裴棟梁 何軍3)? 王杰英 王家超 王軍民3)?

1)(山西大學(xué)光電研究所,太原 030006)

2)(山西大學(xué),量子光學(xué)與光量子器件國(guó)家重點(diǎn)實(shí)驗(yàn)室,太原 030006)

3)(山西大學(xué),極端光學(xué)協(xié)同創(chuàng)新中心,太原 030006)

銫原子里德伯態(tài)精細(xì)結(jié)構(gòu)測(cè)量?

裴棟梁1)2)何軍1)2)3)?王杰英1)2)王家超1)2)王軍民1)2)3)?

1)(山西大學(xué)光電研究所,太原 030006)

2)(山西大學(xué),量子光學(xué)與光量子器件國(guó)家重點(diǎn)實(shí)驗(yàn)室,太原 030006)

3)(山西大學(xué),極端光學(xué)協(xié)同創(chuàng)新中心,太原 030006)

里德伯態(tài)光譜是測(cè)量里德伯態(tài)能級(jí)結(jié)構(gòu)和中性原子間相互作用的常用技術(shù)手段,特別是高精度的里德伯光譜,可以測(cè)量室溫原子氣室中由偶極相互作用等導(dǎo)致的原子能級(jí)頻移.在實(shí)驗(yàn)中利用反向的852 nm激光和509 nm激光實(shí)現(xiàn)了室溫原子氣室中銫原子6S1/2—6P3/2—57S(D)躍遷的級(jí)聯(lián)雙光子激發(fā),實(shí)現(xiàn)了里德伯態(tài)原子的制備.基于階梯型電磁誘導(dǎo)透明獲得了銫原子里德伯態(tài)的高分辨光譜.實(shí)驗(yàn)中,基于速度選擇的射頻邊帶調(diào)制技術(shù),對(duì)光譜信號(hào)進(jìn)行了頻率標(biāo)定,測(cè)量了銫原子里德伯態(tài)57D3/2和57D5/2的精細(xì)分裂,分裂間隔為(354.7±2.5)MHz,與理論計(jì)算結(jié)果基本一致.速度選擇的射頻調(diào)制光譜可以實(shí)現(xiàn)里德伯態(tài)原子的能級(jí)分裂測(cè)量,其測(cè)量精度對(duì)于單光子躍遷的絕對(duì)激光頻率不敏感;實(shí)驗(yàn)中影響57D3/2和57D5/2精細(xì)分裂間隔測(cè)量精度的主要因素是功率加寬導(dǎo)致的電磁感應(yīng)透明信號(hào)的展寬和509 nm激光頻率掃描的非線性.

里德伯態(tài),電磁感應(yīng)透明,精細(xì)結(jié)構(gòu),超精細(xì)結(jié)構(gòu)

1 引 言

里德伯態(tài)原子即主量子數(shù)較高的激發(fā)態(tài)原子［1］,其超長(zhǎng)的激發(fā)態(tài)壽命、較大的電偶極矩以及正比于主量子數(shù)n7的極化率使其在光與原子相互作用、中性原子之間的強(qiáng)相互作用等研究領(lǐng)域有著重要的意義.高里德伯態(tài)的中性原子非常敏感于外界電場(chǎng),基于里德伯原子的這種特性其可以用作傳感器實(shí)現(xiàn)電場(chǎng)或者微波場(chǎng)的測(cè)量［2?6］;里德伯態(tài)的中性原子之間有較強(qiáng)的相互作用,宏觀中性原子的集體效應(yīng)可以實(shí)現(xiàn)量子糾纏［7?10］;里德伯原子作為非線性介質(zhì),可以實(shí)現(xiàn)單光子級(jí)別的相互作用［11］;基于里德伯原子作為中性原子的可控量子比特,可以實(shí)現(xiàn)中性原子量子邏輯門［12］和單光子源［13］.

