Characterization of electrical noise limits in ultra-stable laser systems

We demonstrate thermal noise limited and shot noise limited performance of ultra-stable diode laser systems. The measured heterodyne beat linewidth between such two independent diode lasers reaches 0.74 Hz. The frequency instability of one single laser approaches 1.0 × 10^-15 for averaging time between 0.3 s and 10 s, which is close to the thermal noise limit of the reference cavity. Taking advantage of these two ultra-stable laser systems, we systematically investigate the ultimate electrical noise contributions, and derive expressions for the closed-loop spectral density of laser frequency noise. The measured power spectral density of the beat frequency is compared with the theoretically calculated closed-loop spectral density of the laser frequency noise, and they agree very well. It illustrates the power and generality of the derived closed-loop spectral density formula of the laser frequency noise. Our result demonstrates that a 10^-17 level locking in a wide frequency range is feasible with careful design.