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Laser modulation transfer phenomenon in a four-level heterodyne Rydberg atom system

Yu Tang, Hanbin Zhou, Chuang Yang, Shuang Ren, Siyuan Wang, Chenxi Lu

Published Jun 10, 2025• 0 citations
Publisher

Abstract

This paper investigates the transfer of probe or coupling light modulation interference to density matrix elements in a four-level heterodyne Rydberg system. By combining the density matrix dynamical equations with power spectral density (PSD) analysis, we derive analytical solutions to describe this phenomenon. Our results demonstrate that coherence in multi-level systems fundamentally enables this transfer mechanism, thereby increasing the system's noise floor and degrading microwave detection sensitivity. Building on these findings, we establish a sensitivity-noise-constraint relationship to suppress the influence of noise.

DOI
10.1364/oe.567239

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Acta Physica Sinica•Jan 1, 2018•2 citations
This paper investigates the transfer of probe or coupling light modulation interference to density matrix elements in a four-level heterodyne Rydberg system. By combining the density matrix dynamical equations with power spectral density (PSD) analysis, we derive analytical solutions to describe this phenomenon. Our results demonstrate that coherence in multi-level systems fundamentally enables this transfer mechanism, thereby increasing the system's noise floor and degrading microwave detection sensitivity. Building on these findings, we establish a sensitivity-noise-constraint relationship to suppress the influence of noise.
The four-level heterodyne Rydberg atom receiver has garnered significant attention in microwave detection and communication due to its high sensitivity and phase measurement capabilities. Existing theoretical studies, primarily based on static solutions, are limited in characterizing the system's frequency response. To address this, this paper comprehensively investigates the dynamic solutions of the density matrix elements for the four-level heterodyne structure, establishing a quantitative relationship between system response, signal frequency, and system parameters. This enables theoretical bandwidth calculations and performance analysis. This paper also constructs a noise model for the density matrix elements, revealing the relationship between the ultimate sensitivity of the Rydberg atom receiver and the noise in the density matrix elements. Both theoretical simulation and experimental results demonstrate that the bandwidth of the four-level heterodyne receiver can exceed 10 MHz. This study provides critical theoretical support for the engineering applications and performance optimization of heterodyne Rydberg atom receivers.
We established a theoretical model for the ladder-type EIT laser frequency stabilization method based on the analysis of the system response. By using the method of deriving the density matrix equations, we obtained the density matrix elements of the three-level system and subsequently derived the system’s response function. Based on this, we revealed the complex interference mechanism of the modulated probe light in the atomic medium. Through quantitative analysis of this process, we obtained the output signal, which carries information about the frequency offset of the coupling light, after the probe light passes through the atomic medium. The error signal obtained after demodulation can then serve as the reference signal for the closed-loop feedback system. To make the error signal more intuitively reflect its variation with the coupling light frequency offset, we introduced the equivalent transfer of the modulation frequency based on the locking relationship between the probe light detuning and the coupling light detuning. This paper provides a deep analysis of the impact of the probe light modulation frequency on the error signal and experimentally validates our theoretical analysis results. Finally, we select a modulation frequency of 10 MHz to lock the coupling light and compare the Allan variance before and after locking. The minimum value of σ ( τ ) was reduced from 4.62×10 −10 before locking to 1.70×10 −10 after locking.
This paper systematically analyzes the key noise sources limiting the sensitivity of Rydberg atomic receivers. First, the quantum projection noise inherent to the system is modeled, as this noise sets the theoretical limit for receiver sensitivity. Second, the paper establishes the constraints relationship between photodetector noise and system sensitivity under both direct detection and heterodyne detection methods. Subsequently, this paper establishes the constraint relationships between the laser's intensity noise and receiver sensitivity, and between the phase noise and receiver sensitivity, respectively. The research reveals that the intensity noise of the probe light significantly exceeds that of the coupling light in its effect on receiver performance, while its phase noise exerts a comparable level of influence.
Cross-spectral analysis is widely used for weak-signal extraction due to its ability to suppress uncorrelated noise. The common frequency-correlated noise of the probe laser in different detection channels restricts the cross-spectral noise suppression and degrades sensitivity. We propose and experimentally demonstrate a dual-channel Rydberg heterodyne scheme based on asymmetric optical detuning. This method with cross-spectral density (CSD) processing reduces the interchannel probe-frequency noise correlation while preserving the common microwave-induced atomic response essential for signal coherence. Experimental results confirm that asymmetric detuning selectively suppresses laser-noise-induced coherence without degrading signal correlation and thus improves the signal-to-noise ratio (SNR). Compared with single-channel power spectral density (PSD) analysis, this method reduces the noise floor and improves the SNR by 12 dB for the resonant case and by 3.7 dB for the detuned case. These results provide a practical and readily implementable strategy for suppressing correlated technical noise in Rydberg heterodyne receivers, advancing the development of high-sensitivity electric-field metrology.
We conduct a theoretical investigation into the impacts of local microwave electric field frequency detuning, laser frequency detuning, and transit relaxation rate on enhancing heterodyne Rydberg atomic receiver sensitivity. To optimize the output signal amplitude given the input microwave signal, we derive the steady-state solutions of the atomic density matrix. Numerical results show that laser frequency detuning and local microwave electric field frequency detuning can improve the system detection sensitivity, which can help the system achieve extra sensitivity gain. It also shows that the heterodyne Rydberg atomic receiver can detect weak microwave signals continuously over a wide frequency range with the same sensitivity or even more sensitivity than the resonance case. To evaluate the transit relaxation effect, a modified Liouville equation is used. We find that the transition relaxation rate increases the time it takes to reach steady state and decreases the sensitivity of the system detection.
The transfer mechanism from the amplitude noise of the coupling light to the phase noise of the probe light in a Rydberg electromagnetic induced transparency effect derived from a ladder-type system including 6S1/2↔6P3/2↔62D5/2 of Cs atoms is demonstrated by using Mach-Zehnder interferometer and balanced homodyne detection technology. In our experiments, the transmission signal of 852 nm probe light is measured by scanning the coupling light frequency nearby the transition from 6P3/2 to 62D5/2 Rydberg state, while the frequency of the probe light is locked at the resonance transition of the 6S1/2↔6P3/2. The relative phase stability of two arms of Mach-Zehnder interferometer, which is constructed with the first order diffraction light of probe light through an acoustic-optic modulator, is accomplished by the controlled piezoelectric ceramic with the PID feedback loop. The interferences between the probe light and the reference light of Mach-Zehnder interferometer under the different relative phases are observed. The interference spectrum of probe light is in good agreement with the theoretical simulation result of the ladder-type three-level system. Therefore, we study the transfer characteristics from the frequency noise of coupling light to the phase noise of probe light when coupling light frequency resonance happens at the transition 6P3/2↔62D5/2. We find the significant suppression of the phase noise of probe light at the higher frequency noise. Moreover, we observe the characteristics of the phase noise of the probe light varying with the power of the coupling light under the different detuning degrees of coupling light. In the red detuning side, the transferred phase noise of probe light decreases with the increase of coupling light power, which is different significantly from the scenario under the blue detuning condition. The ions produced in the ionization process of Rydberg atoms will form the local electric field that would cause the energy level of Rydberg states to shift. The investigation of the noise transfer between the coupling light and probe light in the Rydberg electromagnetically induced transparency effect is important for understanding the coherence mechanism of ladder-type system and the some potential applications, such as in Rydberg-atom-based electric field metrology.