PhD in Statistics working in Physics
Statistics is pretty widely applicable, of course. Some parts of physics deal with large sets of data handled with statistics, I'm sure. It isn't my field, but one of the ways to discover things in large data sets (star maps, etc) is to look for statistical anomalies. I'm sure that, along the way, you would learn a lot of physics in some domain. 

I once worked in math and computing with a geologist who was interested in wave action at the shore. We never went very far (and I was pretty unsophisticated then), but I realized I'd need to learn quite a bit about his domain to help with what he needed to study. 

This sort of career could be carried on at a large university with a number of different disciplines represented or at a research institute focused on an area of physics that interests you. You might need to be able to make a case about how you would fit in, but everyone needs to do that anyway.