  The fractional quantum Hall states have long been predicted to be a testing
ground of fractional (anyonic) exchange statistics. These topological states
harbor quasiparticles with fractional charges of both abelian and non-abelian
characters. The quasiparticles' charge is commonly determined by shot noise
measurements (1, 2), and states' statistics can be revealed by appropriately
interfering the quasiparticles. While the multipath Fabry-Perot electronic
interferometer (FPI) is easier to fabricate, it is often plagued by Coulomb
interactions (3), its area breathes with the magnetic field (4), and its bulk's
charges tend to fluctuate (5). Recent FPI experiments employing adequate
screening allowed an observation of Aharonov-Bohm (AB) interference at bulk
filling $\nu$=1/3 (6). In the current work, we chose to employ an
interaction-free, two-path, Mach-Zehnder interferometer (MZI), tuned to bulk
filling $\nu$=2/5. Interfering the outer $\nu$=1/3 mode (with the inner
$\nu$=1/15 mode screening out the bulk), we observed a 'dressed AB'
periodicity, with a combined 'bare AB' flux periodicity of three flux-quanta
(3$\phi_0$) and the 'braiding phase' 2$\pi$/3. This unique interference
resulted with an AB periodicity of a single flux-quantum. Moreover, the
visibility of the interference, $v_{e/3}$, deviated markedly from that of the
electronic one $\it{v}_{e}$, agreeing with the theoretically expected
visibility, $\it{v}_{e/3} \sim {\it{v}_e}^3$. With the two non-equivalent
drains of the MZI, the fractional visibility peaked away from the ubiquitous
transmission-half of the MZI. We provide simple theoretical arguments that
support our results. The MZI proves to be a powerful tool that can be used to
probe further the statistics of more complex anyonic quasiparticles.
