Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman lattice

TL;DR

This paper explores how periodically driven optical lattices can simulate topological insulators and exhibit Floquet dynamic quantum phase transitions, revealing new topological phenomena and potential experimental implementations with cold atoms.

Contribution

It introduces a framework connecting Floquet topological phases, dynamic quantum phase transitions, and skyrmion structures in driven cold atomic systems, with practical realization in Raman lattices.

Findings

Mapping low-frequency modulation to 2D topological insulators

Derivation of effective Floquet Hamiltonian at high frequency

Identification of Floquet dynamic quantum phase transitions

Abstract

Stimulated by the recent progress in engineering topological band structures in cold atomic gases, we study the dynamic topological phenomena for atoms loaded in a periodically driven optical lattice. When the frequency of the periodic modulation is low, the time-dependent Hamiltonian can be mapped to a two-dimensional topological insulator, with the discretized frequency components playing the role of an additional, synthetic dimension. In the high-frequency limit, we derive the effective Floquet Hamiltonian of the system, and reveal the occurrence of Floquet dynamic quantum phase transitions -- an emergent topological phenomenon in the micromotion of the Floquet dynamics. Addressing the relation between the topology of the effective Floquet Hamiltonian and the presence of dynamic topological phenomena, we demonstrate that the topologically non-trivial nature of the Floquet Hamiltonian is a sufficient but not necessary condition for the onset of the Floquet dynamic quantum phase transition. We further discuss the relation of the topology of the Floquet Hamiltonian with the existence of dynamic skyrmion structures in the emergent momentum-time manifold of the micromotion, as well as the fate of these dynamic topological phenomena when the modulation frequency decreases away from the high-frequency limit. Finally, making use of the rich level structures of $^{171}$Yb atoms, we show that the system under study can be implemented in a one-dimensional Raman lattice where states in the $^1S_0$ ground-state manifold are coupled by Raman beams with periodically modulated amplitudes.