  Berry's geometric phase naturally appears when a quantum system is driven by
an external field whose parameters are slowly and cyclically changed. A
variation in the coupling between the system and the external field can also
give rise to a geometric phase, even when the field is in the vacuum state or
any other Fock state. Here we demonstrate the appearance of a vacuum-induced
Berry phase in an artificial atom, a superconducting transmon, interacting with
a single mode of a microwave cavity. As we vary the phase of the interaction,
the artificial atom acquires a geometric phase determined by the path traced
out in the combined Hilbert space of the atom and the quantum field. Our
ability to control this phase opens new possibilities for the geometric
manipulation of atom-cavity systems also in the context of quantum information
processing.
