arXiv subjects

Tian-Rui Liu

Publications and source records attributed to Tian-Rui Liu.

4 recordsLinked to original sources

arXiv2024

Exceptional features in nonlinear Hermitian systems

Non-Hermitian systems and their topological singularities, such as exceptional points (EPs), lines, and surfaces, have recently attracted intense interest. The investigation of these exceptional constituents has led to fruitful applications. The responsivity of the eigenvalue diverges at EPs, and chiral state transfer occurs when encircling an EP. Traditionally, it was believed that these exceptional features were unique to non-Hermitian systems requiring gain, loss, or nonreciprocal hopping. Here, we show that these exceptional features are also present in nonlinear Hermitian systems. We consider two coupled resonators with Kerr nonlinearity in one resonator, and no non-Hermitian terms. We identify EP-like points (ELPs) on the eigenspectra where the critical behaviors are the same as those of typical EPs. Additionally, this nonlinear Hermitian system can be mapped to linear non-Hermitian systems, with ELPs corresponding to EPs. We also demonstrate that encirclement around an ELP in the parameter space leads to unique chiral state transfer behavior.

physics.optics↗

arXiv2024

Arbitrarily configurable nonlinear topological modes

Topological modes (TMs) are typically localized at boundaries, interfaces and dislocations, and exponentially decay into the bulk of a large enough lattice. Recently, the non-Hermitian skin effect has been leveraged to delocalize the wavefunctions of TMs from the boundary and thus to increase the capacity of TMs dramatically. Here, we explore the capability of nonlinearity in designing and reconfiguring the wavefunctions of TMs. With growing intensity, wavefunctions of these in-gap nonlinear TMs undergo an initial deviation from exponential decay, gradually merge into arbitrarily designable plateaus, then encompass the entire nonlinear domain, and eventually concentrate at the nonlinear boundary. Intriguingly, such extended nonlinear TMs are still robust against defects and disorders, and stable in dynamics under external excitation. Advancing the conceptual understanding of the nonlinear TMs, our results open new avenues for increasing the capacity of TMs and developing compact and reconfigurable topological devices.

quant-ph↗

arXiv2023

Braiding topology of symmetry-protected degeneracy points in non-Hermitian systems

Degeneracy points in non-Hermitian systems are of great interest. While a homotopic framework exists for understanding their behavior in the absence of symmetry, it does not apply to symmetry-protected degeneracy points with reduced codimension. In this work, utilizing algebraic topology, we provide a systematic classification of these symmetry-protected degenerate points and investigate the braid conservation rule followed by them. Using a model Hamiltonian and circuit simulation, we discover that, contrary to simple annihilation, pairwise-created symmetry-protected degeneracy points merge into a higher-order degeneracy point, which goes beyond the abelian picture. Our findings empower researchers across diverse fields to uncover new phenomena and applications harnessing symmetry-protected non-Hermitian degeneracy points.

cond-mat.mes-hall↗

arXiv2023

Spin-dependent gain and loss in photonic quantum spin Hall systems

Topological phases are greatly enriched by including non-Hermiticity. While most works focus on the topology of the eigenvalues and eigenstates, how topologically nontrivial non-Hermitian systems behave in dynamics has only drawn limited attention. Here, we consider a breathing honeycomb lattice known to emulate the quantum spin Hall effect and exhibits higher-order corner modes. We find that non-reciprocal intracell couplings introduce gain in one pseudo-spin subspace while loss with the same magnitude in the other. In addition, non-reciprocal intracell couplings can also suppress the spin mixture of the edge modes at the boundaries and delocalize the higher-order corner mode. Our findings deepen the understanding of non-Hermitian topological phases and bring in the spin degree of freedom in manipulating the dynamics in non-Hermitian systems.

cond-mat.mes-hall↗