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

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.