Superconducting traveling-wave parametric amplifiers have emerged as highly promising devices
for near-quantum-limited broadband amplification of microwave signals and are essential for high
quantum-efficiency microwave readout lines. Built-in isolation, as well as gain, would address their
primary limitation: lack of true directionality due to potential backward travel of electromagnetic
radiation to their input port. Here, we demonstrate a Josephson-junction-based traveling-wave
parametric amplifier isolator. It utilizes third-order nonlinearity for amplification and second-order
nonlinearity for frequency upconversion of backward propagating modes to provide reverse isolation.
These parametric processes, enhanced by a novel phase matching mechanism, exhibit gain of up to
20 dB and reverse isolation of up to 30 dB over a static 3 dB bandwidth greater than 500 MHz, while
keeping near-quantum limited added noise. This demonstration of a broadband truly directional
amplifier ultimately paves the way towards broadband quantum-limited microwave amplification
lines without bulky magnetic isolators and with inhibited back-action.