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arXiv:2409.17559 · Physical Review Letters

Zak Phase Induced Topological Nonreciprocity

Xiao Liu, Jiefei Wang, Ruosong Mao, Huizhu Hu, Shi‐Yao Zhu, Xingqi Xu, Han Cai, Da‐Wei Wang

Published May 13, 2025• 13 citations
arXivHTMLPDF

Abstract

Topological physics provides novel insights for designing functional photonic devices, such as magnetic-free optical diodes, which are important in optical engineering and quantum information processing. Past efforts mostly focus on the topological edge modes in two-dimensional (2D) photonic Chern lattices, which, however, require delicate fabrication and temporal modulation. In particular, the 1D nonreciprocal edge mode needs to be embedded in a 2D lattice, contradicting with the compactness of integrated photonics. To address these challenges, we investigate the optical nonreciprocity of the 1D Su-Schrieffer-Heeger (SSH) superradiance lattices in room-temperature atoms. The probe fields propagating in two opposite directions perceive two different SSH topological phases, which have different absorption spectra due to the interplay between the Zak phase and the thermal motion of atoms, resulting in optical nonreciprocity. Our findings reveal the relationship between 1D topological matter and optical nonreciprocity, simplifying the design of topologically resilient nonreciprocal devices.

DOI
10.1103/physrevlett.134.193602

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Topological physics provides novel insights for designing functional photonic devices, such as magnetic-free optical diodes, which are important in optical engineering and quantum information processing. Past efforts mostly focus on the topological edge modes in two-dimensional (2D) photonic Chern lattices, which, however, require delicate fabrication and temporal modulation. In particular, the 1D nonreciprocal edge mode needs to be embedded in a 2D lattice, contradicting with the compactness of integrated photonics. To address these challenges, we investigate the optical nonreciprocity of the 1D Su-Schrieffer-Heeger (SSH) superradiance lattices in room-temperature atoms. The probe fields propagating in two opposite directions perceive two different SSH topological phases, which have different absorption spectra due to the interplay between the Zak phase and the thermal motion of atoms, resulting in optical nonreciprocity. Our findings reveal the relationship between 1D topological matter and optical nonreciprocity, simplifying the design of topologically resilient nonreciprocal devices.
We present a novel set of light-matter topology realized by implementing a finite-component quantum Rabi array with a photonic analog of the Su-Schrieffer-Heeger (SSH) configuration. We demonstrate how complex light-matter couplings with species-dependent phases lead to the closure of superradiance-induced band gap in a manner that differs from that in the SSH model. We uncover an topological superradiant phase transition from a normal phase to a topological superradiant electromagnet phase, which is characterized both by a local order parameter and a global topological invariant. Novel superradiance-enhanced edge states emerge with significantly amplified excitations superior to those in topological normal phase. Strikingly, tuning light-atom coupling induces novel topological superradiant electric and magnetic phases, exhibiting chiral edge-mode excitation at opposite boundaries. Our proposed setup offers a tunable platform for topological quantum optics, advancing applications in topological superradiant lasers.
We investigate quantum correlations and entanglement in a non-Hermitian quantum system modeled by a 2D stacked Su–Schrieffer–Heeger (SSH) lattice incorporating nonreciprocal hopping amplitudes and balanced on-site gain and loss. Focusing on the interplay between non-Hermiticity, topology, and open-boundary conditions, we analyze how these factors shape bipartite entanglement properties, characterized through the entanglement spectrum and entanglement negativity ( E N ). By examining the complex energy spectrum under open boundary conditions, we identify critical points associated with the closing of complex energy gaps, which significantly influence entanglement structure and signal topological phase transitions. Our findings reveal that boundary-localized non-Bloch modes and nonreciprocal couplings can induce highly tunable and unconventional entanglement features, absent under periodic boundary conditions. These results highlight the breakdown of conventional bulk-boundary correspondence and underscore the utility of entanglement measures in diagnosing non-Hermitian topological phases. Beyond advancing the fundamental understanding of quantum correlations in open systems, our study suggests potential pathways to engineer quantum devices and topological materials where gain, loss, and nonreciprocity are intrinsic elements.
We investigate the spectral properties of the Su-Schrieffer-Heeger (SSH) model with sublattice-dependent onsite nonlinearity. Two complementary approaches are employed in our studies. First, Bloch state solutions under periodic boundary conditions are assumed to enable semi-analytical treatment, which allows us to obtain the system's energy band structure and further derive a general expression of the Zak phase that incorporates nonlinearity-induced correction (referred to as nonlinear Zak phase). This analysis reveals that, at sufficiently high nonlinearities, a nonlinearity-induced topological phase transition occurs, marked by a discontinuity in the nonlinear Zak phase. The second approach amounts to numerically obtaining other (non-Bloch) solutions under open boundary conditions, employing the Self-Consistent Field Iterative Method. Its main results include the observation of an edge state's energy that is independent of a nonlinear parameter, a persisting band touching point that only shifts in the presence of perturbations reminiscent of Weyl points in a Weyl semimetal, as well as delocalized solutions that persist even at extreme nonlinearity strengths. These findings illuminate the rich interplay between topology and nonlinearity in lattice models with potential realization in optical/acoustic waveguide settings.
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.
We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.
Magnetic-free nonreciprocal optical devices that prevent backscattering of signals are essential for optical information processing. The achieved nonreciprocal behaviors mostly rely on various optical dispersive effects, leading to dispersive modulations of the spatial beam profiles, such as broadening and discretization, of incident signals. Such deformation inevitably reduces the matching with subsequent functional components. Here, we experimentally demonstrate the nonreciprocal transverse localization of light in a moiré photonic lattice in atomic vapors. When the probe field co- or counter-propagates with the forward coupling field with a honeycomb moiré profile, the output pattern can exhibit localized or dispersive behavior. The nonreciprocal behaviors (in both beam size and transmitted intensity) are from the atomic thermal motion. A backward Gaussian coupling field is also introduced to modulate the size and intensity of the backward probe, which experiences dispersive propagation. The current work provides an approach to control the transverse beam profile in nonreciprocal transmission. The authors demonstrate nonreciprocal transverse localisation of light in a reconfigurable moiré photonic lattice within a rubidium atomic vapor under electromagnetic-induced transparency conditions. This shows selective control of localised or dispersive optical features.