Magnetic field dependence of a Josephson travelling wave parametric amplifier*

We investigate the magnetic field dependence of a photonic-crystal Josephson travelling-wave parametric amplifier (TWPA). We show that the change in photonic bandgap and plasma frequency of the TWPA can be modelled by considering the suppression of the critical current in the Josephson junctions (JJs) of the TWPA due to the Fraunhofer effect and closing of the superconducting gap. This gap closes more suddenly close to the critical field than Ginsburg-Landau theory would predict. This can be modelled accurately using a thin-film BCS model. The JJ geometry is crucial for the field dependence. In one in-plane direction, the TWPA bandgap can be shifted by 2 GHz using up to 60mT of field, without losing gain or bandwidth. In the perpendicular in-plane direction the JJ area for the Fraunhofer effect is larger and modulated to create the bandgap. This leads to magnetic field modulating the bandgap and a lower Fraunhofer period, leading to the TWPA being severely compromised at 2mT. With out-of-plane field, the TWPA's response is hysteretic, and it is severely compromised at 5mT. We can estimate the required magnetic shielding needed to use TWPAs in experiments where high fields are required. Also, we show that TWPAs can be tuned without SQUIDs. Work to integrate the TWPA in a setup with magnetic fields of 6T at the sample position is ongoing.