Predicted third-order sweet spots for phi-junction Josephson parametric amplifiers

Hybrid superconductor-semiconductor nanowire Josephson junctions exhibit skewed and \phi_0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -shifted current phase relations when an in-plane magnetic field is applied along the weak link’s spin-orbit effective field direction. These junctions can have an asymmetric Josephson potential with odd-order nonlinearities. A dominant third-order nonlinearity can be achieved by tuning the magnetic field to a sweet spot. Sweet spots persist when higher order Josephson harmonics are included. This makes it possible to have a single Josephson junction dipole element with three-wave mixing capability, which is favorable for pump-efficient amplification. Electrostatic gate tunability of the semiconductor weak link can make it operable within an extended range of working frequencies, and the inclusion of micromagnets can facilitate near-zero magnetic field operation.