Learn French: Il a déjà analysé la phase de sommeil. - He has already analyzed the sleep phase.

This is a core rule for French adverb placement! In compound tenses like the passé composé, short or common adverbs (such as déjà, bien, or beaucoup) are placed directly between the conjugated helping verb (a) and the past participle (analysé).

Why does the sentence use de sommeil instead of du sommeil?

When de links two nouns where the second noun simply describes the type, purpose, or category of the first (acting almost like an adjective), we drop the definite article. It is a general "sleep phase", not a phase belonging to a specific sleep, so we use de alone instead of du (which would mean de + le).

Since la phase is feminine, shouldn't analysé have an extra "e" at the end?

No, because the helping verb is avoir. In the passé composé with avoir, the past participle only agrees with the direct object if that object is placed before the verb. Since the direct object (la phase de sommeil) comes after the verb here, analysé stays in its default masculine singular form.

Where would I put the negative words to say "He hasn't yet analyzed"?