The Rydberg atom system, through the effects of electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, can strongly respond to weak microwave signals. This makes it a promising candidate for receiving and demodulating microwaves with greater sensitivity than traditional systems. Currently, two methods exist for demodulating amplitude modulation (AM) microwave signals: the indirect method and the direct method. In the indirect method, the process involves scanning the probe or coupling laser frequency near the zero-detuning point and measuring the frequency separation between the split peaks in the probe transmission spectrum. This separation is proportional to the microwave electric field (E-field) strength, which allows for the calculation of the microwave E-field intensity. The direct method, on the other hand, involves detecting variations in the probe laser transmission intensity using a photodetector while the Rydberg atom system is at zero-detuning. The resulting photo-generated current approximates the baseband signal. In this process, the transmittance of the Rydberg atom cell varies with the amplitude of the AM signal. The sensitivity of the atom cell to the baseband signal is reflected in how the atom cell’s transmittance changes with variations in microwave amplitude. A small change in the baseband signal amplitude that leads to a significant change in the atom cell’s transmittance indicates high sensitivity. In this study, we focus on exploring the relationship between the Rydberg atom cell transmittance and the coupling laser, microwave field, and Rydberg atom energy levels to identify the high-sensitivity operating points of the Rydberg atom cell during direct demodulation. To our knowledge, no prior research has explored the relationship between the coupling laser, microwave carrier, and the high-sensitivity operating points of the Rydberg atom cell. In addition, there is no research on enhancing atom cell sensitivity by selecting appropriate atom energy levels, microwave frequencies, and coupling laser intensities.

First, we present the system block diagram for AM microwave signal demodulation based on the Rydberg atom cell, as shown in Fig. 1. Building on the expression for Rydberg atom cell transmittance, we analyze the model for demodulating AM microwave signals using the direct demodulation method, as shown in Fig. 2. To quantify the sensitivity of the atomic vapor cell to microwave amplitude variations (i.e., baseband signal amplitude variations), we define the atom cell gain coefficient as the absolute value of the first derivative of the atom cell transmittance with respect to microwave amplitude. Through numerical simulation, we obtain the relationship between the atom cell gain coefficient and both the coupling laser and microwave field strengths. This relationship is shown in Fig. 3, using the 6S_1/2, 6P_3/2, 49D_5/2, and 50P_3/2 energy levels of ¹³³Cs. Finally, for microwave frequencies in the C-band, we calculate the extreme values of the atom cell gain coefficient under zero detuning and identify the corresponding coupling laser and microwave field intensities. We also analyze the factors that influence the atom cell gain coefficient extremes.

By analyzing the relationship between microwave field intensity and Rydberg atom cell transmittance, as shown in Fig. 2, we find that the atom cell’s static operating point can be adjusted by varying the AM carrier field strength and coupling intensity. Furthermore, when the Rydberg atom’s energy levels are fixed, the atom cell can reach its most sensitive operating point—where the atom cell gain coefficient is at its maximum—by adjusting the AM microwave carrier and coupling field intensities. For example, when ¹³³Cs is at the 6S_1/2, 6P_3/2, 49D_5/2, and 50P_3/2 energy levels, and under zero detuning, setting the coupling laser and AM microwave carrier electric field intensities to 9.04008×10³ V/m and 3.794678×10^-4 V/m respectively, allows the 1 cm-length atom cell to operate at its most sensitive point, where the gain coefficient reaches its maximum value of 943.35 m/V, as illustrated in Fig. 3. In addition, the coupling laser, AM microwave carrier, and the atom’s energy levels all influence the atom cell’s operating point. By setting the 1 and 2 levels to 6S_1/2 and 6P_3/2, and changing the 3 and 4 levels under zero detuning and a principal quantum number below 70, we calculate all extreme values of the atom cell gain coefficient for microwaves in the C-band. Analysis shows that the atom cell gain coefficient increases with the principal quantum number and decreases with the spontaneous decay rate of 3 and 4 levels, as shown in Fig. 4.

In this study, we investigate the relationship between the Rydberg atom cell’s highly sensitive operating point and the coupling laser, microwave carrier electric field intensity, and Rydberg atom level parameters in an AM microwave demodulation system. First, we define the atom cell gain coefficient as the absolute value of the first derivative of atom cell transmittance with respect to the microwave electric field intensity. We then derive the theoretical expression for the atom cell gain coefficient. Through numerical simulation and theoretical analysis, we find that when the Rydberg atomic energy level is fixed and the atom cell remains at zero detuning, the gain coefficient reaches its maximum by adjusting the electric field intensities of the coupling laser and microwave carrier. Finally, under conditions where the microwave frequency is in the C-band, the principal quantum number is below 70, and the atom cell is at zero detuning, we calculate the extreme values of the atom cell gain coefficient. We analyze the factors affecting these extremes, providing a theoretical basis for improving the atom cell’s gain coefficient and optimizing the Rydberg atom cell for maximum sensitivity. The simulation results demonstrate that the 1 cm-length atom cell gain coefficient for ¹³³Cs can reach its extreme value of 1688.2 m/V when 1, 2, 3, and 4 levels are set to 6S_1/2, 6P_3/2, 60D_3/2, and 61P_1/2, the microwave frequency is 4.03012 GHz, and the coupling laser and microwave intensities are 3.929343×10⁴ V/m and 2.144006×10^-4 V/m respectively.