arXiv subjects

Chun-Hui Liu

Publications and source records attributed to Chun-Hui Liu.

9 recordsLinked to original sources

arXiv2024

Scaling of quantum Fisher information for quantum exceptional point sensors

In recent years, significant progress has been made in utilizing the divergence of spectrum response rate at the exceptional point (EP) for sensing in classical systems, while the use and characterization of quantum EPs for sensing have been largely unexplored. For a quantum EP sensor, an important issue is the relation between the order of the quantum EP and the scaling of quantum Fisher information (QFI), an essential quantity for characterizing quantum sensors. Here we investigate multi-mode quadratic bosonic systems, which exhibit higher-order EP dynamics, but possess Hermitian Hamiltonians without Langevin noise, thus can be utilized for quantum sensing. We derive an exact analytic formula for the QFI, from which we establish a scaling relation between the QFI and the order of the EP. We apply the formula to study a three-mode EP sensor and a multi-mode bosonic Kitaev chain and show that the EP physics can significantly enhance the sensing sensitivity. Our work establishes the connection between two important fields: non-Hermitian EP dynamics and quantum sensing, and may find important applications in quantum information and quantum non-Hermitian physics.

quant-ph↗

arXiv2023

Anomalous second-order skin modes in Floquet non-Hermitian systems

The non-Hermitian skin effect under open boundary conditions is widely believed to originate from the intrinsic spectral topology under periodic boundary conditions. If the eigenspectra under periodic boundary conditions have no spectral windings (e.g., piecewise arcs) or a finite area on the complex plane, there will be no non-Hermitian skin effect with open boundaries. In this article, we demonstrate another scenario beyond this perception by introducing a two-dimensional periodically driven model. The effective Floquet Hamiltonian lacks intrinsic spectral topology and is proportional to the identity matrix (representing a single point on the complex plane) under periodic boundary conditions. Yet, the Floquet Hamiltonian exhibits a second-order skin effect that is robust against perturbations and disorder under open boundary conditions. We further reveal the dynamical origin of these second-order skin modes and illustrate that they are characterized by a dynamical topological invariant of the full time-evolution operator.

cond-mat.mes-hall↗

arXiv2022

Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions

Recently, superconductors with higher-order topology have stimulated extensive attention and research interest. Higher-order topological superconductors exhibit unconventional bulk-boundary correspondence, thus allow exotic lower-dimensional boundary modes, such as Majorana corner and hinge modes. However, higher-order topological superconductivity has yet to be found in naturally occurring materials. In this work, we investigate higher-order topology in a two-dimensional Josephson junction comprised of two $s$-wave superconductors separated by a topological insulator thin film. We found that zero-energy Majorana corner modes, a boundary fingerprint of higher-order topological superconductivity, can be achieved by applying magnetic field. When an in-plane Zeeman field is applied to the system, two corner states appear in the superconducting junction. Furthermore, we also discover a two dimensional nodal superconducting phase which supports flat-band Majorana edge modes connecting the bulk nodes. Importantly, we demonstrate that zero-energy Majorana corner modes are stable when increasing the thickness of topological insulator thin film.

cond-mat.mes-hall↗

arXiv2022

Symmetry and topological classification of Floquet non-Hermitian systems

Recent experimental advances in Floquet engineering and controlling dissipation in open systems have brought about unprecedented flexibility in tailoring novel phenomena without any static and Hermitian analogues. It can be epitomized by the various Floquet and non-Hermitian topological phases. Topological classifications of either static/Floquet Hermitian or static non-Hermitian systems based on the underlying symmetries have been well established in the past several years. However, a coherent understanding and classification of Floquet non-Hermitian (FNH) topological phases have not been achieved yet. Here we systematically classify FNH topological bands for 54-fold generalized Bernard-LeClair (GBL)symmetry classes and arbitrary spatial dimensions using $K$-theory. The classification distinguishes two different scenarios of the Floquet operator's spectrum gaps [dubbed as Floquet operator (FO) angle-gapped and FO angle-gapless]. The results culminate into two periodic tables, each containing 54-fold GBL symmetry classes. Our scheme reveals FNH topological phases without any static/Floquet Hermitian and static non-Hermitian counterparts. And our results naturally produce the periodic tables of Floquet Hermitian topological insulators and Floquet unitaries. The framework can also be applied to characterize the topological phases of bosonic systems. We provide concrete examples of one and two-dimensionalfermionic/bosonic systems. And we elucidate the meaning of the topological invariants and their physical consequences. Our paper lays the foundation for a comprehensive exploration of FNH topological bands. And it opens a broad avenue toward uncovering unique phenomena and functionalities emerging from the synthesis of periodic driving, non-Hermiticity, and band topology.

