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Photonics

FPGA-Based 509 nm Laser Frequency Stabilization to Cesium Atomic Transition: Modulation-Free Rydberg Two-Color Polarization Spectroscopy (TCPS) Versus Frequency-Modulated Rydberg–EIT Spectroscopy

Rui Chang, Tao Wang, Yuewei Wang, Yirong Wei, Yuhui Yang, Rui Sun, Yuzhi Yan, Ziwen Wang, Jun He, Junmin Wang

Published Feb 11, 2026• 1 citation
Publisher

Abstract

Frequency stability of a 509-nm single-frequency laser, a core component combined with an 852-nm single-frequency laser for two-step cesium Rydberg transitions, is critical for quantum control and metrology precision. Utilizing atomic transition as the absolute reference, we achieved laser frequency locking via modulation-free Rydberg two-color polarization spectroscopy (Rydberg–TCPS) and frequency-modulated Rydberg electromagnetically-induced transparency (Rydberg–EIT) spectroscopy with discrete instruments combination and with Red Pitaya FPGA module. The results show that the Red Pitaya FPGA module matches discrete instruments combination in stability, being more compact and only one-tenth the cost. Rydberg–TCPS scheme avoids modulation-induced noise and linewidth broadening, outperforming Rydberg–EIT scheme. The Red Pitaya FPGA module provides a cost-effective, compact solution for Rydberg research, lowering experimental barriers.

DOI
10.3390/photonics13020180

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Frequency stability of a 509-nm single-frequency laser, a core component combined with an 852-nm single-frequency laser for two-step cesium Rydberg transitions, is critical for quantum control and metrology precision. Utilizing atomic transition as the absolute reference, we achieved laser frequency locking via modulation-free Rydberg two-color polarization spectroscopy (Rydberg–TCPS) and frequency-modulated Rydberg electromagnetically-induced transparency (Rydberg–EIT) spectroscopy with discrete instruments combination and with Red Pitaya FPGA module. The results show that the Red Pitaya FPGA module matches discrete instruments combination in stability, being more compact and only one-tenth the cost. Rydberg–TCPS scheme avoids modulation-induced noise and linewidth broadening, outperforming Rydberg–EIT scheme. The Red Pitaya FPGA module provides a cost-effective, compact solution for Rydberg research, lowering experimental barriers.
Frequency locking to reference atomic lines using Rydberg electromagnetically induced transparency (EIT) has been recently introduced as an inexpensive and reliable technique for laser frequency stabilization. In this work, we carry out a systematic study of this technique using heterodyne beat spectroscopy. Two different commercial semi-conductor lasers are locked to the same reference frequency using EIT locking, and their relative frequency stability is analyzed and continuously monitored in real time. A substantial improvement in the laser frequency stability is achieved through searching for the optimal proportional–integral settings and EIT probe laser powers. The results show that the cutoff frequency of the beat signal can be lowered to less than 500 kHz. We also compare the frequencies of free running lasers with that of a locked laser and characterize their frequency drifts. This study is important in assessing the use of Rydberg EIT locking in atomic electrometers.
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 demonstrate modulation-free laser stabilization to an atomic Rydberg transition using nonlinear polarization spectroscopy. To stabilize a laser to the upper transition of a three-level ladder scheme, the techniques of standard polarization spectroscopy are adapted to use a narrow, nonlinear coherence feature. We obtain a subnatural linewidth dispersive signal that is directly suitable for laser frequency stabilization. We examine the effect of laser polarization on the dispersive line shape. This technique stabilizes the laser to an absolute frequency reference, can be used with numerous Rydberg levels, and eliminates laser modulation, which can enable high bandwidth feedback.
We have proposed an artificial modulation-free Pound-Drever-Hall (PDH) method for laser frequency stabilization and demonstrated it via two-color polarization spectroscopy of Rydberg electromagnetically induced transparency (EIT) resonance in a room-temperature rubidium vapor. Due to the unique error signal profile, the conventional PDH method owns a large capture range in laser frequency locking. Here we manually construct a PDH error signal via a linear combination of polarization spectroscopies of the Rydberg EIT resonances without and with a magnetic field applied. The artificial modulation-free PDH error signal owns a subnatural linewidth dispersion curve as well as a large capture range with which we successfully stabilize the laser to an absolute atomic frequency reference in a long running time, immune to environmental fluctuation and even manmade impulse perturbation. This method can provide an absolute frequency reference based on atomic transition while keeping similar locking ability to provide corrections for frequency fluctuations over a broad bandwidth as the conventional PDH.
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.
Abstract Electromagnetically induced transparency (EIT) and two‐color polarization spectroscopy (TCPS) with Rydberg atoms are spectroscopic techniques developed based on the interaction between a ladder‐type three‐level atomic system and two light fields. The narrow linewidth and high contrast Rydberg EIT and Rydberg TCPS have important applications in laser frequency stabilization, Rydberg antennas, Rydberg radar and microwave electric fields detection. Here, the EIT and TCPS with cesium Rydberg atoms are investigated using a ladder‐type level system driven by the 509‐nm coupling beam and the 852‐nm probe beam. The 509‐nm coupling beam with three kinds of intensity spatial profile (Laguerre–Gaussian mode, Gaussian mode, Flat‐top mode) is employed one by one in experiments. Due to the different intensity spatial distributions of the three 509‐nm coupling beams, the Autler–Townes (A–T) splitting method is utilized to calibrate the Rabi frequency of the coupling beams. These results show that the linewidth is narrowest when the 509‐nm coupling beam has the Laguerre–Gaussian mode with an equal Rabi frequency among the three cases, the linewidth and contrast of the EIT and TCPS are optimized by varying the beam sizes of the 509‐nm Laguerre–Gaussian beams. The laser frequency stabilization by using of TCPS with three kinds of 509‐nm coupling beams are compared, the Laguerre–Gaussian coupling beam case is more effective for frequency stabilization because of the narrower linewidth.