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Scientists Propose Holographic Quench Dynamics by Utilizing Synthetic Frequency Dimension

In the past decades, the discovery of the topological quantum phase has revolutionized the understanding of the fundamental phases of quantum matter. The classification of the topological quantum phase usually based on the equilibrium state.

Non-equilibrium topological dynamics based on quench dynamics had been proposed to characterize the exotic behaviors beyond the equilibrium state. However, the characterization of non-equilibrium topological invariants typically needs the information of quantum dynamics in both the time and spatial dimension.

In a new paper published in Light Science & Application, a team of scientists, led by Professor Xianfeng Chen and Professor Luqi Yuan from State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Professor Xiong-Jun Liu from International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China proposed the holographic quench dynamics by utilizing the concept of synthetic frequency dimension. The combination of the quench dynamics and the synthetic frequency dimension effectively facilitates the detection of topological invariants by using the information solely along the time dimension. The research potentially points towards the convenience and practicability of non-equilibrium state detection in future experiments.

The pseudo spin mode is constructed in dynamically modulated ring resonators to demonstrate the detection of non-equilibrium topological phase. Resonant modes are used to construct the lattice model in the synthetic frequency dimension. In Fig. 1(a), the left and right ring resonators are used to emulate the up state and down sate of spins. The corresponding resonant frequency modes labelled by red (deep blue) color represent the up (down) state of spin modes in a one-dimensional lattice (Fig. 1(b)). The initial trivial state is prepared and then the quench dynamics is induced. The averaged spin polarizations are then constructed from the collected signal (Fig. 2), where two band inversion points are found. Hence a new dynamical spin texture can be defined, which then exhibits the topological winding feature (Fig. 3). These scientists emphasize the key feature of topological quench dynamics in the synthetic frequency dimension:

"We found two fundamental time scales emerge in the time evolution of the pseudo spin polarization, where the fast time variable mimics the Bloch momentum and the slow time variable denotes the residue time evolution of the state."

"The holographic characterization of the topological phase realized in the ring-resonator system shows the quench dynamics solely in the time dimension carries the complete information." They added.

"This result is in sharp contrast to the previous characterization of equilibrium topological phases through the nonequilibrium topological invariants, which necessitates the information in both the time dimension and momentum space, and hence leads to significant simplification for performing dynamical characterization of topological quantum phases in different synthetic models." The scientists forecast.


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