In the usual Su–Schrieffer–Heeger (SSH) model with an even number of lattice sites, the topological pumping between left and right edge states cannot be easily realized since the edge states occupy two-end sites simultaneously. Here we propose a scheme to investigate the topological edge pumping in an even-sized periodically modulated SSH model mapped by a one dimensional superconducting transmission line resonators array. We find that the photon initially prepared in the first resonator can be finally observed at the two-end resonators with a certain proportion. The final photon splitting at the two-end resonators indicates that the present superconducting circuit is expected to realize the topological beam splitter. Further, we demonstrate that the splitting proportion between the two-end resonators can be arbitrarily tuned from 1 to 0, implying the potential feasibility of implementing the tunable topological beam splitter. Meanwhile, we also show that the tunable topological beam splitter is immune to the mild disorder added into the system due to the topology protection of the zero energy modes, and find that the tunable topological beam splitter is much more robust to the global on-site disorder compared with the nearest neighbor disorder. Our work greatly extends the practical application of topological matter in quantum information processing and opens up a new way towards the engineering of topological quantum optical device.
In the usual Su–Schrieffer–Heeger (SSH) model with an even number of lattice sites, the topological pumping between left and right edge states cannot be easily realized since the edge states occupy two-end sites simultaneously. Here we propose a scheme to investigate the topological edge pumping in an even-sized periodically modulated SSH model mapped by a one dimensional superconducting transmission line resonators array. We find that the photon initially prepared in the first resonator can be finally observed at the two-end resonators with a certain proportion. The final photon splitting at the two-end resonators indicates that the present superconducting circuit is expected to realize the topological beam splitter. Further, we demonstrate that the splitting proportion between the two-end resonators can be arbitrarily tuned from 1 to 0, implying the potential feasibility of implementing the tunable topological beam splitter. Meanwhile, we also show that the tunable topological beam splitter is immune to the mild disorder added into the system due to the topology protection of the zero energy modes, and find that the tunable topological beam splitter is much more robust to the global on-site disorder compared with the nearest neighbor disorder. Our work greatly extends the practical application of topological matter in quantum information processing and opens up a new way towards the engineering of topological quantum optical device.
The Su–Schrieffer–Heeger (SSH) model, commonly used for robust state transfers through topologically protected edge pumping, has been generalized and exploited to engineer diverse functional quantum devices. Here, we propose to realize a fast topological beam splitter based on a generalized SSH model by accelerating the quantum state transfer (QST) process essentially limited by adiabatic requirements. The scheme involves delicate orchestration of the instantaneous energy spectrum through exponential modulation of nearest neighbor coupling strengths and onsite energies, yielding a significantly accelerated beam splitting process. Due to properties of topological pumping and accelerated QST, the beam splitter exhibits strong robustness against parameter disorders and losses of system. In addition, the model demonstrates good scalability and can be extended to two-dimensional crossed-chain structures to realize a topological router with variable numbers of output ports. Our work provides practical prospects for fast and robust topological QST in feasible quantum devices in large-scale quantum information processing.
Abstract We present a feasible scheme to implement a planar and tunable quantum state transfer (QST) via topologically protected zero-energy mode in a splicing Y-junction Su–Schrieffer–Heeger (SSH) chain. The introduction of the elaborate nearest-neighbor (NN) hopping enables one to generate a topological interface at the central site of the Y-junction. By modulating the NN hopping adiabatically in the chain, the quantum state initially prepared at the central site can be simultaneously transferred to the three endpoints of the Y-junction with the equal/unequal probabilities. The planar distribution of QST is expected to realize a quantum router, whose function is to make the quantum information on the central site (input port) appear equally/unequally at the three endpoints (output ports) with different directions. Moreover, the numerical simulations demonstrate that the scheme possesses the robustness on the fluctuations of the NN hopping and the on-site potential in the system. Furthermore, we show that the number of the output ports with different directions can be flexibly increased in an extended X-junction SSH chain, and the experimental feasibility for implementing special QST in a superconducting qubit-resonator system is briefly discussed. Our work extends the space distribution of QST from linear distribution to planar distribution and promotes the construction of large-scale quantum networks.
We propose a scheme to implement the phase-robust topological router based on a one-dimensional dimerized superconducting circuit lattice with long-range hopping. We show that the proposed dimerized superconducting circuit lattice can be mapped into an extended chiral-symmetric Su-Schrieffer-Heeger (SSH) model with long-range hopping, in which the existence of long-range hopping induces a special zero-energy mode. The peculiar distribution of the zero-energy mode enables us to engineer a phase-robust topological router, which can achieve quantum state transfer (QST) from one site (input port) to multiple sites (output ports). Benefiting from the topological protection of chiral symmetry, we demonstrate that the presence of the mild disorder in nearest-neighbor and long-range hopping has no appreciable effects on QST in the lattice. Particularly, after introducing another long-range hopping into the extended SSH lattice, we propose an optimized protocol of the phase-robust topological router, in which the number of the output ports can be efficiently increased. Resorting to the Bose statistical properties of the superconducting circuit lattice, the input port and output ports assisted by the zero-energy mode can be detected via the mean distribution of the photons. Our work breaks the traditional QST form with only one outport by the zero-energy mode and opens a pathway to construct large-scale quantum information processing in the SSH chains with long-range hopping.
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.
We propose a scheme to implement the phase-robust topological router based on a one-dimensional dimerized superconducting circuit lattice with long-range hopping. We show that the proposed dimerized superconducting circuit lattice can be mapped into an extended chiral-symmetric Su-Schrieffer-Heeger (SSH) model with long-range hopping, in which the existence of long-range hopping induces a special zero-energy mode. The peculiar distribution of the zero-energy mode enables us to engineer a phase-robust topological router, which can achieve quantum state transfer (QST) from one site (input port) to multiple sites (output ports). Benefiting from the topological protection of chiral symmetry, we demonstrate that the presence of the mild disorder in nearest-neighbor and long-range hopping has no appreciable effects on QST in the lattice. Especially, after introducing another new long-range hopping into the extended SSH lattice, we propose an optimized protocol of the phase-robust topological router, in which the number of the output ports can be efficiently increased. Resorting to the Bose statistical properties of the superconducting circuit lattice, the input port and output ports assisted by the zero-energy mode can be detected via the mean distribution of the photons. Our work breaks the traditional QST form with only one outport by the zero-energy mode and opens a pathway to construct large-scale quantum information processing in the SSH chains with long-range hopping.
Abstract We propose a scheme to investigate the topological phase transition in the generalized one-dimensional Su–Schrieffer–Heeger (SSH) model based on a circuit quantum electrodynamics (QED) lattice with frequency modulation. We find that, if we keep the resonant counter rotating wave terms to map the p -wave superconducting pairing terms in the topological superconductor by dint of frequency modulation, the circuit QED lattice can be equivalent to the SSH model with p -wave superconducting pairing terms. The numerical results show that the existence of the superconducting pairing terms cannot close the energy gap of the SSH model within the feasible range of parameters, which means that the superconducting pairing terms cannot induce the topological phase transition. To induce the topological phase transition, we add the next-nearest-neighboring (NNN) interaction into the circuit QED-based SSH model simultaneously. We find that, for a given superconducting pairing strength, the appropriate selection of the NNN interaction can induce closing of the energy gap. It indicates that a new topological phase transition between the topologically nontrivial SSH phase and the topologically trivial SSH phase occurs in the SSH model. Our scheme provides a means to explore the topological SSH phase transition based on a circuit QED lattice with frequency modulation.