Observation of fractional statistics

Our present experiment utilizes a novel Laughlin quasiparticle interferometer, where a quasiparticle with charge $e/3$ of the $f=1/3$ FQH fluid executes a closed path around an island of the $f=2/5$ fluid. The interference fringes are observed as peaks in conductance as a function of the magnetic flux $\Phi $ through the $f=2/5$ island, in a kind of the Aharonov-Bohm effect. A similar situation of resonant tunneling in an FQH fluid at filling $f_1 $ surrounding an FHQ island at a different filling $f_2 $ was considered theoretically by Jain et. al.. We observe the interference pattern shift by one fringe upon introduction of five magnetic flux quanta into the $f=2/5$ island, i.e., the Aharonov-Bohm period $\Delta \Phi =5h/e,$ corresponding to excitation of ten $q=e/5$ quasiparticles of the $f=2/5$ fluid. Such ``superperiod'' of $\Delta \Phi >h/e$ has never been reported before. This $\Delta Q=2e$ charge period is directly confirmed in calibrated backgate experiments. These observations imply \textit{relative} statistics of $\Theta _{2/5}^{1/3} =-1/15$, when a charge $e/3$, statistics $\Theta _{1/3}^ =2/3$ Laughlin quasiparticle encircles one $e/5$, $\Theta _{2/5}^ =2/5$ quasiparticle of the $f=2/5$ fluid.