Analysis of a Casimir-driven parametric amplifier with resilience to Casimir pull-in for MEMS single-point magnetic gradiometry

The Casimir force, a quantum mechanical effect, has been observed in several microelectromechanical system (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 device failure, 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 a MEMS offers 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-driven 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. Further development of the proposed design has the potential to revolutionize metrology and may specifically enable the unshielded monitoring of biomagnetic fields in ambient conditions.