Phase-locking transition in a chirped superconducting Josephson resonator

By coupling a harmonic oscillator to a quantum system it is possible to perform a dispersive measurement that is quantum non-demolition (QND), with minimal backaction. A non-linear oscillator has the advantage of measurement gain, but what is the backaction? Experiments on superconducting quantum bits (qubits) coupled to a non-linear Josephson oscillator have thus far utilized the switching of the oscillator near a dynamical bifurcation for sensitivity, and have demonstrated partial QND measurement. The detailed backaction associated with the switching process is complex, and may ultimately limit the degree to which such a measurement can be QND. Here we demonstrate a new dynamical effect in Josephson oscillators by which the bifurcation can be accessed without switching. When energized with a frequency chirped drive with an amplitude close to a sharp, phase-locking threshold, the oscillator evolves smoothly in one of two diverging trajectories - a pointer for the state of a qubit. The observed critical behavior agrees well with theory and suggests a new modality for quantum state measurement.