Formal association with a dissertation adviser normally begins in the third or fourth term after the qualifying examination has been passed and after most required course work has been completed. It is best though to start exploring possible advisors in your first year at Yale. An adviser from a department other than Physics can be chosen in consultation with the DGS, provided the dissertation topic is deemed suitable for a physics PhD.
It is up to you to seek out faculty and talk to them no later than your third term (if not earlier) to discuss your interest and possibilities of collaborating. It is up to you to be proactive in seeking out a mentor because the Department does not “provide” a mentor for you and there is no guarantee that a particular mentor will have an opening (and research funding) available at the time you are ready to begin research. Hence it is imperative that you explore different advising opportunities within a subfield and perhaps even more than one subfield of physics.