This is the famous outdoor staircase of “The Exorcist” horror movie (1973, William Friedkin), in Georgetown. It connects Prospect Street with Canal Road, near the Potomac river.
The movie is an adaptation of a novel by William Peter Blatty, who studied in Georgetown University which is just a few blocks away.
For the full story, read this article of USA today : http://www.usatoday.com/story/life/movies/2013/10/07/exorcist-40th-anniversary/2764565/
You can also watch the scene on Youtube (I love that music): https://m.youtube.com/watch?v=epn1xDLHJkA
Paris - Washington DC 