Manipulating anyons in quantum Hall droplets of light using dissipations*

Whereas anyons are the building blocks in topological quantum computation, it remains challenging to create and control each anyon individually. Here, we point out that dissipative dynamics in cavities deterministically deliver droplets of light in desired fractional quantum Hall states. In these quantum Hall droplets, both the number and locations of anyons are precisely controllable without requiring extra potentials to imprint and localize such quasiparticles. Using the density profile of light, the anyonic statistics is readily accessible. Moreover, preparing a coherent mixuture of a single-quasihole state and a two-quasihole state establishes a direct readout of the braiding statistics. Our work unfolds a promising route for quantum optics to solve challenging problems in quantum Hall physics.