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Detecting Topological Phases Through Dynamics of Chiral Density in Momentum-space Lattices

Rui Tian, Xiayao He, Tianhao Wu, Dongdong Pu, Shuai Li, Bo Liu (127343)

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.6880441

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Collective excitations of long-lived atomic hyperfine states can be synthesized into a Bose-Hubbard model in momentum space, where a spatially long-range interaction is introduced by laser-dressing the hyperfine state to Rydberg states. We explore stationary and dynamical properties of the momentum-space lattice in an artificial magnetic field. The many-body ground states support both chiral and anti-chiral edge currents in momentum space. Their stability against strong interactions is verified by a dynamical mean-field simulation. We show that the interplay of the interaction and chirality leads to correlated chiral dynamics, where an interaction-induced excitation blockade in momentum space suppresses the edge currents. When incorporating an effective decay to the lattice, we find that excitation transportation, whose dynamics is governed by a dissipative Bose-Hubard model, can be prohibited by a strong local dissipation, as a result of the quantum Zeno effect. Our study paves the route to quantum simulate topological phases and exotic dynamics with collective states of interacting atoms in momentum-space lattice.
How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. Based on dimension reduction approach, here we propose a new theory to characterize equilibrium topological phases by far-from-equilibrium quantum dynamics, and further report the experimental observation. For a d-dimensional (dD) topological phase with integer invariants, we show that its characterization can be reduced to lower-dimensional topological invariants in the high-order band inversion surfaces (BIS-s), of which the nth-order BIS is a (d-n)D interface in momentum space. In quenching the system from trivial phase to topological regime, we show that the quantum dynamics exhibits nontrivial topological pattern in the arbitrary nth-order BISs, which universally corresponds to and so characterizes the equilibrium topological phase of the post-quench Hamiltonian. This prediction unveils a high-order dynamical bulk-surface correspondence in the momentum space, and provides new dynamical schemes with experimental advantages to detect topological states. In particular, based on the highest-order BISs which are of zero dimension, the detection of topological phase is achieved with minimal measurements. We experimentally build up a quantum simulator using nitrogen-vacancy center to measure the high-order dynamical bulk-surface correspondence in 3D chiral topological insulator, and show the advantages of characterizing the topological phase with high-order BISs in experiment.
We propose feasible schemes to realize topological phases with cold atoms in momentum-space lattices through carefully engineering artificial gauge potentials for neutral atoms. We show a Floquet approach to design momentum-space lattices with long-range hoppings, which can be applicable to realize the momentum-space Haldane model. We further demonstrate the realization of the two-dimensioanl spin-orbit coupling for a spinful momentum-space lattices, arising from a general formulation of non-Abelian gauge potential. Then we give a minimal realization describing quantum anomalous Hall effect in a spin-orbit-coupling induced Chern insulator. We also provide three different dynamical approaches to extract topological properties of the proposed models. The numerical results show that our approaches are still valid even for a lattice with small size and in a short evolution time, thus making it feasible for realistic experiments.