Abstract
We present a scheme for comparing effective path-lengths through a spatial region by using multipath generalizations of a Mach–Zehnder interferometer. This enables us to identify paths that have different lengths from the others with exponentially fewer measurements than would be required by repeated measurements with a standard two-path interferometer. We show that this scheme is extremely sensitive to small variations in the paths, which means it could be used to measure the variance of the path-lengths accurately and efficiently. Possible applications include accurately measuring spatial variations of potential fields and efficiently identifying which of many cavities contains an atom.
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