taru-adjective, adverb taking the 'to' particle
fast asleep; sound asleep; dead to the world
Describes a state of deep, oblivious sleep. Often used in literary or descriptive contexts with the particle と.
彼は疲れていたので、昏々と眠り続けた。
He was so tired that he slept soundly on and on.
赤ん坊は昏々と眠っていて、物音にも気づかなかった。
The baby was fast asleep and didn't notice any noise.
熟睡 is a noun/suru-verb meaning deep sleep, more clinical and neutral; 昏々 carries a more descriptive, almost poetic nuance.
Reduplication of 昏 (こん, 'dark, dim'), emphasizing a state of deep unconsciousness akin to darkness. The exact historical derivation is uncertain.