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Annalen der Physik

Topological Phase Transition and Topological Quantum State Transfer in Periodically Modulated Circuit‐QED Lattice

Ji Cao, Wen‐Xue Cui, Yi Xue-Xi, Hong‐Fu Wang

Published Jul 5, 2021• 10 citations
Publisher

Abstract

Abstract The topological properties of a circuit‐QED lattice are studied and it is found that the system undergoes a topological phase transition accompanied by the changes of Chern numbers from 2 to −1. For different lattice sizes, the energy eigenvalue spectra and the probability distributions of edge states are shown. Moreover, it is revealed that, depending on the strictly adiabatic evolution of the time‐dependent Hamiltonian, several different topological quantum state transfers between the first two sites and the last two sites can be achieved by employing the topologically protected edge states as the transfer channels. Further, it is demonstrated that, by using resonator‐based input–output process, the photonic topological edge state can be detected by measuring the average photon number in the steady state. The scheme opens up a new prospect for investigating the potential application of topological matter in quantum information processing.

DOI
10.1002/andp.202100120

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Abstract The topological properties of a circuit‐QED lattice are studied and it is found that the system undergoes a topological phase transition accompanied by the changes of Chern numbers from 2 to −1. For different lattice sizes, the energy eigenvalue spectra and the probability distributions of edge states are shown. Moreover, it is revealed that, depending on the strictly adiabatic evolution of the time‐dependent Hamiltonian, several different topological quantum state transfers between the first two sites and the last two sites can be achieved by employing the topologically protected edge states as the transfer channels. Further, it is demonstrated that, by using resonator‐based input–output process, the photonic topological edge state can be detected by measuring the average photon number in the steady state. The scheme opens up a new prospect for investigating the potential application of topological matter in quantum information processing.
We propose schemes to realize robust quantum states transfer between distant resonators using the topological edge states of a one-dimensional circuit quantum electrodynamics (QED) lattice. Analyses show that the distribution of edge states can be regulated accordingly with the on-site defects added on the resonators. And we can achieve different types of quantum state transfer without adjusting the number of lattices. Numerical simulations demonstrate that the on-site defects can be used as a change-over switch for high-fidelity single-qubit and two-qubit quantum states transfer. This work provides a viable prospect for flexible quantum state transfer in solid-state topological quantum system.
We experimentally investigate topological phenomena in one-dimensional discrete-time photonic quantum walks using a combination of methods. We first detect winding numbers of the quantum walk by directly measuring the average chiral displacement, which oscillates around quantized winding numbers for finite-step quantum walks. Topological phase transitions can be identified as changes in the center of oscillation of the measured chiral displacement. The position of topological phase transition is then confirmed by measuring the moments of the walker probability distribution. Finally, we observe localized edge states at the boundary of regions with different winding numbers. We also confirm the robustness of edge states against chiral-symmetry-preserving disorder.
Abstract We propose a theoretical scheme for a one-dimensional superconducting circuit lattice system to achieve that topological phase transition and topological multi-channel transfer, which is adjusted by the asymmetric hopping modulations. The system consists of an array of coupled superconducting microwave cavities, the hopping between its can be modulated by the qubits. Here, we explore topological stages by introducing parameters to expand the hopping modulation range. We found that the energy bands in the system exhibit different structural characteristics, which can achieve topological phase switching. Meanwhile, the edge modes can undergo a flipping process, which can not only realize dual-channel topological quantum information transfer, but also can achieve four-channel. Furthermore, it is noted that the defect can induce new topological phases, which can be optimized by adjusting the hopping parameters, while disorder can only cause band fluctuations and inversions, but does not change the position and period of edge states, verifying that the edge state transport is robust. The results obtained in this work can be applied to the storage and transmission of quantum information, and have a guiding role in the future development of quantum technology.
Abstract A scheme for measuring topological properties in a two‐photon‐driven Kerr‐nonlinear (KNR) resonator subjected to a single‐photon modulation is proposed. The topological properties are revealed through the observation of the Berry curvature and hence the first Chern number, as a nonadiabatic response of the physical observable to the change rate of the control parameter of the modulated drive. The parameter manifold, constructed from the system's Hamiltonian that determines its dynamics constrained in the state space spanned by the even and odd cat states as two basis states, is adjusted so that the degeneracy crossing the manifold indicates a topological transition. The scheme, with such continuous variable states in mesoscopic systems, provides a new perspective for exploration of the geometry and the related topology with complex systems.
We propose a theoretical scheme for a one-dimensional lattice based on a superconducting quantum circuit system consisting of two types of superconducting microwave cavities, the interaction between nearest-neighbor and next-nearest-neighbor unit cells that can be adjusted by the magnetic flux, the system can obtain the collective dynamic evolution and study the topological properties of the system.First, we investigate the energy spectrum and edge states of the odd-even lattice size and find that the odd-even lattice number affects the topological properties of the system. Furthermore, considering the next-nearest interactions, it is found that there are constraints on the next-nearest interactions, which can be tuned to study the topological phase transitions of the system and the transfer of topological quantum states.In addition, considering the influence of defects on topological properties, it is found that the defect potential energy is small, the system energy band is stable, the edge states remain unchanged, and the energy spectrum fluctuation is small and distinguishable. Conversely, the energy band distribution is destroyed, it will become disordered and chaotic. The research results can design some new quantum devices for quantum optics and quantum information processing.
The preparation of Fock states is important for quantum information storage and processing. Herein, a two‐step protocol with topological protection for multi‐photon Fock states synthesizing in a circuit quantum electrodynamics (QED) architecture is presented. Due to photon number‐dependent vacuum Rabi splitting, the dynamics of the Jaynes–Cummings ladder in the resonant regime can be equivalent to a spin‐1/2 chain while a multi‐frequency microwave pulse is applied. Based on the topologically assisted quantum state transfer (QST)technique, multi‐photon Fock states can be conditionally generated. This method significantly reduces the complexity of experimental manipulation compared with previous multi‐step methods and is more robust as a result of topological protection. Furthermore, the protocol indicates that the circuit QED architecture could potentially provide a platform to explore the exotic phase in condensed matter.