Optimized heteronuclear-ion quantum demodulator with ``super-Heisenberg'' and Heisenberg scalings

Abstract Highly efficient and high-precision measurement of electromagnetic signals is an important issue in both fundamental science and practical application. The demodulation is a widely used technique for receiving and recovering the modulated electromagnetic signals. Here we report the first experimental execution of a quantum demodulator using two heteronuclear ions - ⁴⁰Ca⁺ and ⁴³Ca⁺ - to simultaneously detect the amplitudes and frequencies of unknown periodic signals, breaking the constraint of double-parameters optimization. The ⁴⁰Ca⁺ ion serves as the sensor for detecting unknown frequencies, while the ⁴³Ca⁺ ion focuses on measuring unknown amplitudes. Under the optimization of reinforcement learning, the quantum Fisher information for unknown-frequency estimation scales as \(t^4\), achieving the ``super-Heisenberg'' scaling, while for unknown-amplitude estimation scales as \(t^2\), approaching the Heisenberg scaling. These observations present the practical application of two heteronuclear ions in efficient quantum sensing an highlight the advantage of reinforcement learning in improving quantum control techniques.