'Oppenheimer': Meet the Star-Studded Cast of Christopher Nolan's Atomic Bomb Epic (Exclusive Photo)

When Christopher Nolan embarks on a new project, Hollywood's A-list wants in.

His latest epic undertaking, Oppenheimer, based on the Pulitzer Prize-winning biography American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer, attracted one of the starriest casts the Oscar-nominated director has ever assembled, headlined by Cillian Murphy, Emily Blunt, Matt Damon, Florence Pugh and Robert Downey Jr.

The biopic follows J. Robert Oppenheimer, played by Murphy, the scientist who famously led the Manhattan Project — the effort to create an atomic bomb during World War II.

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Blunt stars as Oppenheimer's wife Kitty; Damon portrays Lt. Gen. Leslie Groves, who oversaw the construction of the Pentagon and directed the Manhattan Project; Downey Jr. plays Lewis Strauss, who served two terms on the U.S. Atomic Energy Commission; and Pugh stands out in several scenes as Oppenheimer's mistress.

In a group interview with PEOPLE, Blunt equated filming the movie with the sprawling cast in New Mexico to being at "summer camp."

"We were all in the same hotel in the middle of the New Mexican desert," she recalls. "We only had each other. Me and Matt were roommates and we were like, 'Let's go to have dinner.' "

Sadly for Murphy, he rarely got to join in on the fun due to the daunting task of leading Nolan's film.

"The sheer volume of what he had to take on and shoulder is so monumental," marvels Blunt. "Of course he didn't want to come and have dinner with us." Damon agrees, saying, "He couldn't. His brain was just too full."

Adds Murphy, "You know that when you have those big roles, that responsibility, you feel it's kind of overwhelming."

Oppenheimer will hit theaters on July 21. Moviegoers can see it on standard and IMAX screens.