A Superconducting Phase Shifter and Traveling Wave Kinetic Inductance Parametric Amplifier for W-Band Astronomy

The W-Band ($75-110\; \mathrm{GHz}$) sky contains a plethora of information about star formation, galaxy evolution and the cosmic microwave background. We have designed and fabricated a dual-purpose superconducting circuit to facilitate the next generation of astronomical observations in this regime by providing proof-of-concept for both a millimeter-wave low-loss phase shifter, which can operate as an on-chip Fourier transform spectrometer (FTS) and a traveling wave kinetic inductance parametric amplifier (TKIP). Superconducting transmission lines have a propagation speed that depends on the inductance in the line which is a combination of geometric inductance and kinetic inductance in the superconductor. The kinetic inductance has a non-linear component with a characteristic current, $I_*$, and can be modulated by applying a DC current, changing the propagation speed and effective path length. Our test circuit is designed to measure the path length difference or phase shift, $\Delta \phi$, between two symmetric transmission lines when one line is biased with a DC current. To provide a measurement of $\Delta\phi$, a key parameter for optimizing a high gain W-Band TKIP, and modulate signal path length in FTS operation, our $3.6 \times 2.5\; \mathrm{cm}$ chip employs a pair of $503\; \mathrm{mm}$ long NbTiN inverted microstrip lines coupled to circular waveguide ports through radial probes. For a line of width $3\; \mathrm{\mu m}$ and film thickness $20\; \mathrm{nm}$, we predict $\Delta\phi\approx1767\; \mathrm{rad}$ at $90\; \mathrm{GHz}$ when biased at close to $I_*$. We have fabricated a prototype with $200\; \mathrm{nm}$ thick Nb film and the same line length and width. The predicted phase shift for our prototype is $\Delta\phi\approx30\; \mathrm{rad}$ at $90\; \mathrm{GHz}$ when biased at close to $I_*$ for Nb.