Entanglement-enhanced quantum lock-in detection achieving simultaneous Heisenberg scalings with particle number and time

Quantum lock-in detection (QLID), a cornerstone technique in quantum metrology, enables precise extraction of oscillating signals from noise by leveraging dynamical decoupling to suppress unwanted spectral components. Beyond this, many-body quantum entanglement serves as a critical resource for surpassing the standard quantum limit in precision measurements. Here we report the first experimental realization of entanglement-enhanced QLID using two \(^{40}\text{Ca}^+\) ions confined in a linear Paul trap. The system is initialized into a maximally entangled Greenberger-Horne-Zeilinger state via a M$\phi$lmer-S$\phi$rensen gate, followed by the application of periodic multipulse sequences to implement QLID. Compared to non-entangled states (e.g., a product state), our work demonstrates frequency measurement precision scaling as $1/N$ with particle number (N) , achieving the Heisenberg scaling. Remarkably, the precision in the time domain approaches a super-Heisenberg scaling (i.e., $1/T^2$), significantly outperforming conventional bounds. To enhance practical applicability, we further optimize multipulse sequences to improve robustness against rotation angle inaccuracies and detuning errors. This work establishes QLID as a powerful paradigm for quantum sensing and provides a concrete pathway to Heisenberg-limited detection of oscillating signals in realistic settings.