物理学报2017，Vol.66Issue(10)：92-100,9.DOI:10.7498/aps.66.104201
相位型三头薛定谔猫态的量子统计属性
Quantum statistical properties of phase-type three-headed Schrodinger cat state
摘要
Abstract
Quantum superposition is a fundamental principle of quantum mechanics,which provides a crucial basis to observe phenomena beyond the predictions of classical physics.For example,a quantum entangled state can exhibit stronger correlation than classically possible one.In quantum state engineering,many new quantum states can be obtained from the superposition of many known states.In recent decades,the superposition of coherent states (CSs) with the same amplitude but two different phases has been a subject of great interest.This superposition state was often called Schrodinger cat state (here,we also name it 2-headed cat state (2HCS)),which becomes an important tool to study a lot of fundamental issues.Surprisingly,some studies have extended the quantum superposition to involving more than two component coherent states.In order to produce the superposition of three photons,people have considered the superposition of coherent states with three different phases (here,we also name it 3-headed cat state (3HCS)).Furthermore,in microwave cavity quantum electrodynamics of bang-bang quantum Zeno dynamics control,people have proposed the superposition of coherent states with four different phases (here,we also name it 4-headed cat state (4HCS)).In this paper,we make a detailed investigation on the quantum statistical properties of a phase-type 3HCS.These properties include photon number distribution,average photon number,sub-Poissionian distribution,squeezing effect,and Wigner function,etc.We derive their analytical expressions and make numerical simulations for these properties.The results are compared with the counterparts of the CS,the 2HCS and the 4HCS.The conclusions are obtained as follows.1) The CS,the 2HCS,the 3HCS and the 4HCS have k,2k,3k and 4k photon number components,respectively (k is an integer);2) small difference in average photon number among these quantum states in small-amplitude range can be observed,while their average photon numbers become almost equal in large-amplitude range;3) the CS exhibits Poisson distribution,and the 2HCS,the 3HCS and the 4HCS exhibit superPoisson distributions in most amplitude ranges,however,sub-Poisson distribution can be seen for the 3HCS and the 4HCS in some specific amplitude ranges;4) except for the 2HCS that may have the squeezing property,no squeezing properties can be found in the CS,the 3HCS and the 4HCS;5) negative values can exist in the Wigner functions for the 2HCS,the 3HCS and the 4HCS,while it is not found in the CS.Similar to the 2HCS and 4HCS,the Wigner function of the 3HCS has negative component,which implies its nonclassicality.Different from the 2HCS,the 3HCS exhibits sub-Poisson photon number distribution in a certain amplitude range,it is weaker than that of the 4HCS.At the same time,no squeezing is found in the 3 or 4HCS,which is another difference from the 2HCS.关键词
薛定谔猫态/三头猫态/非经典性/Wigner函数Key words
Schrodinger cat state/three-headed cat state/nonclassicality/Wigner function引用本文复制引用
林悖庆,朱泽群,王祖俭,徐学翔..相位型三头薛定谔猫态的量子统计属性[J].物理学报,2017,66(10):92-100,9.基金项目
国家自然科学基金(批准号:11665013)、江西省高等学校教学改革研究课题(批准号:JXJG-16-2-2)和江西师范大学团队高原计划项目资助的课题.Project supported by National Natural Science Foundation of China (Grant No.11665013),Research on Teaching Reform of Jiangxi Higher Education,China (Grant No.JXJG-16-2-2) and the Gaoyuan Plan Project of Jiangxi Normal University,China. （批准号:11665013）
