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Register a new userNonlinear control of PT-symmetry and non-Hermitian topological states
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Advances in topological photonics and non-Hermitian optics have drastically changed our perception on how interdisciplinary concepts may empower unprecedented applications. Bridging the two areas could uncover the reciprocity between topology and non-Hermiticity in complex systems. So far, such endeavors have focused mainly on linear-optics regime. Here, we establish a nonlinear non-Hermitian topological platform for control of parity-time (PT) symmetry and topological edge states. Experimentally, we demonstrate that optical nonlinearity effectively modulates the gain and loss of a topological interface waveguide in a non-Hermitian Su-Schrieffer-Heeger lattice, leading to switching between PT and non-PT-symmetric regimes accompanied by destruction and restoration of topological zero modes. Theoretically, we examine the fundamental issue of the interplay between two antagonistic effects: the sensitivity close to exceptional points and the robustness of non-Hermitian topological modes. Realizing single-channel control of global PT-symmetry via local nonlinearity may herald new possibilities for light manipulation and unconventional device applications.
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We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $mathcal{PT}$ and chiral symmetry anti-$mathcal{PT}$ ($mathcal{APT}$). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $mathcal{PT}$ symmetric gain and loss on localized edge and defect states in a non-Hermitian Su--Schrieffer--Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the $mathcal{APT}$ symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel $mathcal{PT}$ symmetric $mathbb{Z}_2$ invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not $mathcal{PT}$ symmetric, the topological defect state disappears and only reemerges when $mathcal{APT}$ symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.
According to the topological band theory of a Hermitian system, the different electronic phases are classified in terms of topological invariants, wherein the transition between the two phases characterized by a different topological invariant is the primary signature of a topological phase transition. Recently, it has been argued that the delocalization-localization transition in a quasicrystal, described by the non-Hermitian $mathcal{PT}$-symmetric extension of the Aubry-Andr{e}-Harper (AAH) Hamiltonian can also be identified as a topological phase transition. Interestingly, the $mathcal{PT}$-symmetry also breaks down at the same critical point. However, in this article, we have shown that the delocalization-localization transition and the $mathcal{PT}$-symmetry breaking are not connected to a topological phase transition. To demonstrate this, we have studied the non-Hermitian $mathcal{PT}$-symmetric AAH Hamiltonian in the presence of Rashba Spin-Orbit (RSO) coupling. We have obtained an analytical expression of the topological transition point and compared it with the numerically obtained critical points. We have found that, except in some special cases, the critical point and the topological transition point are not the same. In fact, the delocalization-localization transition takes place earlier than the topological transition whenever they do not coincide.
The effects of gain and loss on the band structures of a bulk topological dielectric photonic crystal (PC) with $C_{6v}$ symmetry and the PC-air-PC interface are studied based on first-principle calculation. To illustrate the importance of parity-time (PT) symmetry, three systems are considered, namely the PT-symmetric, PT-asymmetric, and lossy systems. We find that the system with gain and loss distributed in a PT symmetric manner exhibits a phase transition from a PT exact phase to a PT broken phase as the strength of the gain and loss increases, while for the PT-asymmetric and lossy systems, no such phase transition occurs. Furthermore, based on the Wilson loop calculation, the topology of the PT-symmetric system in the PT exact phase is demonstrated to keep unchanged as the Hermitian system. At last, different kinds of edge states in Hermitian systems under the influences of gain and loss are studied and we find that while the eigenfrequencies of nontrivial edge states become complex conjugate pairs, they keep real for the trivial defect states.
While spin-orbit coupling (SOC), an essential mechanism underlying quantum phenomena from the spin Hall effect to topological insulators, has been widely studied in well-isolated Hermitian systems, much less is known when the dissipation plays a major role in spin-orbit-coupled quantum systems. Here, we realize dissipative spin-orbit-coupled bands filled with ultracold fermions, and observe a parity-time ($mathcal{PT}$) symmetry-breaking transition as a result of the competition between SOC and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables the energy gap, opened by SOC, to be engineered and closed at the critical dissipation value, the so-called exceptional point (EP). The realized EP of the non-Hermitian band structure exhibits chiral response when the quantum state changes near the EP. This topological feature enables us to tune SOC and dissipation dynamically in the parameter space, and observe the state evolution is direction-dependent near the EP, revealing topologically robust spin transfer between different quantum states when the quantum state encircles the EP. This topological control of quantum states for non-Hermitian fermions provides new methods of quantum control, and also sets the stage for exploring non-Hermitian topological states with SOC.
Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here, we demonstrate the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which, serendipitously, are also BICs in a laser-written second-order topological lattice. We further demonstrate nonlinear coupling with edge states at a low nonlinearity, transitioning to solitons at a high nonlinearity. Theoretically, we calculate the analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by both focusing and defocusing nonlinearities. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.
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