We have simultaneously to travel forward to the year 2660 and back into the early history of science fiction to find this word. It was invented by Hugo Gernsback, whom many regard — for better or worse — as the founder of the modern genre. (He is commemorated in the Hugo Awards, one of SF’s annual prizes.)
In 1908, Gernsback started publishing his science-based stories in his magazine Modern Electrics (for which he coined the term scientifiction that has thankfully not survived). In 1911-12 he wrote and published a serial with the snappy title Ralph 124C 41+, set 750 years in the future. The personage of the title was "one of the greatest living scientists and one of ten men on the whole planet earth permitted to use the Plus sign after his name".
The writing was appalling and the plot mundane — Ralph falls in love with a beautiful young woman and saves her from the clutches of an evil fellow scientist — but as part of the story, Gernsback has him invent a remarkable device: "It remained to Ralph, however, to perfect the Hypnobioscope, which transmitted words direct to the sleeping brain in such a manner that everything could be remembered in detail the next morning. This was made possible by having the impulses act directly and steadily on the brain. For thousands of years humanity had wasted half of its life during sleep — the negative life."
This was the first reference in print to the idea that several decades later became known as sleep learning or hypnopaedia (Greek hupnos, sleep, plus paideia, education; the term was first used by Aldous Huxley in Brave New World in 1932). These have necessarily been tried using the indirect method of playing recordings to people while they were asleep, since even now we don’t know how to beam information directly into the brain, a failure which has rendered hypnopaedia less than fully effective.