  Synthetic anyons can be implemented in a noninteracting many-body system, by
using specially tailored localized (physical) probes, which supply the demanded
nontrivial topology in the system. We consider the Hamiltonian for
noninteracting electrons in two-dimensions (2D), in a uniform magnetic field,
where the probes are external solenoids with a magnetic flux that is a fraction
of the flux quantum. The Hamiltonian could also be implemented in an ultracold
(fermionic) atomic gas in 2D, in a uniform synthetic magnetic field, where the
probes are lasers giving rise to synthetic solenoid gauge potentials. We find
analytically and numerically the ground state of this system when only the
lowest Landau level states are occupied. It is shown that the ground state is
anyonic in the coordinates of the probes. We show that these synthetic anyons
cannot be considered as emergent quasiparticles. The fusion rules of synthetic
anyons are discussed for different microscopic realizations of the fusion
process.
