Abstract
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.
Highlights
Topological insulator [1,2,3,4] opens up a new way of material classification in condensed matter physics due to the distinct topological construction in geometric space
If treating the first resonator as one input port and treating the two-end resonators as two output ports, the present superconducting circuit can be mapped into a topological beam splitter (TBS), in which the injected photon at the input port can be observed at the two output ports with a certain proportion
We reveal that the resonators array can be mapped into a topological tight-binding SSH model, in which the nearest neighbor (NN) hopping can be periodically modulated via the external field
Summary
Topological insulator [1,2,3,4] opens up a new way of material classification in condensed matter physics due to the distinct topological construction in geometric space. Corresponding to an SSH model with an odd number of lattice sites, the system has a zero energy mode being localized at the leftmost site when the intra-cell coupling is weaker than the inter-cell coupling or being localized at the rightmost site when the intra-cell coupling is larger than the inter-cell coupling In this way, if we modulate the intra-cell and inter-cell couplings periodically, the zero energy mode in the odd-sized SSH model naturally provides the topological channel to realize the topological edge pumping between topological left and right boundary states [25,49]. To further explore the confusion mentioned above, in this paper, we propose a scheme to investigate the topological edge state pumping in an SSH chain with the even number of lattice sites, which is mapped by a 1D superconducting transmission line resonators array.
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