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Applied Optics

Laser frequency stabilization method based on a ladder-type Rydberg atom electromagnetically induced transparency

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

Published Apr 28, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1364/ao.553565

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Chinese Optics Letters•Nov 16, 2022•22 citations
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.
We herein develop and demonstrate a stable frequency-locking scheme for Rydberg atomic experiments. We use the Zeeman effect to modulate the three-level ladder-type Rydberg electromagnetically induced transparency (EIT) signal to lock the laser frequency of the coupling light for transition from its intermediate state to a Rydberg state. The effects of polarization of the probe and coupling lights, and the amplitude of the AC modulated magnetic field B 0 on the EIT and the corresponding dispersive error signal, are both analyzed. The results show that both the EIT signal and dispersive error signal are the strongest when the polarizations of coupling and probe fields are circular and equal. The signal-to-noise ratio of the dispersive error signal increases with B 0 . The slope of the dispersive error signal increases first and then decreases with B 0 , which is related to the increase of the EIT linewidth caused by the higher B 0 . The linewidth of the laser is significantly less than 500 kHz after frequency locking, which satisfies the requirements of most experiments involving Rydberg atoms. The method proposed herein can generally be applied to any cascade system of Rydberg atoms.
We present a laser frequency locking to Rydberg transition with electromagnetically induced transparency (EIT) spectra in a room-temperature cesium vapor cell. Cesium levels 6S 1/2 , 6P 3/2 , and the n D 5/2 state, compose a cascade three-level system, where a coupling laser drives Rydberg transition, and probe laser detects the EIT signal. The error signal, obtained by demodulating the EIT signal, is used to lock the coupling laser frequency to Rydberg transition. The laser frequency fluctuation, ∼0.7 MHz, is obtained after locking on, with the minimum Allan variance to be 8.9 × 10 −11 . This kind of locking method can be used to stabilize the laser frequency to the excited transition.
The conversion of the modulation signal from the coupling light to the probe light and the conversion of the additional phase noise from the coupling light to the amplitude noise of the probe light in the electromagnetically induced transparency (EIT) spectrum of the cesium atomic ladder type three level system were investigated by detecting the probe light output noise spectrum. It was demonstrated that frequency stabilization via external modulation can effectively avoid the transfer of modulation noise. In the experiment, two frequency stabilization methods external modulation transfer spectroscopy and internal modulation transfer spectroscopy were employed to achieve the frequency stabilization of the coupling light. The probe light noise spectra at the frequency stabilized output terminal and the detection output terminal were measured under both methods.
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.
Rydberg atoms, with large principal quantum number n, have been widely investigated in recent years due to their peculiar properties, such as big sizes, long lifetimes and strong interactions with fields and other Rydberg atoms. Rydberg atoms are very sensitive to external fields due to their large polarizabilities scaling as n7.These make Rydberg atoms an ideal candidate for the quantum information, the many-body interaction, etc.In this work, we investigate the Rydberg atoms using electromagneticlly induced transparency (EIT) in a ladder three-level system. The EIT is a quantum interference effect between two excitation path-ways driven by two laser fields. The main idea is performed in a room temperature cesium vapor cell, where the probe laser frequency is modulated. The ground state (6P1/2), excited state (6P3/2), and Rydberg state (nS1/2) constitute a Rydberg three-level system, in which the probe laser is fixed to the 6S1/2 (F = 4)6P3/2 (F = 5) transition by saturated absorption spectrum technique, whereas the coupling laser is scanned across the 6P3/249S1/2 transition. We detect the demodulated EIT signal with the lock-in amplifier (SR830). The modulated EIT signal shows a two-peak structure. The measured spacing between two peaks increases with the frequency detuning, caused by the modulation amplitude, and half the spacing between the peak-to-peak is nearly 1.67 times the modulation amplitude of the probe laser; the measured result shows that the splitting is independent of the modulation frequency. The experimental results are in agreement with the theoretical calculations. The results in our work can be used for real-time monitoring of the laser-line profiles and the fluctuation of laser frequency.
Based on the Rydberg cascade electromagnetically induced transparency, we propose a simultaneous dual-wavelength locking method for Rydberg atomic sensing at room temperature.The simplified frequency-locking configuration uses only one signal generator and one electro-optic modulator, realizing real-time feedback for both lasers.We studied the effect of the different probe and coupling laser powers on the error signal.In addition, the Allan variance and a 10 kHz amplitudemodulated signal are introduced to evaluate the performance of the laser frequency stabilization.In principle, the laser frequency stabilization method presented here can be extended to any cascade Rydberg atomic system.