Four teams (Arkansas, Boston College, North Carolina, and Wisconsin) have each been ranked #1 exactly once so they each obviously have a one week stay.
I was curious about these so I looked them up:
Arkansas:The Razorbacks were #6 in the 1965 preseason poll. This was during the short-lived 10-team era (1961-1967). They won their first four games (OkSU, Tulsa, TCU, Baylor) and climbed to #3 in the October 11, 1965 poll which set them up for a humongous game against #1 Texas on October 16, 1965. Arkansas won that and leapfrogged #2 Nebraska to move to #1 in the October 18, 1965 poll.
The Razorbacks didn't lose the #1 spot by losing. In their one-and-only game as #1, they beat North Texas 55-20 but N. TX was an unranked 1-4 team. That same day #2 Michigan State beat #6 Purdue in West Lafayette and the Spartans leapfrogged Arkansas to claim the #1 spot. Arkansas remained at #2 until they lost the Cotton Bowl to LSU and dropped to #3 in the final poll.
Boston College:In 1942 the first poll was not until October 12 when most teams had already played three or four games. The Eagles were 2-0 with wins over WVU and Clemson and were #11 in the first poll of 1942. They continued winning and climbed to #3 in the November 9 and November 16 polls then ascended to #1 in the November 23 poll compliments of a road win by unranked Auburn over #1 Georgia.
In their one-and-only game as the #1 team, Boston College got obliterated by Holy Cross, 55-12. That dropped them to #8.
North Carolina:The Tar Heels were 2-0 and #2 in the first poll of 1948 (October 4) but it was REALLY close. Notre Dame was #1 with 50 first place votes and 1,200 points while UNC was #2 with 55 first place votes and 1,190 points. Both teams won that weekend (ND 26-7 vs MSU, UNC 28-6 at Wake) and apparently UNC's win was more impressive because the Tar Heels were #1 in the October 11, 1948 poll.
Like Arkansas, the Tar Heels didn't lose the #1 spot by losing. On October 16, 1948 they beat NCST at home 14-0 but they got leapfrogged by both Michigan (beat #3 NU 28-0) and Notre Dame (beat UNL 44-13 on the road).
Wisconsin:The Badgers were #7 in the 1952 preseason poll and dropped to #8 on September 29. That weekend they beat #2 Illinois and jumped all the way up to #1 in the October 6, 1952 poll. Unfortunately for Wisconsin their next game was in Columbus where they lost 23-14 to Ohio State in Wisconsin's one-and-only game as #1.