Efficiently estimating waveforms on a compressive ultracold atom sensor

Quantum waveform estimation is extremely resource-intensive, as each of the many points in a waveform are sampled by a quantum measurement. Current implementations average thousands of measurements, and hence can only sense periodic, or otherwise repeatable, waveforms. This thesis describes the design and construction of a magnetometer, which is made of ultracold atoms, and reduces the required number of quantum measurements using compressive sensing theory. It successfully recovered sparse magnetic waveforms, emulating applications in non-invasive neurosensing.