Detecting topological exceptional points in a parity-time symmetric system with cold atoms.

Jian Xu,Wei Huang,Dan-Wei Zhang,Yan-Xiong Du

doi:10.1364/oe.25.015786

Abstract

We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space constructed by a four-level cold atomic system. We show that a tunable parameter in the presented system for simulating the non-Hermitian Hamiltonian can be tuned to sweep the eigenstates through the exceptional points in parameter space. The non-trivial Berry phases of the eigenstates obtained in this loop from the exceptional points can be measured by the atomic interferometry. Since the proposed operations and detection are experimentally feasible, our scheme may pave a promising way to explore the novel properties of non-Hermitian systems.

Highlights

Non-Hermitian Hamiltonian used to describe open or dissipative systems usually have complex eigenvalues
We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space constructed by a four-level cold atomic system
We show that a tunable parameter in the presented system for simulating the non-Hermitian Hamiltonian can be tuned to swept the eigenstates through the exceptional points in parameter space

Summary

INTRODUCTION

Non-Hermitian Hamiltonian used to describe open or dissipative systems usually have complex eigenvalues. The chirality leads to an unique effect that the eigenstates exchange themselves but only one of them obtains a π Berry phase in a cyclic evolution [25, 26] This chiral phenomenon of EPs has been experimentally demonstrated in microwave cavity for the first time [27, 28]. We propose a scheme to realize the PT-symmetric Hamiltonian in cold atomic systems that the parameters can be exactly controlled in time. The proposed scheme provides a promising approach to realize the PT-symmetric Hamiltonian in cold atomic systems and to further explore the exotic properties of the EPs. The paper is organized as follows.

TOPOLOGICAL EXCEPTIONAL POINTS IN A PT-SYMMETRIC SYSTEM

REALIZATION OF THE TWO-LEVEL PT-SYMMETRIC HAMILTONIAN IN A FOUR-LEVEL

DETECTING THE BERRY PHASE IN THE PT-SYMMETRIC SYSTEM

DISCUSSION AND SUMMARY