  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.
