Minimal construction of fully directional parametric amplifier

Quantum-limited parametric amplifiers based on Josephson junctions are indispensable components of superconducting quantum information processing machines. Traditionally, these are reflection amplifiers which need external non-reciprocal elements to separate the input from the output. It is possible however, to achieve non-reciprocal amplification in a multi-mode device by interfering multiple signal pathways between the input and the output mode. However, directional amplifiers based on this technique have lacked either output matching or adequate reverse isolation. In this talk, we present a new design for a fully directional parametric amplifier whose input and output ports are matched, and whose reverse transmission is much smaller than the inverse of the forward gain. We show that at least four modes and six parametric couplings are required to implement these amplifiers with Josephson-junction-only circuits. We further show that under realistic operating conditions, these devices can generate 20 dB forward gain and less than -20 dB reverse transmission, therefore enabling high efficiency quantum measurements and on-chip integration with qubit-cavity system.