The word appears as an adverb. Only "deeply" should be used.

Yan, this is a good question. I agree with you that it is better to use "deep" here (as adverb). "Deep" can be an adjective or an adjective (or even a noun). For instances where the meaning is "penetrate", we usually use "deep". See these examples from the Oxford Dictionary: "The peroxide, he says, wouldn't penetrate very deep beneath the surface." "Some short trails lead to viewpoints; longer and more difficult trails penetrate deep into the forest and wilderness."

In English, words with the -ly ending are used as adverbs. However, as Ben pointed out, deep is listed in the dictionary as both an adjective and adverb. Deeply is listed only as an adverb. I think both deep and deeply would be correct in your example sentence, and I think both sound equally well.