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Physical Review A

Topological quantum state transfer beyond the single-excitation assumption

Xiao‐Lei Hao, X. Y. Zhang, X. X. Yi

Published Mar 17, 2025• 2 citations
Publisher

Abstract

As is well known, within the single-excitation subspace, the Su-Schrieffer-Heeger (SSH) model exhibits a remarkable ability to transfer an excitation from one end of the lattice to the other. In this work, by relaxing the restriction of the single excitation, we find that a topological channel formed by the topological edge modes of the SSH model can also realize the transfer of arbitrary Gaussian states. Specifically, we investigate the state transfer process within a one-dimensional (1D) optomechanical lattice, which can be mapped to the SSH model with tunable coupling strength. By initially preparing the first optical mode in a squeezed vacuum state and adiabatically varying the system parameters over a full cycle, the squeezed vacuum state can be transferred to the $N\mathrm{th}$ mechanical mode. Furthermore, we extend our investigation to the transfer of arbitrary Gaussian states. Since Gaussian states can be described by the covariance matrix of the system, we reformulate the evolution equation of the covariance matrix in a Schr\"odinger-type equation. This reformulation provides us with an intuitive way to show how an arbitrary Gaussian state is transferred. Our work broadens the application of topological systems for quantum state transfer, demonstrating that not only single-excitation states but also arbitrary Gaussian states, which include multiple excitations and quantum coherence, can be efficiently transferred, with potential implications for quantum information processing.

