Microwave bifurcation of a Josephson junction: Embedding-circuit requirements
V. E. Manucharyan, E. Boaknin, M. Metcalfe, R. Vijay, I. Siddiqi, M. Devoret
DOI 10.1103/PhysRevB.76.014524 · Physical Review B
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Abstract
A Josephson tunnel junction which is rf driven near a dynamical bifurcation point can amplify quantum signals. However, the bifurcation point will exist robustly only if the electrodynamic environment of the junction meets certain criteria. We develop a general formalism for dealing with the nonlinear dynamics of a Josephson junction embedded in an arbitrary microwave circuit. We find sufficient conditions for the existence of the bifurcation regime: (a) the embedding impedance of the junction needs to present a resonance at a particular frequency ωR, with the quality factor Q of the resonance and the participation ratio p of the junction satisfying Qp⪢1, and (b) the drive frequency should be low frequency detuned away from ωR by more than 3ωR∕(2Q).
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