Entanglement-enhanced quantum lock-in detection achieving Heisenberg scaling

Quantum lock-in detection (QLID) is a powerful technique for extracting weak oscillating signals within noise. While entanglement may enhance measurement precision beyond the standard quantum limit (SQL), its integration with QLID is still an experimental challenge. Here we report the first experimental realization of entanglement-enhanced QLID using two trapped ⁴⁰Ca⁺ ions. We prepare a Greenberger-Horne-Zeilinger (GHZ) state using a Mϕlmer-Sϕrensen gate and then apply periodic multipulse sequences to execute QLID. Using the GHZ state, the measurement precision approaches the Heisenberg limit (Δω ∝ N^-1), surpassing the SQL (Δω ∝ N^-1/2) achievable with non-entangled states. Notably, QLID achieves a superior inverse-quadratic temporal scaling (Δω ∝ T^-2), exceeding the conventional inverse-linear scaling (Δω ∝ T^-1), regardless of entanglement. We further optimize pulse sequences for enhanced robustness against experimental errors. This work establishes a powerful pathway to Heisenberg-limited quantum sensing of weak oscillating signals within noise.