Many-body Josephson diode effect in superconducting quantum interferometers

We propose a many-body mechanism for a strong Josephson diode effect (JDE) in an interacting nanoscale SQUID formed by two parallel quantum dots coupled to superconducting leads. Unlike conventional diode behavior, where nonreciprocity originates from a skewed current-phase relation within a single, continuously evolving ground state, the JDE reported here is \emph{branch selected}: the positive and negative critical currents are optimized on different many-body branches across the $0$-$\pi$ phase boundary, yielding a substantial enhancement of the diode efficiency. We further show that a \emph{nonlocal} Cooper-pair tunneling channel, which binds the two electrons on different arms, is essential: it reshapes the $0$-$\pi$ boundary and produces a pronounced ``diode band'' in parameter space, in sharp contrast to the fragile hotspot obtained when only local Cooper-pair transfer is available. While the key physics is captured by an effective model in the superconducting atomic limit, our conclusions remain robust for realistic finite-gap devices, as demonstrated within a generalized atomic-limit framework.