Quantum gas microscopy of a geometrically frustrated Hubbard system

Frustrated quantum systems host exotic phases such as spin liquids, while their extensive ground state degeneracy poses a significant challenge to condensed matter theory. Here we present our recent work on quantum simulation of electronic systems using ultracold atoms arranged in a geometrically frustrated lattice. A triangle is the paradigm example for geometric frustration. In a triangular lattice, the degree of frustration is tunable via interactions. In the Heisenberg limit, 120 degree spiral order is expected in contrast to the staggered ordered in the square lattice. In this talk, we present a Mott insulator of lithium-6 on a symmetric triangular lattice with a lattice spacing of 1003 nm. The atoms in the triangular lattice are imaged in-situ with an imaging fidelity of 98% [1]. We calibrated tunneling and interaction by lattice modulation spectroscopy. The temperature of our atoms is below one-fifth of the Fermi temperature before loading to the lattice. We used a spin removal technique [2] to resolve either spin up or down to detect spin-spin correlations. We measured the nearest neighbor spin-spin correlations versus different interactions and compare the results to a numerical linked cluster expansion calculation as well as Quantum Monte Carlo simulations [3]. Currently, we are planning to implement spin-resolved imaging via Stern-Gerlach splitting to reach full density resolution [4] and explore a bound state in a strongly repulsive interacting system [5].

[1] J. Yang, PRX Quantum 2, 020344 (2021)

[2] M. F. Parsons, Science 353, 1253-1256 (2016)

[3] Mongkolkiattichai et al., arXiv:2210.14895 (2022)

[4] Phys. Rev. Lett. 125, 010403 (2020)

[5] Phys. Rev. B 97, 140507R (2018)