Quantum-Limited Spectroscopy

Abstract: Spectroscopy has an illustrious history delivering serendipitous discoveries and providing a stringent testbed for new physical predictions, including applications from trace materials detection, to understanding the atmospheres of stars and planets, and even constraining cosmological models. Reaching fundamental-noise limits permits optimal extraction of spectroscopic information from an absorption measurement. Here we demonstrate a quantum-limited spectrometer that delivers high-precision measurements of the absorption lineshape. These measurements yield a ten-fold improvement in the accuracy of the excited-state (6P$_{1/2}$) hyperfine splitting in Cs, and reveals a breakdown in the well-known Voigt spectral profile. We develop a theoretical model that accounts for this breakdown, explaining the observations to within the shot-noise limit. Our model enables us to infer the thermal velocity-dispersion of the Cs vapour with an uncertainty of 35ppm within an hour. This allows us to determine a value for Boltzmann's constant with a precision of 6ppm, and an uncertainty of 71ppm.