Fast iterative, adaptive frequency sensing scheme of a two-level system (experiment)

We experimentally implement the iterative adaptive sensing (IAS) protocol to precisely determine the frequency splitting of a high Q nanomechanical two-mode system. The system under investigation consists of the strongly coupled fundamental flexural in-plane and out-of-plane mode of a nano string resonator. The application of coherent control pulses to the classical two-mode system relies on dielectric frequency tuning. Tuned on resonance, the two modes coherently exchange energy, orders of magnitude faster than the decay time, allowing us to investigate the system dynamics in time-resolved measurements. To this end, we perform the IAS protocol for short signals. The protocol is based on the application of the Magnus-based strategy to the coherent control pulses of the two-level system to overcome experimental constraints such as the bandwidth limitation in pulse generation and mitigates leakage in the sensing and readout state preparation of the Ramsey protocol. In strong agreement with the theoretical prediction, the experimental results show high accuracy in frequency estimate associated to the splitting of the modes. Comparison with the traditional Ramsey protocol reveals that precise results can be obtained on much shorter time scales using IAS.