Quantum interferometric measurements of temperature

We provide a detailed description of the quantum interferometric thermometer, which is a device that estimates the temperature of a sample from the measurements of the optical phase. We rigorously analyze the operation of such a device by studying the interaction of the optical probe system prepared in a single-mode Gaussian state with a heated sample modeled as a dissipative thermal reservoir. We find that this approach to thermometry is capable of measuring the temperature of a sample in the nanokelvin regime. Furthermore, we compare the fundamental precision of quantum interferometric thermometers with the theoretical precision offered by the classical idealized pyrometers, which infer the temperature from a measurement of the total thermal radiation emitted by the sample. We find that the interferometric thermometer provides a superior performance in temperature sensing even when compared with this idealized pyrometer. We predict that interferometric thermometers will prove useful for ultraprecise temperature sensing and stabilization of quantum optical experiments based on the nonlinear crystals and atomic vapors.