Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas

Abstract

Three-dimensional topological Weyl semimetals can generally support a zero-dimensional Weyl point characterized by a quantized Chern number or a one-dimensional Weyl nodal ring (or line) characterized by a quantized Berry phase in the momentum space. Here, in a dissipative system with particle gain and loss, we discover a new type of topological ring, dubbed Weyl exceptional ring consisting of exceptional points at which two eigenstates coalesce. Such a Weyl exceptional ring is characterized by both a quantized Chern number and a quantized Berry phase, which are defined via the Riemann surface. We propose an experimental scheme to realize and measure the Weyl exceptional ring in a dissipative cold atomic gas trapped in an optical lattice.Recently, condensed matter systems have proven to be a powerful platform to study low energy gapless particles by using momentum space band structures to mimic the energy-momentum relation of relativistic particles [1,2] and beyond [3][4][5][6]. One celebrated example in three dimensions is the zero-dimensional Weyl point [7][8][9][10][11][12][13][14][15][16][17][18] described by the Weyl Hamiltonian, which has been long sought-after in particle physics but only experimentally observed in condensed matter materials [19][20][21]. Such a Weyl point can be viewed as a magnetic monopole [22] in the momentum space and possesses a quantized Chern number on a surface enclosing the point. Another example is the one-dimensional Weyl nodal ring [3,[23][24][25], which has no counterpart in particle physics. It can be regarded as the generalization of zero-dimensional Dirac cones in two-dimensional systems, such as in graphene, to three-dimensional systems. Such a nodal ring has a quantized Berry phase over a closed path encircling it but does not possess a nonzero quantized Chern number. This leads to a natural question of whether there exists a topological ring exhibiting both a quantized Chern number and a quantized Berry phase in the momentum space.So far, studies on those gapless states focus on closed and lossless systems. However, particle gain and loss are generally present in natural systems. Such systems can often be described by non-Hermitian Hamiltonians [26][27][28][29], which are widely applied to many different systems [30][31][32][33][34][35][36][37][38][39][40]. Due to the non-Hermiticity, eigenvalues of the Hamiltonian are generically complex unless the PT symmetry [41] is conserved and the imaginary part of energy is associated with either decay or growth. Another intriguing feature of a non-Hermitian system is the existence of exceptional points (EPs) [26][27][28][29] at which two eigenstates coalesce and the Hamiltonian becomes defective, leading to many novel phenomena, such as lossinduced transparency [30], single-mode lasers [36,37], and reversed pump dependence of lasers [33].In this paper, we investigate a system of Weyl points in the presence of a spin-dependent non-Hermitian term and find a Weyl exceptional ring composed of EPs. In stark contrast to a Weyl nodal ...

Perspective on topological states of non-Hermitian lattices

“…Exceptional points may also acquire different flavors by becoming anisotropic [90], packing onto exceptional surfaces as reported by Okugawa and Yokoyama [91], exceptional lines driven by disorder [92], or exceptional rings [93][94][95]. They can also be engineered [96] or used as a means to interpret the physics of surface states in three-dimensional systems [97].…”

Why does bulk boundary correspondence fail in some non-hermitian topological models

“…In the last decade, some authors try to spread these ideas to the models with non-hermitian(NH) Hamiltonian [2][3][4][5][6][7][8]. Besides the topological phase that is smoothly extended from the hermitian cases [5,9], the NH models can possess new topological phases stemming from a new kind of degenerate points, the exceptional points (EPs) [10][11][12][13][14][15][16][17][18].…”

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

“…Understanding the topological properties of non-Hermitian systems has also been the focus of many research efforts [55][56][57][58][59]. Initial interest revolved around exceptional points exhibiting unique topological features with no counterparts in Hermitian systems, such as Weyl exceptional rings [60], bulk Fermi arcs and half-integer topological charges [61]. Further observations of a seemingly breakdown of the bulk-boundary correspondence principle [62,63] has led to proposals for a general classification of the topological phases of non-Hermitian systems [55,56,64].…”