Coupled Superconducting Quantum Oscillators

Voltage biasing of a single superconducting weak link results in coherent electromagnetic oscillation at the frequency $\nu =\frac{V}{{\Phi }_0}$; simultaneous voltage biasing of two weak links in a superconducting ring produces two strongly coupled oscillators at the same frequency. The electromagnetic phase difference is the difference in the gauge-invariant quantum phases across the two contacts. Because of the quantization of the superconducting ring, this phase difference is $\frac{2\pi 〈\Phi 〉}{{\Phi }_0}$, where $〈\Phi 〉$ is the time-averaged magnetic flux in the superconducting circuit and ${\Phi }_0$ is the flux quantum. We can characterize the coupled system in terms of normal modes, and we have experimentally observed these modes of oscillation at 30 MHz. This provides a means of understanding the earlier observations of quantum interference in the resistive state.