Mixing of counterpropagating signals in a traveling-wave Josephson device

Light waves do not interact in vacuum but can mix in nonlinear media. A strong pump wave can thus convert the frequency of a weaker signal, provided energy and momentum are conserved. These conditions are typically satisfied when all waves propagate with comparable phase velocity along a given axis. Here, we investigate an alternative scheme by which a microwave signal propagating along a one-dimensional Josephson metamaterial is converted into a counter-propagating wave through interaction with a slower pump. In this regime, the input wave is exponentially attenuated, enabling an on-chip microwave isolator reconfigurable into a reciprocal, tunable coupler. The device's operating mode and working frequency can be selected in situ over a broad microwave range. We measure isolation exceeding 5 dB in the 5-8.5 GHz range and 10 dB in the 7-8.5 GHz range, with a typical 200 MHz bandwidth. Further improvements are expected through design optimization and reduced fabrication disorder, opening new possibilities for microwave routing and processing in superconducting circuits.