Phase-locked amplification enhanced by spin squeezing

TL;DR

The paper addresses enhancing phase sensitivity in quantum lock-in amplification by incorporating spin squeezing into a multi-atom, phase-locked sensor. It derives an optimal pulse scheme combining four $\pi/2$ squeezing pulses with a phase-locked sequence, yielding an effective $H_{\text{eff}} = \chi J_z^2$ that cooperates with $H = \chi J_z^2 + M(t) J_z + \Omega(t) J_x$ to improve phase estimation. The results show that spin squeezing broadens the high-contrast fringe window and improves the minimal detectable phase, with sensitivity gains scaling with the number of squeezed atoms and sequence duration (e.g., $\approx 0.513\ \text{Hz}\,\text{Hz}^{-1/2}$ at $T \approx 149.49\ \text{ms}$). This approach potentially pushes quantum sensors toward Heisenberg-limited performance in weak-field detection by distributing uncertainty across a multi-particle ensemble while maintaining robust phase locking.

Abstract

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 $π/2$-pulse and $π$-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.

Figures (4)

• Figure 1: Experimental setup. (a)Schematic of the setup. Atoms are trapped inside an optical cavity. By inserting a half-wave plate (HWP) in front of the polarizing beam splitter (PBS), the probe beam is split into $x$- and $y$-polarized beams in the output ports of PBS and then detected by two photon detectors. (b)Pulse sequence. The atoms are initially prepared in a CSS by optical pumping propagating along the $x$ direction. The orange pulse train indicates the squeezing pulse scheme, and the yellow-green pulse train indicates the quantum phase locked measurement pulse scheme.
• Figure 2: Fringe contrast with spin squeezed and without squeezed. Photon number and atom number are $N_{s}=N_{a}=50$ and squeezing pulse separation is $\tau=1\times10^{-4}g^{-1}$, the effective interaction strength is set to $\chi=6.25\times10^{-4}g$.
• Figure 3: Comparison of fringe contrast versus the number of atoms.
• Figure 4: Sensitivity (solid blue line) versus the phase locked sequence duration $T$.