I would say rapt is an equivalent in English.
totally absorbed; engrossed; spellbound, esp through or as if through
emotion: rapt with wonder.
transported with emotion; enraptured.
The etymology of the word gives us a hint also:
late 14c., "carried away in an ecstatic trance," from Latin raptus, past participle of rapere "seize, carry off". A figurative sense, the notion is of "carried up into Heaven (bodily or in a dream)," as in a saint's vision.
As you mentioned poetry; rapt, rapture and enrapt are used in this sense with a bit of religious connotations in British romantic poetry also. And even the rapture itself is a feeling in poetry. You can also see this usage in the poetic style works of Shakespeare.
From the book "The Cambridge Introduction to British Romantic Poetry" By Michael Ferber:
Note: You can read further about how it is used in poems from page 24 and on.
From the book "Shakespeare's Poetic Styles: Verse Into Drama" By John Baxter:
Shakespeare also used enrapt in his work Troilus and Cressida to mean "seized by prophetic ecstasy.":
Come, Hector, come, go back:
Thy wife hath dream'd; thy mother hath had visions;
Cassandra doth foresee; and I myself
Am like a prophet suddenly enrapt
To tell thee that this day is ominous:
Therefore, come back.
Also, mast is directly used in Sufism:
In Sufi philosophy, a mast (pronounced "must") is a person who is overcome with love for God, with concomitant external disorientation resembling intoxication. The word originates from the Sufi term mast-Allah meaning "intoxicated with God." from Persian mast, lit. "intoxicated." Another interpretation of its origin is that it is derived from masti, a Persian word meaning "overpowered."