Has there ever been an atheist President?

A recent profile in the New Yorker claimed that if elected, Mitt Romney "would arguable be the most actively religious President in American history". Has religiosity always been an necessary trait of US presidents?

Slate argues that Jimmy Carter (1977-1981) was probably the most religious "It’s impossible to know the contents of a man’s heart, but historians who study the religious lives of the presidents point again and again to the words and deeds of James Earl Carter Jr, " writes Forrest Wickman. "The Georgia Baptist set a new standard during his 1976 presidential campaign when he described himself as “born again,” and he was frank about his religious beliefs throughout his presidency. While in office, Carter attended church wherever he went, even while on the road, and continued to teach Sunday school when at home."

But what about the non-believers? Thomas Jefferson (1801-1809) reportedly called the Book of Revelation the "ravings of a maniac" but Slate says the title of most atheistic President is a toss up between James Monroe (1817-1825) and Ulysses S. Grant (1869 - 1877), pictured, who "seems to have refused to ever profess his faith, even when a bishop of his wife's Methodist denomination pressed him on his deathbed."