Noise Limits in Differential Atom Interferometry 

Differential interferometry is a common technique in which two interferometers are used to characterize signals having a fluctuating common phase that is not important, but a constant differential phase that is of interest. One way to extract the differential phase is to plot the two signals as points in a plane, which produces an elliptical shape. The eccentricity of the ellipse is determined by the differential phase. Uncertainty in the extracted phase can arise both from noise in the data and from the finite number of data points used. The noise sensitivity also depends on the value of the differential phase itself. We compare the sensitivities of algebraic, geometric, and Bayesian fitting methods, and we also discuss a novel “reciprocal” technique that offers some performance advantages. In general, we find that it is possible to approach the standard quantum limit at a differential phase of 90 degrees, but that the performance of different methods varies when the phase differs from this optimal value.