Jim, yes the detached company was Cochran's Louisiana company, which eventually rejoined the 2nd Arkansas Cavalry, probably about the time that Captain Cochran was promoted to lieutenant-colonel, July 1864. I'm pretty sure it was after May 1864, because during that month a report of officers present for duty in the Trans-Mississippi Department doesn't list Cochran, though it does mention many other officers of Slemons' regiment.

Art Bergeron knows "all things Louisiana" and may have additional information.