Was the Ark of the Covenant taken to Babylon?

This text is from a letter written by David Gooding in 1994.

We are nowhere told whether Nebuchadnezzar took the ark to Babylon or not. It is reported that, when the Roman general Pompey entered the temple in 63 BC, he found no ark inside, only a large stone.

One wonders, of course, if that was still so in Herod's temple, and if it was, how the high priest could carry out all the necessary functions of the Day of Atonement, if there was no ark in the most holy place when he entered with the blood of the atonement.

Yours very sincerely,