Without complicated processes, in direct demodulation, it is simply to detect the variance of probe laser transmission intensity using photodetector while the Rydberg atom system is at the zero-detune. The photo-generated current is approximately the baseband signal. However, due to the nonlinear relationship between the transmissivity of the Rydberg atom cell and microwave E-field strength, the direct demodulation method will result in nonlinear distortion. The optimum linear operation point of the Rydberg atom system should be studied to decrease the distortion.As far as we know, until now, there is no theoretical analysis about the optimal linear operation point of the Rydberg atom system, and the relationship between the baseband signal amplitude and nonlinear distortion in the AM microwave demodulation. We focus on the optimal linear operation point and nonlinear distortion in the Rydberg atom system.Firstly, we analyze the AM microwave direct demodulation model of the Rydberg atom system. In this model, we explain the nonlinear relationship between probe laser transmissivity and microwave E-field strength.Secondly, we calculate the first and second derivatives of probe laser transmissivity concerning microwave Rabi frequency and analyze the relationship between the first/second derivatives and optimal linear operation point.Thirdly, we adopt total harmonic distortion (THD) to explore the relationship among the Rydberg atom cell operation point, the baseband signal amplitude, and the nonlinear distortion.When THD is introduced to describe the degree of demodulation nonlinear distortion, we find two parameters that will affect the THD value. One is the operation point of the Rydberg atom system, and the other is the Rabi frequency of the microwave baseband signal.The simulation shows that by adjusting the operation point, THD will reach a minimum value, which is consistent with the value that we obtain theoretically from the transmissivity second derivative of zero.Fig. 4(b) shows that when the system is at the optimum linear operation point, the nonlinear distortion of the system declines with the decreasing baseband signal amplitude. Meanwhile, by comparing the THD at three different coupling laser Rabi frequencies, we find that the demodulation nonlinear distortion can be reduced by increasing the coupling laser Rabi frequency.

Rydberg atom system can strongly respond to weak microwave signals on the electromagnetically induced transparency (EIT) effect and Aulter-Townes (AT) effect. Therefore, people want to utilize this system to detect and demodulate microwaves instead of the traditional mode. At present, there are two methods to demodulate amplitude modulation (AM) microwave signals using the Rydberg atom system, including indirect demodulation and direct demodulation. In the indirect method, the first step is to scan the probe or coupling laser frequency near the zero-detune point, and the second step is to measure the splitting peak-to-peak frequency separation in the probe transmission spectrum. The third step is to calculate the microwave electric field (E-field) strength because the above frequency separation is proportion to the microwave E-field strength.

We build a simplified Rydberg atom system model (Fig. 1) and numerically simulate the probe laser transmissivity in the Rydberg atom system when ¹³³Cs (energy levels of 6S_1/2, 6P_3/2, 47D_5/2, and 48P_3/2) is chosen as Rydberg atom. Our simulation assumes the coupling laser Rabi frequencies separately are 2π×2.7 MHz, 2π×3.2 MHz, and 2π×3.7 MHz. Additionally, our simulation is kept under the frequency-zero-detune, which means probe and coupling laser frequencies are both locked to the energy transition frequency of the Rydberg atom. In these conditions, we conduct the following research.

By mathematical analysis we obtain the optimal linear operation point of the Rydberg atom system from the second derivative of zero (Fig. 3). When the system is operating at that point, the nonlinear distortion of AM microwave demodulation is minimum.

We study the relationship between the nonlinear distortion and the operation point in the Rydberg atom system demodulating the AM microwave signals by the direct method. First, we analyze the demodulation model of the Rydberg atom system in the frequency-zero-detune condition. Second, we calculate the first and second derivatives of the probe laser transmissivity for the microwave Rabi frequency. Utilizing the second derivatives of zero, we find the optimal linear operation point of the Rydberg atom cell in which the nonlinear distortion is the minimum in demodulating AM microwave. Third, the THD is adopted to explore the relationship between the operation point of the Rydberg atom cell, the baseband signal amplitude, and the nonlinear distortion. The simulation shows that the THD of the demodulation system with the Rydberg atom ¹³³Cs (energy levels of 6S_1/2, 6P_3/2, 47D_5/2, and 48P_3/2) can reach -95.4984 dB, when the Rydberg atom cell is near the optimum operation point, at 2π×2.7 MHz (coupling laser Rabi frequency) and 1 mV/m (baseband signal electrical field amplitude).