  We show theoretically that strong electron coupling to circularly polarized
photons in non-singly-connected nanostructures results in the appearance of an
artificial gauge field that changes the electron phase. The effect arises from
the breaking of time-reversal symmetry and is analogous to the well-known
Aharonov-Bohm phase effect. It can manifest itself in the oscillations of
conductance as a function of the intensity and frequency of the illumination.
The theory of the effect is elaborated for mesoscopic rings in both ballistic
and diffusive regimes.
