Optimization of polarization spectroscopy signal for laser-frequency stabilization

We experimentally generate polarization spectroscopy (error) signals corresponding to the D 2 -line hyperfine transitions, F g = 2 → F e = 1 , 2 , 3 of 87 Rb, and F g = 3 → F e = 2 , 3 , 4 of 85 Rb, and show that the strongest error signals correspond to the closed hyperfine transitions (oscillator strength ∼ 0.7 ), F g = 2 → F e = 3 and F g = 3 → F e = 4 , respectively. We make the generated error signal robust to fluctuations in external parameters by finding optimum values for the vapor cell temperature and pump-probe intensities at two different beam diameters. We further employ these optimized error signals to directly (without the need for frequency/phase modulation) lock the laser frequency—reducing the rms drift/linewidth from ∼ 10 MHz to < 500 kHz, when measured over a ∼ 60 min duration. In addition, by comparing theoretically calculated and experimentally measured error signals for the pump intensities ranging from ∼ 0.1 I sat 0 − 10 I sat 0 (where, I sat 0 ∼ 1.6 mW cm −2 is the two-level saturation intensity for the Rb D 2 -line transitions), we discuss the applicability and limitations of existing numerical and analytical approaches based on a full multi-level rate equation model for polarization spectroscopy.