Statistical transmutation in Floquet driven optical lattices

TL;DR

This paper demonstrates that periodically-driven 2D optical lattices can induce bosons to behave like fermions through Floquet engineering and Chern-Simons flux attachment, revealing a novel form of statistical transmutation.

Contribution

It introduces a mechanism for bosonic to fermionic statistical transmutation in 2D optical lattices using Floquet band shaping and Chern-Simons flux attachment.

Findings

Floquet band develops a moat shape with a degenerate minimum

Velocity distribution reveals fermionic nature of bosons

Statistical transmutation achieved via Chern-Simons flux attachment

Abstract

We show that interacting bosons in a periodically-driven two dimensional (2D) optical lattice may effectively exhibit fermionic statistics. The phenomenon is similar to the celebrated Tonks-Girardeau regime in 1D. The Floquet band of a driven lattice develops the moat shape, i.e. a minimum along a closed contour in the Brillouin zone. Such degeneracy of the kinetic energy favors fermionic quasiparticles. The statistical transmutation is achieved by the Chern-Simons flux attachment similar to the fractional quantum Hall case. We show that the velocity distribution of the released bosons is a sensitive probe of the fermionic nature of their stationary Floquet state.