An approach to direct velocity estimation using magnetomechanics

Today's mechanical sensors are capable of detecting extremely weak external perturbations while operating near the fundamental limits of quantum noise. However, further improvements can be made in both sensitivity and bandwidth if we can reduce the noise originating from the process of measurement itself --- the quantum mechanical backaction of measurement. One of the ways to eliminate this noise is by measuring a quantum non-demolition variable such as momentum in a free-particle system. Here we propose and characterize a theoretical model for direct velocity measurement that utilizes a magnetic-based approach. By exploiting fundamental electromagnetic principles, we demonstrate how a traditional voice-coil configuration provides a convenient detector design by generating a momentum-momentum coupling as well as a signal voltage directly proportional to velocity. Given the very small voltage signals anticipated and the need to transition from the low frequencies of this detector scheme to the much higher frequencies associated with microwave readout, we consider the coupling of the voice-coil to a voltage-sensitive superconducting circuit, namely, the well-studied Cooper-pair box (CPB). We then explore the general analytical set-up, sensitivity, and feasibility of this collective system for the purposes of achieving extremely sensitive direct-velocity measurements of a magnetic detection mass.