Phase-locked amplification enhanced by spin squeezing

Quantum lock-in amplification raises the detection sensitivity of magnetic fields to unprecedented levels by phase-locked pumping the Zeeman levels of a single trapped atom. However, random spin precessions limits the useful detection range of arming times for locking high-contrast signals. To extend this range imposed by the uncertainty limit, quadrature spin squeezing can be introduced, on top of the phase-locking mechanism. We propose a detection scheme using an atomic ensemble whose collected spin is pumped by two lasers for simultaneous squeezing and phase locking. We derive the optimal $\pi/2$-pulse and $\pi$-pulse schemes that accomplishes this concurrent action and prove that the resulting phase sensitivity is enhanced while the usable detection window for phase locking is widened.