Interband Berry connection measurement in the optical honeycomb lattice

TL;DR

This paper demonstrates how optical excitation responses in ultracold atoms within honeycomb lattices can directly measure the interband Berry connection, revealing geometrical features like Dirac strings.

Contribution

It introduces a method to map the interband Berry connection via optical responses in optical lattices, linking optical excitations to band geometry in a novel way.

Findings

Resonant excitation strength maps out interband Berry connection.

Identification of transparency lines at specific quasimomenta.

Observation of Dirac strings connecting K and K' points.

Abstract

The geometry of Bloch bands affects many physical properties of crystalline solids and other spatially periodic systems. Direct experimental determination of such geometry is an active area of research. In this work, we focus on the fundamental connection between optical excitations and the relative geometry of pairs of Bloch bands, as characterized by the interband Berry connection. We simulate the response of electrons in solids to optical excitation by the response of ultracold fermionic atoms in optical lattices to periodic modulation of the lattice position. The strength of resonant excitation between bands, measured at each quasimomentum and for various lattice-shaking polarizations, directly maps out the interband Berry connection. We apply this method to the optical honeycomb lattice, driving excitations between the ground $n=1$ band and the excited $n'=\{2,3,4\}$ bands. We observe transparency lines of quasimomenta at which the response to excitation of specific polarization is zero. Further, the interband Berry connection between bands 1 and 3 shows irreducible Dirac strings connecting the $K$ and $K'$ points in the Brillouin zone, lines along which the interband Berry connection abruptly changes orientation. Our work establishes optical response as a powerful tool for characterizing geometrical and topological properties of band structure.