07/03/2013 AT 01:10 PM EDT
Henry Cavill and Kaley Cuoco's new romance is heating up – even if it's just to burn calories.
The new couple
squeezed in some one-on-one time together in Los Angeles this week.
The Man of Steel
star, 30, and The Big Bang Theory
's leading lady, 27, went on a hike, followed by a stop for sushi near Cuoco's Sherman Oaks, Calif., home.
Both wearing caps and fitness attire, the duo strolled casually side-by-side when they were photographed mid-workout.
"They were both single and started dating recently," a source told PEOPLE on Monday, of the actress and Cavill – who split from Fast & Furious 6
star Gina Carano in early May.