Probing Su–Schrieffer–Heeger-like behavior in a tilted synthetic flux ladder*

Tilted optical lattice systems have been widely used in both quantum metrology and quantum simulations. In recent years, progress has been made to combine tilted optical lattices with optical lattice clocks using fermionic alkaline-earth atoms (AEAs), resulting in a new platform with pristine quantum coherence and exquisite quantum control. In addition, the fermionic AEAs, with their n internal levels, have unique SU(n) symmetric collisions. This platform offers new capabilities to simulate and understand spin-orbit-coupled, interacting many-body fermionic systems. In this talk, I discuss our theoretical studies of quantum dynamics of two-level fermionic atoms in a tilted synthetic flux ladder, where we see a non-trivial interplay of the tilt, the nearest-neighbor hopping and the spin-orbit-coupled laser drives. In a specific parameter regime, accessible under current conditions, we can simulate a tilted Su–Schrieffer–Heeger (SSH) model with tunable inter- and intra-cell couplings without the need of an additional superlattice potential. The topologically trivial and non-trivial phases of the untilted SSH model manifest on the long-time dynamics of chiral Bloch oscillations, which can be accessed via Ramsey spectroscopy. Our work paves the way to understand dynamics in tilted, multi-level quantum many-body systems.