激發(fā)正交相干態(tài)的構(gòu)建及其量子特性

吳亞女

激發(fā)正交相干態(tài)的構(gòu)建及其量子特性

吳亞女

(漳州工業(yè)學(xué)校, 福建 漳州, 363000)

利用產(chǎn)生算符作用在正交相干態(tài)上構(gòu)造新的量子態(tài)的方法, 構(gòu)造了激發(fā)正交相干態(tài)。采用數(shù)值計(jì)算方法, 通過(guò)對(duì)光場(chǎng)的兩個(gè)正交分量漲落、二階關(guān)聯(lián)函數(shù)、Mandel Q參量的計(jì)算, 討論了該量子態(tài)的統(tǒng)計(jì)性質(zhì), 并研究了產(chǎn)生算符作用次數(shù)和相干態(tài)平均光子數(shù)對(duì)其量子特性的影響。結(jié)果表明: 激發(fā)正交相干態(tài)不呈現(xiàn)壓縮效應(yīng), 但呈現(xiàn)出反聚束效應(yīng)和亞泊松分布性質(zhì), 并且隨平均光子數(shù)增大它的反聚束效應(yīng)、亞泊松分布性質(zhì)均減弱。另外, 算符作用次數(shù)對(duì)其量子特性有重大影響, 選擇二次作用對(duì)增強(qiáng)態(tài)的反聚束效應(yīng)和亞泊松分布性質(zhì)有利。

量子光學(xué); 算符重復(fù)作用; 激發(fā)正交相干態(tài); 量子特性

光場(chǎng)量子態(tài)的構(gòu)建, 量子特性的研究, 及其在開(kāi)放系統(tǒng)中量子特性的保持等, 長(zhǎng)期以來(lái)一直是量子光學(xué)領(lǐng)域研究的重要課題。在量子態(tài)構(gòu)建方面, 常用的方法有2種: 一是利用量子力學(xué)態(tài)疊加原理, 如薛定諤貓態(tài)等[1–2]; 另一種是利用算符作用在參考態(tài)上構(gòu)建新的量子態(tài)。

在算符作用方法方面, Agarwal等[3]最早引入了利用光子產(chǎn)生算符構(gòu)造激發(fā)相干態(tài)的方案, Agarwal等[4]討論了單光子減壓縮真空態(tài)的非經(jīng)典性質(zhì)。隨著研究的深入, 研究者們?cè)阡螞](méi)算符和產(chǎn)生算符單獨(dú)作用的研究基礎(chǔ)上, 將算符作用推廣到算符疊加作用, 產(chǎn)生算符和湮沒(méi)算符先后作用, 以及算符累次作用等情況[5–13]。如: Wu等[5]通過(guò)一模光子增加到雙模壓縮真空態(tài)上來(lái)構(gòu)建新的量子態(tài), 并討論了它的統(tǒng)計(jì)性質(zhì); Wang等[6]研究了多光子減雙模壓縮相干態(tài)的非經(jīng)典性質(zhì); Xu等[7]提出了湮沒(méi)算符和產(chǎn)生算符先后多次作用在壓縮真空態(tài)上, 構(gòu)建新的量子態(tài)方案, 并考察了它的量子特性。實(shí)驗(yàn)上, Zavatta等[14]實(shí)現(xiàn)了利用Bose產(chǎn)生算符作用產(chǎn)生單光子激發(fā)相干態(tài)。近年來(lái), 研究者們還提出了構(gòu)建參考態(tài)的正交態(tài)的新思想, 并在實(shí)驗(yàn)上提出制備正交態(tài)的方案[15–17]。受前面研究的啟發(fā), 本文將產(chǎn)生算符作用在正交相干態(tài)上構(gòu)建了激發(fā)正交相干態(tài), 并討論其統(tǒng)計(jì)性質(zhì), 如壓縮效應(yīng)、反聚束效應(yīng)、亞泊松分布等。

1 激發(fā)正交相干態(tài)的構(gòu)建

式中(,)為歸一化常數(shù)。利用積分公式[19]

為了計(jì)算簡(jiǎn)單起見(jiàn), 以下我們僅考慮= 1的情況, 這時(shí)

利用式(3), 具體計(jì)算得出

,

2 壓縮效應(yīng)

3 反聚束效應(yīng)

光場(chǎng)的反聚束效應(yīng)可用二階關(guān)聯(lián)函數(shù)來(lái)描述, 定義為[19]

定義=2-1, 若< 0, 則稱光場(chǎng)呈現(xiàn)出反聚束效應(yīng)。

4 光場(chǎng)的統(tǒng)計(jì)性質(zhì)

Mandel Q參量描述了光場(chǎng)的統(tǒng)計(jì)分布性質(zhì), 定義為[19]

= 0表示其統(tǒng)計(jì)分布性質(zhì)為泊松分布, 而> 0 (< 0)表示其統(tǒng)計(jì)分布為超泊松分布(亞泊松分布)。

將式(4)的結(jié)果代入式(7), 可對(duì)Mandel Q參量隨平均光子數(shù)的演化進(jìn)行數(shù)值計(jì)算。計(jì)算結(jié)果如圖3所示。由圖3可知: 圖3(a), 激發(fā)數(shù)= 1, 這時(shí)> 0, 表明EOCS態(tài)呈現(xiàn)出超泊松分布; 圖3(b)和3(c), 激發(fā)數(shù)分別等于2和3, 在小于一定值的區(qū)域內(nèi)< 0, 這時(shí)EOCS態(tài)表現(xiàn)出亞泊松分布性質(zhì)。激發(fā)數(shù)= 2的曲線負(fù)值區(qū)域要比= 3的曲線負(fù)值區(qū)域大, 說(shuō)明其亞泊松分布性質(zhì)要比= 3的強(qiáng)。比較圖3(a)、(b)、(c), 發(fā)現(xiàn)激發(fā)數(shù)對(duì)EOCS態(tài)的統(tǒng)計(jì)分布性質(zhì)也有重要影響。計(jì)算結(jié)果表明, 選擇激發(fā)數(shù)= 2對(duì)增強(qiáng)EOCS態(tài)的亞泊松分布性質(zhì)也有利。另一方面, 其亞泊松分布性質(zhì)隨相干態(tài)平均光子數(shù)增大而減弱, 相干態(tài)平均光子數(shù)大于一定值后, 亞泊松分布性質(zhì)消失。

5 結(jié)論

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The construction of the excited orthogonal coherent state and its quantum properties

Wu Ya’nv

(Zhangzhou Industrial School, Zhangzhou 363000, China)

Excited orthogonal coherent state (EOCS) is constructed by repeat operation of photon creation operator on the orthogonal coherent state. The squeezing, anti-bunching effect and sub-poissonian statistical property of EOCS are studied by using numerical calculation method. The influences of the repeat operation number of creation operator and the average number of photon in the coherent state on its quantum properties are discussed. Numerical results show that EOCS does not exhibit squeezing effect, but it displays the anti bunching effect and the sub-poissonian statistical property; in addition, its anti-bunching effect and sub-poissonian statistical property are weakened with increase of the average number of photon in the coherent state. On the other hand, the repeat operation number of creation operator has a significant impact on its quantum properties, and the two times operation of creation operator is benefit to strengthen its quantum properties.

quantum optics; the repeat operation of creation operator, excited orthogonal coherent state; quantum property

O 431.2

A

1672–6146(2020)03–0014–05

10.3969/j.issn.1672–6146.2020.03.003

吳亞女, lin_xi1998@sina.com。

2019–10–16

(責(zé)任編校: 張紅)