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arXiv:2605.11597

Interband Berry connection measurement in the optical honeycomb lattice

Shao‐Wen Chang, Malte N. Schwarz, Erin G. Moloney, Ke Lin, Dan Stamper-Kurn

Published May 12, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2605.11597

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Ultracold atoms in optical lattices have recently emerged as promising candidates for investigating the geometric and topological aspects of band structures. In this thesis, we exploit the high degree of control available in these systems to directly probe the band geometry of an optical honeycomb lattice. In the first series of experiments, we realize an atomic interferometer in quasimomentum space to measure the singular Berry flux associated with a Dirac point. This technique enables us to determine the distribution of Berry curvature in the Brillouin zone with high quasimomentum resolution. Next, we realize strong-force dynamics that are described by matrix-valued Wilson lines, which are generalizations of the Berry phase to degenerate systems. In this strong-force regime, we show that the evolution in the band populations directly reveals the band geometry. This method enables the reconstruction of both the cell-periodic Bloch states at every quasimomentum and the eigenvalues of Wilson-Zak loops. Our techniques can be used to determine the topological invariants, such as the Chern and Z2 numbers, that characterize the band structure. Lastly, having established our ability to detect the band geometry, we present preliminary experiments on engineering band structures.
Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in an optical lattice, a method which so far has only been applied to explore simple lattice structures. In my talk I will report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice [1]. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking the inversion symmetry of the lattice. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials where the topology of the band structure plays a crucial role, but also provide the possibility to explore many-body phases resulting from the interplay of complex lattice geometries with interactions.
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