Fig. 5: Schematic of the quantum double lock-in amplifier via five-level double-Λ coherent population trapping (CPT) in 87Rb.
a Five-level double-Λ configuration of 87Rb atom which includes \(\left\vert 1\right\rangle =\left\vert F=1,{m}_{F}=-1\right\rangle\), \(\left\vert 2\right\rangle =\left\vert F=2,{m}_{F}=-1\right\rangle\), \(\left\vert 3\right\rangle =\left\vert F=1,{m}_{F}=1\right\rangle\), \(\left\vert 4\right\rangle =\left\vert F=2,{m}_{F}=1\right\rangle\) and \(\left\vert 5\right\rangle =\left\vert {F}^{{\prime} }=1,{m}_{F}=0\right\rangle\). b Realization of the quantum double lock-in amplifier. Initialization: preparing the two dark states as the initial states. Sensing: coupling the two ground states \(\{\left\vert 1\right\rangle ,\left\vert 2\right\rangle \}\) and \(\{\left\vert 3\right\rangle ,\left\vert 4\right\rangle \}\) through the periodic dynamical decoupling (PDD) and Carr-Purcell (CP) sequences respectively. Here, TΩ denotes the π pulse length, τm is the pulse repetition periods and the total sensing time is tn = nτm. Detection: a CPT pulse with 2 μs is imposed to detect the common excited state population via fluorescence or transmission spectrum.
