  We propose a protocol to locally detect the Berry curvature of a three
terminal Josephson junction with a quantum dot based on a synchronic detection
when an AC modulation is applied in the device. This local gauge invariant
quantity is expressed in terms of the instantaneous Green function of the
Bogoliubov-de Gennes Hamiltonian. We analyze the contribution to the Berry
curvature from both the quasi-particle excitations and the Andreev bound state
levels by introducing an effective low-energy model. In addition, we propose to
induce topological properties in the junction by breaking time-reversal
symmetry with a microwave field in the non-resonant regime. In the last case,
the Floquet-Andreev levels are the ones that determine the topological
structure of the junction, which is formally equivalent to a 2D-honeycomb
Haldane lattice. A relation between the Floquet Berry curvature and the
transconductance of the driven system is derived.
