Frequency stabilization of quantum-cascade lasers by use of optical cavities

We report a heterodyne beat with a linewidth of $5.6\pm 0.6 \mathrm{Hz}$ between two cavity-stabilized quantum-cascade lasers operating at $8.5 \mathit{\mu }\mathrm{m}$. We also present a technique for measuring this beat that avoids the need for extreme isolation of the optical cavities from the environment, that of employing a third servo loop with low bandwidth to force one cavity to track the slow drifts and low-frequency fluctuations of the other. Although it is not fully independent, this technique greatly facilitates heterodyne beat measurements for evaluating the performance of cavity-locked lasers above the bandwidth of the third loop.