RQC Seminar

95th RQC Seminar

• Speaker

  Ph.D. student Zhiyu Jiang
  ( Department of Applied Physics, Hokkaido University )

• Date

  16:00-17:00, November 13, 2023 (Monday)

• Venue

  Hybrid(ZOOM・ Wako Main Research 3F 345-347 Seminar Room C01）

• Title

  Z_2 Point-Gap Topology of a Non-Unitary Quantum Walk with Time-Reversal Symmetry

• Inquiries

  rqc_info[at]ml.riken.jp

Abstract
Introduction
The study of non-Hermitian systems has gained significant attention in recent years due to its potential for novel physical phenomena and practical applications. Non-Hermitian physics is characterized by systems with non-Hermitian Hamiltonian, which can lead to topological properties different from Hermitian systems such as non-Hermitian skin effects (NHSE) [1]. In the Hatano-Nelson (HN) model exhibiting NHSE, the energy spectrum can be significantly affected by the boundary conditions due to a non-zero point-gap topological number which is defined by the winding number (∈Z). However, the winding number vanishes in time-reversal systems consisting of two coupled HN chains with opposite non-reciprocity. Even in that case, the system can remain NHSE because of the emergence of Z_2 topological number, which is called Z_2 non-Hermitian skin effect [2]. One promising area of exploration within topology of non-Hermitian physics is the study of non-unitary quantum walks. The standard quantum walks consist of a walker moving on lattices, whose state is defined by unitary operators with each step. However, the non-unitary quantum walks incorporate gain and loss, resulting in non-Hermitian Hamiltonian dynamics. Some models of non-unitary quantum walks have been realized theoretically and experimentally by temporally alternating photon losses [3,4] while there is limited research focused on the topological properties of time-reversal symmetric non-unitary quantum walks, which is worth studying to realize Z_2 NHSE by quantum walks.
In our work [5], we introduce a quantum walk, where the walker traverses two non-unitary quantum-walk chains to achieve non-Hermitian time-reversal symmetry (TRS^†). We demonstrate that for the quantum walk, the quasi-energy spectrum strongly depends on the boundary conditions at certain energy points that exhibit Z_2 topological behavior [Fig.1 (a)]. Kramers doublets with topologically non-trivial energies are confined to the edges of the chains, indicating the emergence of the Z_2 NHSE in this quantum walk. Our work highlights the potential for non-unitary quantum walks to serve as a platform for exploring novel physical phenomena and paves the way for further investigations into non-Hermitian systems with time-reversal symmetry.
Details : Abstract by Mr. Jiang