cond-mat.mes-hall↗

arXiv2021

Information constraint in open quantum systems

We propose an effect called information constraint which is characterized by the existence of different decay rates of signal strengths propagating along opposite directions. It is an intrinsic property of a type of open quantum system, which does not rely on boundary conditions. We define the value of information constraint ($I_C$) as the ratio of different decay rates and derive the analytical representation of $I_C$ for general quadratic Lindbladian systems. Based on information constraint, we can provide a simple and elegant explanation of chiral and helical damping, and get the local maximum points of relative particle number for the periodical boundary system, consistent with numerical calculations. Inspired by information constraint, we propose and prove the correspondence between edge modes and damping modes. A new damping mode called Dirac damping is constructed, and chiral/helical damping can be regarded as a special case of Dirac damping.

cond-mat.mes-hall↗

arXiv2021

Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect

Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary condition. To unveil the origin of boundary sensitivity, we present exact solutions for one-dimensional non-Hermitian models with generalized boundary conditions and study rigorously the interplay effect of lattice size and boundary terms. Besides the open boundary condition, we identify the existence of non-Hermitian skin effect when one of the boundary hopping terms vanishes. Apart from this critical line on the boundary parameter space, we find that the skin effect is fragile under any tiny boundary perturbation in the thermodynamic limit, although it can survive in a finite size system. Moreover, we demonstrate that the non-Hermitian Su-Schreieffer-Heeger model exhibits a new phase diagram in the boundary critical line, which is different from either open or periodical boundary case.

quant-ph↗

arXiv2020

Topological classification of defects in non-Hermitian systems

We classify topological defects in non-Hermitian systems with point gap, real gap and imaginary gap for all the Bernard-LeClair classes or generalized Bernard-LeClair classes in all dimensions. The defect Hamiltonian $H(\bf{k}, {\bf r})$ is described by a non-Hermitian Hamiltonian with spatially modulated adiabatical parameter ${\bf r}$ surrounding the defect. While the non-Hermitian system with point gap belongs to any of 38 symmetry classes (Bernard-LeClair classes), for non-Hermitian systems with line-like gap we get 54 non-equivalent generalized Bernard-LeClair classes as a natural generalization of point gap classes. Although the classification of defects in Hermitian systems has been explored in the context of standard ten-fold Altland-Zirnbauer symmetry classes, a complete understanding of the role of the general non-Hermitian symmetries on the topological defects and their associated classification are still lacking. By continuous transformation and homeomorphic mapping, these non-Hermitian defect systems can be mapped to topologically equivalent Hermitian systems with associated symmetries, and we get the topological classification by classifying the corresponding Hermitian Hamiltonians. We discuss some non-trivial classes with point gap according to our classification table, and give explicitly the topological invariants for these classes. We also study some lattice or continuous models and discuss the correspondence between the topological number and zero modes at the topological defect.

cond-mat.mes-hall↗

arXiv2020

Helical damping and anomalous critical non-Hermitian skin effect

Non-Hermitian skin effect and critical skin effect are unique features of non-Hermitian systems. In this Letter, we study an open system with its dynamics of single-particle correlation function effectively dominated by a non-Hermitian damping matrix, which exhibits $\mathbb{Z}_2$ skin effect, and uncover the existence of a novel phenomenon of helical damping. When adding perturbations that break anomalous time reversal symmetry to the system, the critical skin effect occurs, which causes the disappearance of the helical damping in the thermodynamic limit although it can exist in small size systems. We also demonstrate the existence of anomalous critical skin effect when we couple two identical systems with $\mathbb{Z}_2$ skin effect. With the help of non-Bloch band theory, we unveil that the change of generalized Brillouin zone equation is the necessary condition of critical skin effect.

cond-mat.mes-hall↗

arXiv2019

Topological classification of non-Hermitian systems with reflection symmetry

We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced chiral symmetry, our topological classification is thus equivalent to classifying Hermitian systems with both chiral and reflection symmetries, which effectively change the classifying space and shift the periodical table of topological phases. According to our classification tables, we provide concrete examples for all topologically nontrivial non-Hermitian classes in one dimension and also give explicitly the topological invariant for each nontrivial example. Our results show that there exist two kinds of topological invariants composed of either winding numbers or $\mathbb{Z}_2$ numbers. By studying the corresponding lattice models under the open boundary condition, we unveil the existence of bulk-edge correspondence for the one-dimensional topological non-Hermitian systems characterized by winding numbers, however we did not observe the bulk-edge correspondence for the $\mathbb{Z}_2$ topological number in our studied $\mathbb{Z}_2$-type model.

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