Topological holographic quench dynamics in a synthetic frequency dimension

Danying Yu,Luqi Yuan,Xiong-Jun Liu,Bo Peng,Xianfeng Chen

doi:10.1038/s41377-021-00646-y

Abstract

The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of nonequilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and momentum dimensions. Here, we propose the topological holographic quench dynamics in synthetic dimension, and also show it provides a highly efficient scheme to characterize photonic topological phases. A pseudospin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state, which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is encoded in quench dynamics solely in the time dimension, and is further mapped to lower-dimensional space, manifesting the holographic features of the dynamics. In particular, two fundamental time scales emerge in the dynamical evolution, with one mimicking the topological band on the momentum dimension and the other characterizing the residue time evolution of the state after the quench. For this, a universal duality between the quench dynamics and the equilibrium topological phase of the spin model is obtained in the time dimension by extracting information from the field evolution dynamics in modulated ring systems in simulations. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological nonequilibrium dynamics.

Highlights

The discovery of topological quantum phases has revolutionized the understanding of the fundamental phases of quantum matter and ignited extensive research in condensed matter physics over the past decades[1,2,3,4,5]
In order to go beyond the spatial degree of freedom and capture the extensive information of quantum dynamics, the synthetic dimensions[45,46,47] were proposed and opened an intriguing avenue towards the quantum simulation of exotic topological physics beyond physical dimensions[48,49,50]
By extracting information of the field onto two time scales in simulations, we find the dynamical topological patterns obtained on band inversion surfaces (BISs), which render an emergent dynamical bulk-surface duality and provide a holographic characterization of the topological spin model, with the complete information being encoded in the single variable, i.e., the time evolution, in sharp contrast to the conventional nonequilibrium topological states

Summary

Introduction

The discovery of topological quantum phases has revolutionized the understanding of the fundamental phases of quantum matter and ignited extensive research in condensed matter physics over the past decades[1,2,3,4,5]. The experimental platforms for generating the synthetic dimension along the frequency axis have been proposed and demonstrated using the ring resonator[52,53,57,65,66], in which the photonic modes at spanned frequencies are coupled through the dynamic modulation In this system, the band structure in the synthetic dimension can be measured in the static steady-state regime in the experiment[65]. By extracting information of the field onto two time scales in simulations, we find the dynamical topological patterns obtained on BISs, which render an emergent dynamical bulk-surface duality and provide a holographic characterization of the topological spin model, with the complete information being encoded in the single variable, i.e., the time evolution, in sharp contrast to the conventional nonequilibrium topological states. This work shows advantages in exploring the topological phases with holographic quench dynamics in the synthetic dimensions and provides an insight into classifying the far-fromequilibrium dynamics with nontrivial topology based on the synthetic photonic crystals

Results

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Results analysis

Materials and methods