From Longman Dictionary of Contemporary Englishsleep deeplysleep deeplyto be in a deep sleep, from which it is hard to wake up → deeply
Examples from the Corpus
sleep deeply• Stephen settled on his back and slept deeply.• She felt numb and tired and surprised herself by managing to sleep deeply and well.• He slept deeply and when he awoke he was refreshed.• Lily at his side was sleeping deeply, breathing softly.• One man slept deeply, the other lightly and Aicha not at all.• Now and again he would reach a hand over to the boy but he slept deeply through the night.• He slept deeply until around 9.30, when he arose, breakfasted, and took his children out for a walk.• After three doses, she slept deeply, waking intermittently during the night only to urinate. 