STRONG ENVIRONMENTAL COUPLING IN A JOSEPHSON PARAMETRIC AMPLIFIER: SUPPLEMENTARY INFORMATION LJPA Fabrication The resonant circuit of the impedance transformed parametric ampli er (IMPA) is based on a previous experiment with lumped-element josephson

The resonant circuit of the impedance transformed parametric ampli er (IMPA) is based on a previous experiment with lumped-element josephson parametric ampli ers (JPAs) coupled directly to a 50Ω environment [1]. This design is shown in Fig. S1, along with a circuit diagram for the device. The circuit consists of 5 separate layers of optical lithography as well as a nal e-beam lithography step to deposit the junctions. First, a base layer of 100 nm of aluminum was sputtered onto a sapphire substrate and patterned optically to form the bulk of the circuit. The insulator, 250 nm amorphous silicon (a-Si), was then deposited and patterned to create vias between the top wiring and base wiring layers. After an in-situ argon ion mill to remove the native oxide from the base layer to ensure good electrical contact between base and top wiring, a 100 nm of aluminum top-wiring was sputter deposited. The top wiring and insulator layers were then patterned and etched to form the parallel plate capacitor of the resonator and the crossovers. Finally e-beam lithography was used to pattern the junctions for the superconductin quantum interference device (SQUID), which were deposited using double angle evaporation and lifto in an e-beam evaporator.