  The Casimir Force, a quantum mechanical effect, has been observed in several
microelectromechanical systems (MEMS) platforms. Due to its extreme sensitivity
to the separation of two objects, the Casimir Force has been proposed as an
excellent avenue for quantum metrology. Practical application, however, is
challenging due to attractive forces leading to stiction and failure of the
device, called Casimir pull-in. In this work, we design and simulate a
Casimir-driven metrology platform, where a time-delay based parametric
amplification technique is developed to achieve a steady state and avoid
pull-in. We apply the design to the detection of weak, low frequency, gradient
magnetic fields, similar to those emanating from ionic currents in the heart
and brain. Simulation parameters are selected from recent experimental
platforms developed for Casimir metrology and magnetic gradiometry, both on
MEMS platforms. While MEMS offer many advantages to such an application, the
detected signal must typically be at the resonant frequency of the device, with
diminished sensitivity in the low frequency regime of biomagnetic fields. Using
a Casimir-drive parametric amplifier, we report a 10,000 fold improvement in
the best-case resolution of MEMS single-point gradiometers, with a maximum
sensitivity of 6 Hz/(pT/cm) at 1 Hz. The development of the proposed design has
the potential to revolutionize metrology, and specifically may enable
unshielded monitoring of biomagnetic fields in ambient conditions.
