Quantum spectral analysis by Landau-Zener transitions

Spectral analysis is a fundamental concept in science and mathematics, and spectrum analysers are essential tools in scientific research and engineering. This thesis presents a quantum spectrum analyser which uses a microscopic cloud of ultracold atoms to sense sparse spectra in a single experimental shot. Linearly sweeping a radiofrequency amplitude drives Landau-Zener transitions with unique structure depending on the amplitude, frequency and phase of a harmonic signal. A Faraday interface makes a continuous and minimally-destructive measurement of the evolution and multiparameter estimation retrieves the signal parameters. This sensor may enable chemical NMR measurements of individual biological cells.