Quantum double lock-in amplifier

Quantum lock-in amplifiers have been proposed to extract an alternating signal from a strong noise background. However, due to the typical target signal has unknown initial phase, it is challenging to extract complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in amplifier by employing two quantum mixers operating under orthogonal pulse sequences. To demonstrate the practical implementation, we discuss the experimental feasibility using a five-level double-Lambda coherent population trapping system with Rb atoms. Here, each Lambda structure acts as a quantum mixer, and two applied dynamical decoupling sequences serve as orthogonal reference signals. Notably, the system significantly reduces the total measurement time by nearly half and mitigates time-dependent systematic errors compared to conventional two-level systems. Furthermore, our quantum double lock-in amplifier is robust against experimental imperfections. This study establishes a pathway to alternating signal measurement, thereby facilitating the development of practical quantum sensing technologies. In analogy to the classical double lock-in amplifier, this work presents a general protocol for achieving a quantum double lock-in amplifier to extract complete information about the signal's amplitude, frequency, and initial phase. The realization of the quantum double lock-in amplifier is illustrated using a five-level double-Lambda coherent population trapping system as an example.