SLUG Microwave Amplifier: Theory

We describe a novel scheme for low-noise phase-insensitive linear amplification at microwave frequencies based on the Superconducting Low-inductance Undulatory Galvanometer (SLUG). Direct integration of the junction equations of motion provides access to the full scattering matrix of the SLUG. We discuss the optimization of SLUG amplifiers and calculate amplifier gain and noise temperature in both the thermal and quantum regimes. Loading of the SLUG element by the finite input admittance is taken into account, and strategies for decoupling the SLUG from the higher-order modes of the input circuit are discussed. The microwave SLUG amplifier is expected to achieve noise performance approaching the standard quantum limit in the frequency range from 5-10 GHz, with gain around 15 dB for a single-stage device and instantaneous bandwidths of order 1 GHz.