  A new type of cold/ultracold neutron detector that can realize a spatial
resolution of less than 100 nm was developed using nuclear emulsion. The
detector consists of a fine-grained nuclear emulsion coating and a 50-nm thick
$^{10}$B$_4$C layer for the neutron conversion. The detector was exposed to
cold and ultracold neutrons (UCNs) at the J-PARC. Detection efficiencies were
measured as (0.16$\pm$0.02)% and (12$\pm$2)% for cold and ultracold neutrons
consistently with the $^{10}$B content in the converter. Positions of
individual neutrons can be determined by observing secondary particle tracks
recorded in the nuclear emulsion. The spatial resolution of incident neutrons
were found to be in the range of 11-99 nm in the angle region of tan$\theta\leq
1.9$, where $\theta$ is the angle between a recorded track and the normal
direction of the converter layer. The achieved spatial resolution corresponds
to the improvement of one or two orders of magnitude compared with conventional
techniques and it is comparable with the wavelength of UCNs.
