Double-heterodyne probing for ultra-stable laser based on spectral hole burning in a rare-earth doped crystal

We present an experimental technique for realizing a specific absorption spectral pattern in a rare-earth-doped crystal at cryogenic temperatures. This pattern is subsequently probed on two spectral channels simultaneously, thereby producing an error signal allowing frequency locking of a laser on the said spectral pattern. Appropriate combination of the two channels leads to a substantial reduction of the detection noise, paving the way to realizing an ultra-stable laser for which the detection noise can be made arbitrarily low when using multiple channels. We use such technique to realize a laser with a frequency instability of $1.7\times 10^{-15}$ at 1 second, not limited by the detection noise but by environmental perturbation of the crystal. This is comparable with the lowest instability demonstrated at 1 second to date for rare-earth doped crystal stabilized lasers.