In 2006, Australian sleep researcher Chin Moi Chow of the University of Sydney, studied fifteen normal sleepers for four consecutive days (to establish a baseline, they were on a conventional diet for the first day). She found that moving from a conventional diet to an Atkins diet quickly produced a two-and-a-half fold increase in the number of dreams recalled. Most of the dreams were unpleasant, but not nightmares. The change of diet was associated with the volunteers sleeping more deeply but waking more frequently.
In 2007, a physician who had recorded his sleep history for 66 years and had been on the Atkins diet for eight weeks, reported that bad dreams had increased from about once a month before the diet to every night and even during naps. He persisted with the diet because he felt the physical benefits outweighed this unpleasant side effect. He became aware of the following study, but whether it subconsciously affected him, I do not know.