The aim of this project was to develop a quantum sensing protocol that can retrieve information such as amplitudes and phases of different frequency components of a signal. When exposing a cold atom cloud to an external signal the quantum state the cloud is in will undergo a Landau-Zener transition when a sweeping bias field goes through resonance with the signal. This transition follows a simple pattern for one frequency but becomes much more complicated when the signal has multiple dominant frequency components.
The protocol developed utilises quantum sensors to identify the dominant frequency components of an unknown signal. The transition made by the quantum state can be described, when the signal is considered small, by an inner product of a chirp defined by the bias field and the signal itself. If the chirp is changed slightly for a set of different atom clouds, the output of multiple measurements can be viewed as a convolution between the signal and a chirp. This preserves frequency components that are swept over by the bias field, creating a bandpass filter effect so only the frequencies in the tone within the frequency range that was swept by the bias field are kept in the output.
To retrieve the frequencies the protocol makes use of compressive sensing techniques to minimise the number of quantum sensors required. Once the frequencies are identified, the previous protocol is employed to find the amplitude of each of the dominant frequency components. This in essence is a quantum spectrum analyser. The protocol can take an unknown signal and identify its dominant frequency components and their amplitudes.