JOSEPHSON PARAMETRIC DEVICES HAVING SAME-FREQUENCY PORTS

A Josephson parametric device (e.g., a circulator/isolator or directional amplifier) can include a plurality of resonant modes, a plurality of couplings, an input port and an output port. The plurality of resonant modes includes first, second, and third resonant modes, the first and third resonant modes both configured to operate at a first resonant frequency and the second resonant mode configured to operate at a second resonant frequency that is different than the first resonant frequency. The plurality of couplings includes a passive coupling between the first and third resonant modes, a first parametric coupling between the first and second resonant modes, and a second parametric coupling between the second and third resonant modes. The input port is coupled to the first resonant mode of the device, and the output port is coupled to the third resonant mode of the device.