  Photon number resolving (PNR) measurements are beneficial or even necessary
for many applications in quantum optics. Unfortunately, PNR detectors are
usually large, slow, expensive, and difficult to operate. However, if the input
signal is multiplexed, photon "click" detectors, that lack an intrinsic photon
number resolving capability, can still be used to realize photon number
resolution. Here, we investigate the operation of a single click detector,
together with a storage line with tunable outcoupling. Using adaptive feedback
to adjust the storage outcoupling rate, the dynamic range of the detector can
in certain situations be extended by up to an order of magnitude relative to a
purely passive setup. An adaptive approach can thus allow for photon number
variance below the quantum shot noise limit under a wider range of conditions
than using a passive multiplexing approach. This can enable applications in
quantum enhanced metrology and quantum computing.
