1D anyons infographic

In three dimensions (plus one time dimension), particles do not cross paths (or braid) when exchanging places, as their trajectories through time can easily be unwound – this is topologically equivalent to doing nothing. As such, the exchange operator, denoted here as \(\hat{P}\), is either plus or minus the original state (or wavefunction, \(\psi\)); a boson or a fermion respectively. In 1D, there is no room for the trajectories to wiggle around one another through time — they must cross, and as such the exchange operator depends on the twists and turns of the path, here operationalized as \(\alpha\). Excitingly, the researchers have found the experimental recipe for directly influencing \(\alpha\), allowing researchers control over how bosonic or fermionic the 1D particle is.