Anyon fusion spaces with polar molecules

We derive an infinite family of equivalences between fusion-tree Hilbert spaces of certain su(2) level-k anyons and atomic ladders constrained by an excitation blockade. The level-3 case reduces to the well-known equivalence between the Hilbert space of a blockaded atomic chain and fusion trees of Fibonacci anyons [1]. These equivalences provide physical realizations of anyonic Hilbert spaces, on top of which one can construct anyonic Hamiltonians and height models. We show how to simulate the level-4 chain using ultracold polar molecules in optical lattices by employing two novel capabilities of molecules which are not widely appreciated. Our work paves the way for new directions with ultracold polar molecules that are highly relevant in burgeoning experimental efforts [2].

Keywords: 06.01.04 Non-Equilibrium Physics with Cold Atoms and Molecules, Rydberg Gases, and Trapped Ions (DAMOP, DCMP); 06.01.02 Topological States in AMO Systems (DAMOP, DCMP)

[1] I. Lesanovsky and H. Katsura, Phys. Rev. A 86, 041601 (2012).
[2] S. A. Moses, J. P. Covey, M. T. Miecnikowski, D. S. Jin, and J. Ye, Nature Physics 13, 13-20 (2017).