Fig. 3: Frequency offset heterodyne readout.
a Principle of the readout scheme. fϕ is the reference frequency defined by the sequence, and f1, f2 are the frequencies of the signals. The colored regions mark where the quantum phase is accumulated in the Hahn-echo sequence, while phase accumulations at the other areas are canceled in the spin evolution. The figure shows identical heterodyne signals due to fϕ − f1 = f2 − fϕ. b Frequency responses of the Hahn-echo sequence and CPMG-2 sequence. The applied ac fields have an 5 Hz offset to the denoted signal frequencies so that they are detected as a 5 Hz heterodyne readout. Both theoretical and experimental results are plotted after normalization. c Signal frequency response of Hahn-echo measurements with 1/Tseq = 10 kHz. The dash line indicates the filter introduced by the lock-in amplifier. d Heterodyne frequency dependency to sequences and signal. The reference signal is the result of detecting 20.005 kHz signal with sequence that uses Tϕ = 50 μs and Tseq = 20Tϕ. In meas. 1, Tϕ is changed by ±4 ns. In meas. 2, we keep Tϕ unchanged, and offset Tseq with ±4 ns. In meas. 3, the applied field is changed to 16.005 kHz while the other parameters are the same as meas. 2.
