Searching for stochastic background of ultra-light fields with atomic sensors

We propose a cross-correlation method for the searches of ultra-light fields, in particular, with a space network of atomic sensors. The main motivation of the approach is cancellation of uncorrelated noises in the observation data and unique pattern the fields leave on the cross-spectrum, depending on their nature (i.e., scalar, vector or tensor). In particular, we analytically derive a dependence of the cross-spectrum on the angle between two pairs of detectors. We then confirm obtained angular curves with a numerical simulation. We imply application of the method to the detection of dark matter and gravitational waves.