Selective braiding of different anyons in the even-denominator fractional quantum Hall effect

Even-denominator quantum Hall states can host several types of anyons with distinct exchange statistics. Depending on the anyon type, exchanging two quasiparticles can impart a phase to the many-body wave function or even transform it into a different state. Here, we realize a gate-tunable Fabry-P\'erot interferometer with an embedded antidot that provides local control over the number of anyons within the interference loop. By independently tuning the magnetic field, carrier densities across the device, and the antidot potential, we access regimes in which localized anyons form reproducibly and measure the associated statistical phases $e^{i \theta_\mathrm{braid}}$. We resolve braiding phases of $\theta_{\mathrm{braid}}=\pi$ and $\theta_{\mathrm{braid}}=\frac{\pi}{2}$, which we attribute to $e/2$ quasiparticles encircling either $e/2$ or $e/4$ quasiparticles, respectively. We further observe switching between different anyon occupancies of the antidot over time, directly resolving individual anyon tunnelling events into the interference loop. Similar behavior occurs at filling factor one third. Our work addresses one of the two key challenges in observing non-Abelian braiding, which requires control of both localized and interfering anyon types.