There is a detailed account given of the items taken to Babylon from the "king's house" and the "house of the Lord" in 2 Kings 24:13, 2 Kings 25:13-18, and Jeremiah 52:17-23 but the Ark is not mentioned. Nor is it mentioned in the lists of things brought back from Babylon in Ezra 1:7-1:11. Clearly the ark was never removed.
But an answer to the location of the ark can be found in the following,
2 Baruch 6:1-10 "And it came to pass on the morrow that, lo! the army of the Chaldees surrounded the city, and at the time of the evening, I, Baruch, left the people, and I went forth and stood by the oak. And I was grieving over Zion, and lamenting over the captivity which had come upon the people. And lo! suddenly a strong spirit raised me, and bore me aloft over the wall of Jerusalem. And I beheld, and lo! four angels standing at the four corners of the city, each of them holding a torch of fire in his hands. And another angel began to descend from heaven. and said unto them: 'Hold your lamps, and do not light them till I tell you. For I am first sent to speak a word to the earth, and to place in it what the Lord the Most High has commanded me.' And I saw him descend into the Holy of Holies, and take from there the veil, and holy ark, and the mercy-seat, and the two tables, and the holy raiment of the priests, and the altar of incense, and the forty-eight precious stones, wherewith the priest was adorned and all the holy vessels of the tabernacle. And he spoke to the earth with a loud voice: 'Earth, earth, earth, hear the word of the mighty God, And receive what I commit to you, And guard them until the last times, So that, when you are ordered, you may restore them, So that strangers may not get possession of them. For the time comes when Jerusalem also will be delivered for a time, Until it is said, that it is again restored for ever.' And the earth opened its mouth and swallowed them up."
The Second Book of the Maccabees 2:4-8 "It was also contained in the same writing, that the prophet, being warned of God, commanded the tabernacle and the ark to go with him, as he went forth into the mountain, where Moses climbed up, and saw the heritage of God. And when Jeremy came thither, he found an hollow cave, wherein he laid the tabernacle, and the ark, and the altar of incense, and so stopped the door. And some of those that followed him came to mark the way, but they could not find it. Which when Jeremy perceived, he blamed them, saying, As for that place, it shall be unknown until the time that God gather his people again together, and receive them unto mercy. Then shall the Lord shew them these things, and the glory of the Lord shall appear, and the cloud also, as it was shewed under Moses, and as when Solomon desired that the place might be honourably sanctified."
The Israeli government admits that they know of a cavern beneath the temple mount, and how to access it, but refuse to for fear of an Arab uprising should they do so.
There can be no doubt that the items are indeed below the temple mount.
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