  We propose a threshold detector with an operation principle, based on a
parametric period-doubling bifurcation in an externally pumped nonlinear
resonance circuit. The ac-driven resonance circuit includes a dc-current-biased
Josephson junction ensuring parametric frequency conversion (period-doubling
bifurcation) due to its quadratic nonlinearity. A sharp onset of oscillations
at the half-frequency of the drive allows for detection of small variations of
an effective inductance and, therefore, the read-out of the quantum state of a
coupled Josephson qubit. The bifurcation characteristics of this circuit are
compared with those of the conventional Josephson bifurcation amplifier, and
its possible advantages are discussed.
