Single step zero-thermal-expansion temperature measurement of optical reference cavities

State-of-the-art laser frequency stability has been pushed to the 10^-17 level. The laser reference cavity is typically nested in a multi-layer thermal enclosure to increase vacuum thermal time constant and thermally controlled at the zero-thermal-expansion temperature to reduce the external temperature fluctuation effect. It is rather time consuming to accurately determine the zero-thermal-expansion temperature for a large thermal time constant system. Here we develop a fast method for measuring the zero-thermal-expansion temperature of the cavity by relying on just one single temperature scan. We first develop a theoretical model to predict the performance of the laser locked to the reference cavity, and then construct an evaluation system for verification of the model. The zero-thermal-expansion temperature of a 30-cm cavity is measured to be 4.3±0.5 °C. The fast and high precision method for determining the zero-thermal-expansion temperature will be valuable in improving long-term frequency stabilities of cavity stabilized lasers.