Session X02: Beyond Hypercubic Optical Lattices

Strong pairing in mixed dimensions

Among the key motivations for the development of quantum simulation experiments using ultra cold atoms is the goal to understand the Fermi-Hubbard model, and in particular identifying a possible pairing mechanism which could lead to high-temperature superconductivity. In this talk, I will present a string-based binding mechanism, which leads to high temperature pairing of fermions in a microscopically repulsive model. In particular, I will introduce a general, highly efficient pairing mechanism for mobile dopants in antiferromagnetic Mott insulators, which leads to binding energies proportional to $t^{1/3}$, where $t$ is the hopping amplitude of the charge carriers. The pairing is caused by the energy that one charge gains when retracing a string of frustrated bonds created by another charge. I will show that this mechanism leads to the formation of highly mobile, but tightly bound pairs in the case of mixed-dimensional Fermi-Hubbard bilayer systems. 

This setting is closely related to the Fermi-Hubbard model believed to capture the physics of copper oxides, and can be realized in ultracold atom experiments. In particular, due to the large binding energies, pairing can be experimentally observed at currently achievable temperatures.    

Direct Geometric Probe of Singularities in Band Structure

The band structure of a crystal may have points where two or more bands are degenerate in energy, which may reflect singularities in the geometry of the Bloch state manifold with consequences for material and transport properties. To date, ultracold atoms in optical lattices have been used to characterize such points only indirectly, for example, by detection of an Abelian Berry phase. These studies have only investigated singularities with linear dispersion (Dirac points).  In this work, we probe band-structure singularities through the non-Abelian transformation produced by transport directly through the singular points.  We prepare atoms in one Bloch band, accelerate them along a quasi-momentum trajectory that enters the singularity along a ray, turns by a variable angle, exits on a different ray, and then we measure the final band populations. We apply this technique to both linear and quadratic band-touching points of a honeycomb lattice, and we observe band population variations that identify the winding numbers of these singularities to be 1 and 2, respectively.

    

Quantum gas microscopy of triangular lattice Mott insulators

Frustrated quantum systems can host quasi-particles with fractional statistics and pose significant challenges to condensed matter theory due to their extensive ground state degeneracy. Here, we aim at quantum simulation of electronic systems on triangular lattice geometries using ultracold atoms in a quantum gas microscope.

In this talk, I present the site-resolved imaging of fermionic lithium atoms in our novel triangular optical lattice geometry and the realization of Mott insulators in the triangular lattice. Our experiment allows for the preparation of triangular Hubbard systems of several hundred atoms and we image these systems with 98% detection fidelity. I will report on our progress in characterizing the triangular Hubbard systems using site-resolved density and correlation observables in the experiment and discuss comparisons of experimental data to Numerical Linked Cluster Expansion calculations as well as Quantum Monte Carlo simulations.

Our new experimental platform opens the path for studies of kinetic frustration, searches for spin-liquids and investigations of transport properties in frustrated lattices.   

Accessing new optical-lattice regimes with a matter-wave microscope

Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice. However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to 2D systems.

In this talk, I will present our new imaging approach of a quantum gas magnifier, where matter-wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in 3D systems [1]. I will discuss the observation of nanoscale dynamics, precision thermometry and local magnetic-resonance addressing as well as a surprising density-wave formation with spontaneous symmetry breaking in a strongly tilted optical lattice with large occupation numbers [2]. The method opens the path for spatially resolved studies of new quantum many-body regimes including sub-wavelength lattices or single-atom-resolved imaging of exotic atomic species.

[1] L. Asteria et al., Nature 599, 571 (2021). [2] H. P. Zahn et al., arXiv:2108.11917 (2021).