Objective Rydberg atoms became increasingly crucial in the last decade because of their fascinating characteristics that distinguish them from conventional radio frequency (RF) sensors. First, the Rydberg atoms are self-calibrating thanks to the invariance of the atomic parameters, and their response is linked to Plank's constant. Second, atomic sensing systems break a key assumption behind the Chu limit of traditional electronic sensors by allowing a small vapor cell to operate over multiple octaves of frequencies from DC to THz. Third, instead of demodulated circuitry, Rydberg atoms can naturally extract the baseband signals from the carrier frequency. Fourth, Rydberg atoms may avoid internal thermal (Johnson) noise, even at room temperature. In recent years, the amazing introduction of the local oscillator (LO) RF field has assisted us in controlling ensembles of Rydberg atoms. However, most current reports on Rydberg atomic heterodyne sensors focus on measurements in the resonant region, which can only achieve highly sensitive detection at discrete frequencies due to the quantum nature of the atomic energy level. In this work, by extending the Rydberg atomic heterodyne technique from the resonant region to the off-resonant region, we experimentally validated the continuous broadband and high sensing sensitivity of Rydberg atoms. Methods When a strong LO field and a weak signal (SIG) field with frequency detuning on the order of kHz are irradiated to the atoms, the energy level will be modulated by the intermediate frequency (IF) in the resonant and off-resonant regions, which can be directly detected by optical electromagnetically induced transparency (EIT). At room temperature, a probe laser of 852 nm and a coupling laser of 509 nm propagate in opposite directions and overlap inside a 2 cm-long vapor cell containing cesium atoms, exciting the atoms to the Rydberg state for atomic sensing. In the resonant region, the LO frequency is set to 2. 63 GHz, and the SIG frequency is set to 2. 63 GHz+ 10 kHz. Both fields are illuminated into the vapor cell by a horn antenna 7 cm away from the optical path, and the polarization of the two RF fields is the same as that of the probe and coupling beams and propagates in a vertical direction to the laser beams. While in the off-resonant region, the frequencies of the LO and SIG fields are tuned to 300 MHz and 300 MHz+ 10 kHz, respectively. An aluminum parallel-plate waveguide serves as the microwave transmitter in the off-resonant region. The reflection coefficient ( S11) of the input port is below - 20 dB from DC to 850 MHz (Fig. 2), indicating the excellent port matching performance of the parallel-plate waveguide. Results and Discussions In the resonant region, we calibrated the electric (E) field strength of the RF field using the Autler-Townes (AT) splitting effect. By adjusting the output power of the signal generator to satisfy the linear relationship between AT-splitting and RF field amplitude, we obtained the relationship between the square root of the signal generator output power and the E-field intensity calculated by AT- splitting (Fig. 3). The results show excellent linearity, and the weak RF E- field strength can be inferred from the fit line. Then, a spectrum analyzer was used to measure the intensity of the beat-note signal under Rydberg atomic heterodyne conditions. We measured a series of data points of the beat-note signal strength versus the applied SIG power (Fig. 4). The intensity of the received beat- note signal is approximately proportional to the strength of the applied SIG field with a linear dynamic range of over 45 dB. The minimum SIG output power is - 85 dBm, which is limited by the background noise of the spectrum analyzer. By leveraging the gradient of the fit line, we can obtain the minimal detectable E-field of 220. 94 nV/ cm, with the corresponding sensing sensitivity of - 131. 9 (dBm/ cm(2))/ Hz. Similarly, in the off-resonant region, through the relationship between the power injected in the parallel-plate waveguide and the E-field strength, we measured the minimum E-field strength of 19 mu V/cm in the offresonant region at 300 MHz, with a sensitivity of - 93. 2 (dBm/ cm(2))/ Hz. Besides, we also measured the instantaneous bandwidth of the system in the off-resonant region (Fig. 5). By taking into account the negative detuning of the SIG and LO fields, the instantaneous bandwidth of 3 dB of the system reaches 90 kHz. Conclusions In the present study, two typical frequency points in the resonant and off-resonant regions were selected to experimentally verify the broadband and high sensitivity detection capability of Rydberg atomic sensors. During the measurement, a horn antenna and a parallel-plate waveguide were used as microwave transmitters in the resonant and offresonant regions, respectively. Using the Rydberg atomic heterodyne technique, we successfully measured a minimum Efield strength of 220. 94 nV/ cm with a sensitivity of - 131. 9 ( dBm/cm(2))/Hz in the resonant region at 2. 63 GHz and a minimum E- field strength of 19 mu V/cm with a sensitivity of - 93. 2 (dBm/cm(2))/Hz in the off-resonant region at 300 MHz, respectively. In principle, by adjusting the laser frequency to excite the alkali metal atoms to various Rydberg states and incorporating the distinct responses of Rydberg atoms to E-fields in the resonant and off-resonant regions, highly sensitive sensing of microwave E-fields can be achieved in the broadband continuous spectral range.
