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$thetaleq 1.9$, 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.
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