Rydberg atomic spectrum analyzer with microwave-dressed-state-locking and multimode Floquet theory

We propose a Rydberg atomic spectrum analyzer (RASA) utilizing microwave-dressed-state-locking (MWDSL) in conjunction with multimode Floquet theory (MFT). By leveraging a strong local microwave (MW) field resonant with Rydberg states to implement MWDSL, we analyze the second-order effect of MFT induced by the interplay of controllable bias and signal MW fields. This effect facilitates the coupling of locked dressed states, providing a pathway for measuring the signal MW field. We demonstrate that the RASA can simultaneously characterize multiple MW fields across distinct frequencies, with both the frequency and strength of each MW field discernible in the spectral response. This capability renders RASA suitable for measuring unknown-frequency MW fields, thereby expanding the utility of Rydberg atom-based electrometers in complex spectral analysis scenarios.