromagnetic modes in nanowires with a small volume $V \simeq 10^{-4}\text{um}^3$. Using this concept, we realize microwave-frequency Kerr cavities with a maximum Kerr-shift per photon of $K/2\pi = 123.5 \pm 3$ kHz and report a nonlinearity-to-linewidth ratio $K/\gamma = 21\%$. With improved design, our devices are expected to approach the regime of strong quantum nonlinearity in the millimeter-wave spectrum.