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.

6 pages