It is very interesting that after Jerusalem was destroyed as mentioned in the verses above, the land was not desolate because some Jews remained under a governor named Gedaliah who was ironically assassinated by a man named Ismael. It was after this event that the king of Babylon sent the remaining Jews to Babylon and the land began to be actually desolate.
The empty land myth has been debunked here decades ago. Even the post exile additions of Jeremiah 52 and the contradictory addition in 2 Kings 24:14,16 imagine 4-10,000 exiles. The Jewish Encyclopedia many years ago said:
Furthermore, if it be assumed that the total population of the kingdom of Judah was about 120,000 (the figures should probably be somewhat higher, as the country was at that time more densely populated than it is to-day), about one-fourth of the population (according to II Kings xxiv. 16) or, perhaps more correctly, one-eighth (according to Jer. lii. 28-30) was led captive into Babylonia.
Archaeology confirms that the land was continuously inhabited.