  In quantum mechanics, collisions between two particles are captured by a
scattering matrix which describes the transfer from an initial entrance state
to an outgoing final state. Analyticity of the elements of this $S$-matrix
enables their continuation onto the complex energy plane and opens up a
powerful and widely used framework in scattering theory, where bound states and
scattering resonances for a physical system are ascribed to $S$-matrix poles.
In the Gedankenexperiment of gradually changing the potential parameters of the
system, the complex energy poles will begin to move, and in their ensuing flow,
two poles approaching will interact. An actual observation of this intriguing
interaction between scattering poles in a collision experiment has, however,
been elusive. Here, we expose the interplay between two scattering poles
relating to a shape resonance and a magnetically tunable Feshbach resonance by
studying ultracold atoms with a laser-based collider. We exploit the tunability
of the Feshbach resonance to observe a compelling avoided crossing of the poles
in their energies which is the hallmark of a strongly coupled system.
