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 I 0 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 = 2 Q ( 1 − ω d / ω p ) > 3 , the oscillator enters the bistable regime where two nondissipative dynamical states O L and O H , which differ in amplitude and phase, can exist. The sharp I 0 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).