According to a study published in the scientific journal, Current Biology, it may very well be possible to learn new information while we are asleep.
The ability to learn a new language while asleep
Despite not being able to carry out new tasks that require use of our motor skills during deep sleep, such as swimming or cooking, language learning was shown to be a possibility.
Scientists from the Institute of Psychology in Bern gave participants of the study headphones to listen to while they slept. During their slumber, words from an artificial language were played, along with their translations into German.
When the second word of a pair was played repeatedly in an 'ascending state,' word-to-meaning association was naturally formed in the brain. Our brain alternates between two phases every half a second or so: active phases or 'ascending states' and passive phases, also called 'descending states.'
External stimuli affects the brain during sleep
The words being uttered in the recordings suggested that 'tofer' meant 'key' and 'guga' meant 'elephant.' Once the participant woke up from their slumber, each and every one of them was able to determine whether 'tofer' or 'guga' referred to larger or smaller objects. Marc Züs, co-author of the study, explained that:
It was particularly interesting to find that language areas and the hippocampus - which normally regulate language learning when we are awake—were also activated when learning vocabulary learned in deep sleep.
It seems that these structures regulate memory formation independently of the state of consciousness we are in—whether unconsciously during sleep, or consciously when we are awake.
Ultimately, what the study found was that when our brain finds itself in an unconscious state, such as during deep sleep, it does not prevent the external world and its stimuli to affect it. This goes against previous widely believed knowledge in sleep research.