Dispersive magnetometry with a quantum limited SQUID parametric amplifier

There is currently fundamental and technological interest in measuring and manipulating nanoscale magnets, particularly in the quantum coherent regime. To observe the dynamics of such systems requires a magnetometer with not only exceptional sensitivity but also high gain, wide bandwidth and low backaction. We demonstrate a dispersive magnetometer consisting of a two-junction SQUID in parallel with an integrated, lumped-element capacitor. Input flux signals are encoded as a phase modulation of the microwave drive tone applied to the magnetometer, resulting in a single quadrature voltage signal. For strong drive power, the nonlinearity of the resonator results in quantum limited, phase sensitive parametric amplification of this signal. We have achieved a bandwidth of 20 MHz -- approximately two orders of magnitude higher than dispersive devices of comparable sensitivity -- with an effective flux noise of 0.29 $\mu\Phi_{0}$Hz$^{-1/2}$. This performance is in excellent agreement with our theoretical model.