As the reform of the International System of Units (SI) progresses, many quantum metrology standards based on the superior characteristics of the atomic system have been successfully developed to replace physical standards, such as atomic clocks, atomic magnetometers, and atomic gravimeters. Recently, a new method of microwave electric field measurement with a wide frequency band and high sensitivity has been developed based on the quantum coherent spectroscopy of Rydberg atoms. Compared with conventional techniques, the Rydberg-atom-based microwave electric field measurement technique can transform the microwave field strength measurement into a higher-accuracy Rabi frequency measurement through atomic constants and directly link the microwave electric field strength to the SI. However, the discrete distribution of Rydberg energy levels leads to the limitations of discrete frequencies and narrow bandwidths in microwave electric field measurement. Although various methods for continuously tuning the frequency of the microwave field have been developed, such as resonant microwave tuning, far-detuned microwave AC Stark tuning, and DC Stark tuning, these methods often involve complex experimental setups and rely on discrete energy levels. Therefore, we use an off-resonant strong microwave field to measure the continuous tuning frequency range of the measured microwave electric fields through the AC Stark shift characteristics of Rydberg energy levels.

We conduct continuously tunable frequency measurements of the microwave electric field based on the near-off-resonant AC Stark effect in a rubidium atomic vapor cell. A ladder-type electromagnetically induced transparency (EIT) three-level configuration is formed by a ground state, 5S_1/2, an excited state, 5P_3/2 (F'=3), and a Rydberg state, 73S_1/2. The probe laser and the coupling laser with the same linear polarization are overlapped and counter-propagated through the vapor cell. The weak probe laser with a wavelength of 780 nm is locked to the transition of 5S_1/2(F=2)→5P_3/2(F'=3). The strong coupling laser with a wavelength of about 480 nm is frequency scanned across the transition of 5P_3/2(F'=3)→73S_1/2. The near-off-resonant strong microwave tuning field and the measured microwave electric field are simultaneously applied to the atomic vapor cell through a single microwave horn antenna. When a weak resonant microwave electric field is applied, which is read out by an all-optical Rydberg electromagnetically induced transparency and exhibits Autler?Townes (AT) splitting spectrum as the measured field, the strong near-off-resonant microwave as tuning fields is then used to tune the Rydberg level by the AC Stark effect. By varying the frequency and power of the tuning field, we measure the resonance frequency of the AT splitting spectrum for 73S_1/2 to adjacent nP_j Rydberg states under different AC Stark shifts and obtain the continuous tuning frequency range of the measured microwave electric field.

We measure the coupling resonance frequency ranges from 73S_1/2 to 72P_1/2, 72P_3/2, 73P_1/2, and 73P_3/2 Rydberg states by the AC Stark shift characteristics induced by the near-off-resonant strong microwave field. We investigate in detail the influence of the frequency and power of the tuning field on the resonance frequency of the measured microwave field. Under the influence of the tuning field, the resonance frequency of the measured microwave electric field changes with the frequency shift of Rydberg energy levels, with the corresponding EIT-AT splitting peak resonance frequency shift (Fig. 2). The maximum unidirectional resonance frequency tuning range of the measured microwave field is about 151 MHz. Considering the bidirectional frequency shift characteristics, the maximum continuous tunable range of the resonance frequency reaches over 200 MHz. The maximum continuous frequency tuning range reaches 400 MHz by combining the bidirectional tuning characteristics and different coupling state combinations (Fig. 3). Additionally, we investigate the variation of Autler?Townes splitting frequency intervals with microwave power under different resonance conditions. For the same resonance frequency shift, small detuning and low-power tuning fields have a smaller effect on the strength measurement of the test field compared with large detuning and high-power tuning fields and have a larger linear dynamic range (Fig. 4).

We introduce a novel method for continuous tunable microwave electric field measurement based on the near-off-resonant AC Stark effect in a Rydberg atomic vapor cell. We measure the continuous resonance frequency tuning range of microwave coupling between rubidium Rydberg atom 73S_1/2 and adjacent nP_j states. The maximum unidirectional tunable range for measurement is 151 MHz, and the maximum continuous frequency tuning range reaches 400 MHz by combining the bidirectional tuning characteristics and different coupling state combinations. Different from the resonant tuning method that depends on extra Rydberg levels, this method based on the AC Stark shift can achieve continuously tunable frequency measurement with a single Rydberg state and single microwave horn antenna. This approach not only overcomes the limitations of discrete frequency and narrow band of the existing Rydberg atomic microwave electric field measurement but also simplifies the system structure and enhances the practicability of the system. Our study lays the foundation for quantum metrology and the traceable measurement of microwave electric fields based on Rydberg atoms.