Fig. 7: The influence of finite pulse length on the quantum double lock-in amplifier.
a For the weak target signal measurement, the normalized excited state population ρ55/a versus (τm − τ) with different pulse length TΩ = 0 (solid blue line), TΩ = 2 μs (dashed red line) and TΩ = 4 μs (dotted green line). It indicates that the pulse length does not affect the lock-in point when TΩ ≤ 0.4 τ. Here,B0 = 1 nT, ω = 2π × 50 kHz (τ = 10 μs), β = −π/6, n = 200 (nτ = 2 ms). b For the strong target signal measurement, the inverse participation ratio (IPR) versus (τm − τ) with different pulse length TΩ = 0 (solid blue line), TΩ = 2 μs (dashed red line) and TΩ = 4 μs (dotted green line). It also indicates that the pulse length does not affect the lock-in point. c The fast Fourier transform (FFT) results of \({\tilde{\rho }}_{{{{{{{{\rm{55,n}}}}}}}}}\) in the case of τm = τ with different pulse length TΩ = 0 (solid blue line), TΩ = 2 μs (dashed red line) and TΩ = 4 μs (dotted green line). d The relative error relative deviation of the amplitude B0 and the phase β versus the pulse length TΩ. The effect of pulse length TΩ can be ignored if TΩ ≤ 0.4 τ. Here, B0 = 2 μT, ω = 2π × 50 kHz (τ = 10 μs), β = −π/6 and n = 0, 2, 4,⋯, nm(nm = 400, nmτ = 4 ms).