DOI
10.1103/physreva.111.032417

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As is well known, within the single-excitation subspace, the Su-Schrieffer-Heeger (SSH) model exhibits a remarkable ability to transfer an excitation from one end of the lattice to the other. In this work, by relaxing the restriction of the single excitation, we find that a topological channel formed by the topological edge modes of the SSH model can also realize the transfer of arbitrary Gaussian states. Specifically, we investigate the state transfer process within a one-dimensional (1D) optomechanical lattice, which can be mapped to the SSH model with tunable coupling strength. By initially preparing the first optical mode in a squeezed vacuum state and adiabatically varying the system parameters over a full cycle, the squeezed vacuum state can be transferred to the NthN\mathrm{th}Nth mechanical mode. Furthermore, we extend our investigation to the transfer of arbitrary Gaussian states. Since Gaussian states can be described by the covariance matrix of the system, we reformulate the evolution equation of the covariance matrix in a Schr"odinger-type equation. This reformulation provides us with an intuitive way to show how an arbitrary Gaussian state is transferred. Our work broadens the application of topological systems for quantum state transfer, demonstrating that not only single-excitation states but also arbitrary Gaussian states, which include multiple excitations and quantum coherence, can be efficiently transferred, with potential implications for quantum information processing.
In this paper, we study the interaction between atom and the finite-size Su-Schrieffer-Heeger (SSH) model. We find that when the finite SSH model in the trivial phase, it can be viewed as the atom coupling with the waveguide with the finite bandwidths and non-linear dispersion relation. However, for the SSH model in the topological phase, when we consider the frequency of the atom is resonant with the edge mode of the SSH model, we find that the atom state couples to the two edge states. In this case, we find that there exists a special channel that can be utilized to transfer the atomic excitation to the ends of the SSH model using adiabatic processes. When the atom couples to the different sub-lattice, the excitation of the atom can be transferred to the leftmost or rightmost end of the chain, which provides the potential application toward quantum information processing. Furthermore, The excitation transfer of excited states of atoms to the ends of the chain can also be realized without the adiabatic process. Our work provides a pathway for realizing controllable quantum information transfer based on the atom couples topological matter.
We propose a scheme for realizing high-fidelity topological state transfer via the topological edge states in a one-dimensional cavity–magnon system. It is found that the cavity–magnon system can be mapped analytically into the generalized Su–Schrieffer–Heeger model with tunable cavity–magnon coupling. It is shown that the edge state can be served as a quantum channel to realize the photonic and magnonic state transfers by adjusting the coupling strength between adjacent cavity modes. Further, our scheme can realize the quantum state transfer between photonic state and magnonic state by changing the cavity–magnon coupling strength. With the numerical simulation, we quantitatively show that the photonic, magnonic and magnon-to-photon state transfers can be achieved with high fidelity in the cavity–magnon system. Spectacularly, three different types of quantum state transfer schemes can be even transformed into each other in a controllable fashion. The Su–Schrieffer–Heeger model based on the cavity–magnon system provides us a tunable platform to engineer the transport of photon and magnon, which may have potential applications in topological quantum processing.
Quantum state transfer is one of the basic tasks in quantum information processing. We here propose a theoretical approach to realize arbitrary entangled state transfer through a qubit chain, which is a class of extended Su-Schrieffer-Heeger models and accommodates multiple topological edge states separated from the bulk states. We show that an arbitrary entangled state, from two qubits to N\mathcal{N}N qubits, can be encoded in the corresponding edge states, and then adiabatically transferred from one end to the other of the chain. The dynamical phase differences resulting from the time evolutions of different edge states can be eliminated by properly choosing evolution time. Our approach is robust against both the qubit-qubit coupling disorder and the evolution time disorder. For concreteness of discussions, we assume that such a chain is constructed by an experimentally feasible superconducting qubit system, but our proposal can also be applied to other systems.
We propose a scheme to control excitation transfer between an atom and the ends of the Su-Schrieffer-Heeger (SSH) chain. When the finite SSH chain is in the topological phase, and the frequency of the atom is resonant with the center frequency of the SSH chain, an effective transition between the atomic excited state and the band-gap states can be obtained. The system can be equal to the three-states model. Under this case, we can adiabatically transfer the atomic excitation to one of the ends of the SSH chain. Which end of the SSH chain is the receiver depends on which sublattice of the cell the atom is coupled to. Furthermore, the excitation can also be transferred from the atom to the ends of the chain by fixing the parameters under the dynamic evolution. Our paper provides a method for realizing controllable quantum information transfer based on the coupling of an atom with topological matter.
Topological insulators have inspired the study with various quantum simulators. Exploiting the tunability of the qubit frequency and qubit-qubit coupling, we show that a superconducting qubit chain can simulate various topological band models. When the system is restricted to the single-spin excitation subspace, the Su-Schrieffer-Heeger (SSH) model can be equivalently simulated by alternating the coupling strength between neighboring qubits. The existence of topological edge states in this qubit chain is demonstrated in the quench dynamics after the first qubit is excited. This excitation propagates along the chain where the qubit-qubit coupling is homogeneous. In contrast, in our qubit chain, the spin-up state localizes at the first qubit and the rest qubits remain in the spin-down state. We further show that the spin-up state can be transported along the chain by modulating the coupling strengths and the qubit frequencies. This demonstrates adiabatic pumping based on the Rice-Mele model. Moreover, we also discuss possible ways to construct other topological models with different topological phenomena within the current technology of superconducting qubits.
We investigate the influence of long-range hoppings in a structured photonic bath on atom-photon interactions. Considering a system comprising a two-leg giant atom coupled to an extended Su-Schrieffer-Heeger (SSH) model incorporating beyond-nearest-neighbor hoppings while preserving chiral symmetry, we demonstrate the formation of an unconventional bound state in the continuum (BIC) when the atomic transition frequency resonates with a mode inside the propagation band. In particular, the spatial distribution of the photoinc wavefunction of the BIC can be modified by the long-range hoppings. Consequently, when multiple identical giant atoms are included in the system, the resulting decoherence-free interactions between them are rendered less sensitive to the specific topological configuration (e.g., braided, separated, or nested) of the emitters. Furthermore, we propose two efficient and controllable quantum state transfer protocols enabled by the extended SSH model coupled to normal atoms. We show that by appropriately engineering the long-range hopping strengths, perfect excitation transfer can be achieved between two atoms coupled to the edge sites of an infinite SSH chain. In a second scheme, a single atom coupled to the center of a finite SSH chain can transfer its excitation to one of the topological edge modes. Our paper provides a method for controlling atom-photon interactions with significant implications for quantum information transfer and processing.