Experimental subdiffraction source discrimination enabled by spatial demultiplexing and single-photon detectors

Abstract: We experimentally demonstrate a universal, parameter-independent test for asymmetric source discrimination. The test allows us to discriminate faint sources well beyond the diffraction limit by exploiting spatial mode demultiplexing (SPADE) and single-photon detectors. Our test yields a rate of false negatives well below what can be achieved by diffraction-limited direct imaging. Our tabletop experimental setup is inspired by the problem of exoplanet detection, where one aims at detecting the presence of a faint source in the proximity of a brighter one. We present a complete theory, modelling arbitrary modal crosstalk, and collect data across a range of values for the source separations and intensity ratios. We show that SPADE retains an advantage over direct imaging in the relevant regime of small separations and low intensity ratios. Remarkably, we identify an experimentally accessible crosstalk threshold $C_{\mathrm{th}}\simeq 0.1$ below which the exponential rate of false negatives stays well below that of direct imaging. For example, for crosstalk of $10^{-2}$, SPADE needs up to one order of magnitude fewer photons than direct imaging to achieve the same error rate. These results demonstrate that SPADE offers an effective methodology for subdiffraction asymmetric hypothesis testing, under realistic imperfections and crosstalk, paving the way to photon-starved imaging tasks.