fast(of sleeping: deeply or soundly) adverb [UK: fɑːst] [US: ˈfæst]My husband and daughter are fast asleep. = Mio marito e mia figlia dormono profondamente.
profoundly(in a profound manner) adverb [UK: prə.ˈfaʊnd.li] [US: proˈfaʊnd.li]John slept profoundly. = John dormiva profondamente.