陳 靜, 候邦品

(四川師范大學物理與電子工程學院,四川成都610066)

1 預備知識

壓縮和糾纏是表征光場量子特性的重要物理量.與相干態(tài)相比,壓縮態(tài)能夠提高信噪比,因此在量子信息和量子計算中有廣泛的應用[1-4].正因如此,對壓縮和糾纏的制備,操控和量度成了研究熱點[5-8].對連續(xù)變量的糾纏的研究已經(jīng)有較成熟的理論和一定的實驗成果[9-10].腔量子電動力學(QED)的飛速發(fā)展開啟了利用原子和腔耦合來制備壓縮態(tài)和輸出壓縮(糾纏)光的研究,比如囚禁在腔中二能級原子與腔模的相互作用制備壓縮態(tài)[11-12].也有單個多能級原子在大失諧的條件下與腔模相互作用制備糾纏態(tài)[13-14].眾多的研究表明腔的衰變率在制備壓縮(糾纏)態(tài)中有重要影響[14-18].微波場容易調(diào)控的優(yōu)點被廣泛運用在電磁誘導透明和糾纏等領(lǐng)域的研究中[19-21],微波場作用在三能級Δ型原子的2個基態(tài)間,可實現(xiàn)循環(huán)封閉的結(jié)構(gòu)[21].另一方面,量子比特的發(fā)展為人造原子的產(chǎn)生奠定了基礎(chǔ),可采用人造原子實現(xiàn)封閉的Δ型原子系統(tǒng)[22-26].同時超導傳輸共振器(TLR)與傳統(tǒng)腔相比的諸多優(yōu)點也引起了廣泛關(guān)注.于是人們將人造原子與超導傳輸共振器耦合來實現(xiàn)腔 QED,把這樣的體系稱為電路 QED體系[25-28].

本文采用的模型是將原子囚禁在腔中,該原子在微波場的作用下與腔模耦合,討論輸出場的壓縮和糾纏特性.通過計算輸出場的壓縮(糾纏)譜,討論了有效耦合常數(shù)、腔的衰變系數(shù)以及微波場的強度對輸出場雙模糾纏度的影響.最后討論用電路QED對本文理論的實驗實現(xiàn).

2 物理模型

采用的三能級封閉系統(tǒng)如圖1所示.頻率為υ1和υ2的2個腔模分別與|1〉?|2〉和|0〉?|2〉耦合,耦合常數(shù)為g1和g2,腔模的湮滅算符為a1和a2.經(jīng)典相干光場驅(qū)動場頻率為ω1和ω2,Rabi頻率為Ω1和Ω2,相位為φ1和φ2,分別作用到原子躍遷|0〉?|2〉和|1〉?|2〉上.另有微波場Ω0作用在2基態(tài)間的躍遷|0〉?|1〉,微波場的相位為φ0,頻率為ω0.光場相對于原子躍遷頻率的失諧量分別為Δ1=ω12-υ1=ω02-ω1,Δ2=υ2-ω02=ω2-ω12.

3 討論

為了研究輸出場的糾纏和壓縮特性,定義雙模振幅正交算符的差算符和相位正交算符的和算符[11]

的解析式來解釋.

另外,腔的衰變率會影響壓縮譜(糾纏譜)的寬度,κ越大,壓縮譜越寬(見圖3).

如圖4所示,在Ω0≠0時,最大糾纏度還是出現(xiàn)在中心頻率ω=0處,且在腔衰變率κ和一定的情況下,Sout(0)和壓縮譜寬度會隨微波場的增大而逐漸減小.

如果λ2＞λ1,糾纏譜可能會出現(xiàn)3個極小值(見圖5).當時,將出現(xiàn)3個極小值,且極小值出現(xiàn)在ω=0,處[12].如圖6所示,微波場Ω0對處的糾纏度的調(diào)節(jié)作用大于對ω=0處的糾纏度的調(diào)節(jié).從圖7最大糾纏度Sout(0)隨λ2/λ1的變化中不難看出,當λ2＜λ1時,最大糾纏度Sout(0)隨λ2/λ1的增大而增大.當λ2＞λ1時,最大糾纏度Sout(0)隨λ2/λ1的增大而減小.

封閉Δ型原子也可用超導磁通量量子比特來實現(xiàn).用一根超導線將超導Josephson結(jié)兩端連起來構(gòu)成1個封閉的超導環(huán),在這個環(huán)里加上額外的磁場φe.當時(其中,磁通量子),這個量子比特就相當于一個Λ型自然原子,基態(tài)之間躍遷是被禁止的.但是當時,這種躍遷定則被打破,任意2個態(tài)之間都能發(fā)生躍遷,這樣就形成了封閉三能級系統(tǒng)[22-23].圖1中與人造封閉三能級原子耦合的量子光場是由超導傳輸線共振器提供的.超導傳輸線共振器是將1塊超導金屬平板2側(cè)分別用2塊超導金屬平板夾主(平板的長度遠遠大于寬度和平板間的間隔),而這塊超導金屬平板的首尾通過電容與外界電路耦合.超導傳輸線共振器作為一種微波腔,它具有品質(zhì)高的優(yōu)點,容易實現(xiàn)強耦合,在量子計算和量子信息方面有很重要的意義.

4 結(jié)論

本文研究了封閉三能級Δ型原子在經(jīng)典相干場和微波場的驅(qū)動下與腔模的相互作用,通過絕熱去掉激發(fā)態(tài)|2〉,得到有效哈密頓量.再通過輸入輸出理論,最終計算出輸出場的壓縮(糾纏)譜.我們發(fā)現(xiàn)輸出場的壓縮譜(糾纏譜)的寬度容易受腔衰變系數(shù)的影響,但可以通過調(diào)節(jié)有效耦合常數(shù)和微波場Ω0來控制.最大壓縮(糾纏)度隨Ω0的增大而增大.當Ω0=0時,最大壓縮度與腔衰變系數(shù)無關(guān).希望本文的研究能為量子通信提供一點理論價值.

致謝四川師范大學研究生優(yōu)秀學位論文培育基金(201314)對本文給予了資助,謹致謝意.

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