Extension of Noether's theorem in PT-symmetry systems and its experimental demonstration in an optical setup  

作　　者：Qi-Cheng Wu Jun-Long Zhao Yu-Liang Fang Yu Zhang Dong-Xu Chen Chui-Ping Yang Franco Nori 

机构地区：[1]Quantum Information Research Center,Shangrao Normal University,Shangrao 334001,China [2]School of Physics,Nanjing University,Nanjing 210093,China [3]Department of Physics,Hangzhou Normal University,Hangzhou 311121,China [4]Theoretical Quantum Physics Laboratory,RIKEN,Wako-shi,Saitama 351-0198,Japan [5]RIKEN Center for Quantum Computing,RIKEN,Wako-shi,Saitama 351-0198,Japan [6]Physics Department,The University of Michigan,Ann Arbor 48109-1040,USA

出　　处：《Science China(Physics,Mechanics & Astronomy)》2023年第4期13-27,共15页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12264040,12204311,11804228,11865013,and U21A20436);the Jiangxi Natural Science Foundation(Grant Nos.20212BAB211018,20192ACBL20051);the Project of Jiangxi Province Higher Educational Science and Technology Program(Grant Nos.GJJ190891,and GJJ211735);the Key-Area Research and Development Program of Guangdong Province(Grant No.2018B03-0326001);supported in part by the Nippon Telegraph and Telephone(NTT)Corporation Research;the Japan Science and Technology(JST)Agency[via the Quantum Leap Flagship Program(Q-LEAP);Moonshot R&D Grant Number JPMJMS2061];the Japan Society for the Promotion of Science(JSPS)[via the Grants-in-Aid for Scientific Research(KAKENHI)Grant No.JP20H00134];the Army Research Office(ARO)(Grant No.W911NF-18-1-0358);the Asian Office of Aerospace Research and Development(AOARD)(Grant No.FA2386-20-1-4069);the Foundational Questions Institute Fund(FQXi)(Grant No.FQXi-IAF19-06)。

摘　　要：Noether’s theorem is one of the fundamental laws in physics,relating the symmetry of a physical system to its constant of motion and conservation law.On the other hand,there exist a variety of non-Hermitian parity-time(PT)-symmetric systems,which exhibit novel quantum properties and have attracted increasing interest.In this work,we extend Noether’s theorem to a class of significant PT-symmetry systems for which the eigenvalues of the PT-symmetry Hamiltonian HPTchange from purely real numbers to purely imaginary numbers,and introduce a generalized expectation value of an operator based on biorthogonal quantum mechanics.We find that the generalized expectation value of a time-independent operator is a constant of motion when the operator presents a standard symmetry in the PT-symmetry unbroken regime,or a chiral symmetry in the PT-symmetry broken regime.In addition,we experimentally investigate the extended Noether’s theorem in PT-symmetry single-qubit and two-qubit systems using an optical setup.Our experiment demonstrates the existence of the constant of motion and reveals how this constant of motion can be used to judge whether the PT-symmetry of a system is broken.Furthermore,a novel phenomenon of masking quantum information is first observed in a PT-symmetry two-qubit system.This study not only contributes to full understanding of the relation between symmetry and conservation law in PT-symmetry physics,but also has potential applications in quantum information theory and quantum communication protocols.

关 键 词：Noether’s theorem PT-symmetry systems chiral symmetry optical setup 

分 类 号：O316[理学—一般力学与力学基础]