  We show that bosonic fields may present anyonic behavior when interacting
with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished
via the interaction of a two-level system with two quantized modes of a
harmonic oscillator; under suitable conditions, the system acquires a
fractional geometric phase. A crucial role is played by the entanglement of the
system eigenstates, which provides a two-dimensional confinement in the
effective evolution of the system, leading to the anyonic behavior. For a
particular choice of parameters, we show that it is possible to transmute the
statistics of the system continually from fermions to bosons. We also present
an experimental proposal, in an ion-trap setup, in which fractional statistical
features can be generated, controlled, and measured.
