Invited Review Article: The Josephson bifurcation amplifier

We review the theory, fabrication, and implementation of the Josephson bifurcation amplifier (JBA). At the core of the JBA is a nonlinear oscillator based on a reactively shunted Josephson junction. A weak input signal to the amplifier couples to the junction critical current I₀ and results in a dispersive shift in the resonator plasma frequency ω_p. This shift is enhanced by biasing the junction with a sufficiently strong microwave current I_rf to access the nonlinear regime where ω_p varies with I_rf. For a drive frequency ω_d such that Ω =2Q_{(1-ωd/ωp)>√3 , the oscillator enters the bistable regime where two nondissipative dynamical states OL and OH, which differ in amplitude and phase, can exist. The sharp I0} dependent transition from O_L to O_H forms the basis for a sensitive digital threshold amplifier. In the vicinity of the bistable regime (Ω <√3 ), analog amplification of continuous signals is also possible. We present experimental data characterizing amplifier performance and discuss two specific applications—the readout of superconducting qubits (digital mode) and dispersive microwave magnetometry (analog mode).