里德伯態(tài)制備的方法目前有單光子激發(fā)［14］、雙光子激發(fā)［15］和三光子激發(fā)［16］.對(duì)于雙光子激發(fā),可以利用對(duì)射的激光光束,通過(guò)速度選擇接近零速度群的原子與兩個(gè)光場(chǎng)相互作用,實(shí)現(xiàn)室溫原子氣室中的里德伯態(tài)原子的制備,獲得接近原子自然線寬的亞多普勒光譜.對(duì)于里德伯態(tài)原子的能級(jí)結(jié)構(gòu)測(cè)量,熱原子氣室中通常利用電磁誘導(dǎo)透明(electromagnetically induced transparency,EIT)或者光抽運(yùn)光譜來(lái)實(shí)現(xiàn).EIT是利用一束較強(qiáng)相干光場(chǎng)與原子系統(tǒng)相互作用使本應(yīng)被吸收的探測(cè)光吸收減弱的現(xiàn)象［17］,三能級(jí)結(jié)構(gòu)的EIT一般包括Λ型,V-型和階梯型(又稱級(jí)聯(lián)型),通常用綴飾態(tài)理論［18］和量子相消干涉［19］來(lái)解釋.利用EIT現(xiàn)象,可實(shí)現(xiàn)原子里德伯態(tài)能級(jí)結(jié)構(gòu)的非破壞性測(cè)量.基于EIT光譜技術(shù),國(guó)內(nèi)外多個(gè)小組已實(shí)現(xiàn)室溫原子氣室中中性原子里德伯態(tài)的光譜測(cè)量［20?24］.

對(duì)于銫原子里德伯態(tài)的制備,雙光子激發(fā)是非常有效的實(shí)驗(yàn)方案,實(shí)驗(yàn)上一般采用852 nm和509 nm的激光雙光子激發(fā)［20］制備銫原子里德伯態(tài).509 nm激光可通過(guò)搭建1018 nm激光倍頻系統(tǒng)獲得［25］.在本文中,我們通過(guò)1018 nm激光倍頻系統(tǒng)獲得了實(shí)驗(yàn)所需的509 nm激光,進(jìn)一步通過(guò)852 nm和509 nm激光兩步激發(fā)實(shí)現(xiàn)了133Cs里德伯態(tài)的制備.基于階梯型EIT實(shí)現(xiàn)了銫原子里德伯態(tài)光譜的識(shí)別和測(cè)量.基于速度選擇的邊帶調(diào)制光譜技術(shù),測(cè)量了里德伯態(tài)精細(xì)結(jié)構(gòu)分裂,同時(shí)測(cè)量了銫原子中間態(tài)的超精細(xì)分裂.

2 實(shí)驗(yàn)原理

圖1 (網(wǎng)刊彩色)133Cs的階梯型EIT能級(jí) ?P為探測(cè)光失諧量,6S1/2→ 6P3/2(F′=3,4,5)→ 57S和6S1/2→ 6P3/2(F′=3,4,5)→ 57D分別為不同里德伯態(tài)EIT能級(jí)結(jié)構(gòu),57D態(tài)由于精細(xì)相互作用分裂為57D3/2和57D5/2態(tài)Fig.1.(color online)Energy-levels of133Cs laddertype EIT:?Pis the detuning frequency of probe laser,the ladder-type EIT 6S1/2→ 6P3/2(F′=3,4,5)→nS and 6S1/2→6P3/2(F′=3,4,5)→nD are achieved by two-photon excitation.The state 57D split into 57D3/2and 57D5/2since the fi ne interaction;the energy splitting of 6P3/2and 6S1/2are due to the hyper fi ne structure interaction.

圖1為133Cs的階梯型EIT能級(jí)結(jié)構(gòu).對(duì)于133Cs原子,由于超精細(xì)相互作用,基態(tài)6S1/2態(tài)分裂為F=3和F=4兩個(gè)超精細(xì)態(tài),6P3/2態(tài)分裂為F′=(2,3,4,5)四個(gè)能態(tài);高的里德伯態(tài)由于原子半徑較大,通常不考慮超精細(xì)相互作用,只考慮低軌道角動(dòng)量S,P,D等的精細(xì)結(jié)構(gòu)分裂態(tài).我們利用852 nm激光作為探測(cè)光,509 nm激光作為耦合光,實(shí)現(xiàn)階梯型的里德伯態(tài)EIT.當(dāng)852 nm激光頻率鎖定于6S1/2→6P3/2(F′=5),509 nm激光在6P3/2→57S(D)之間掃描時(shí),在雙光子共振處可以觀測(cè)到階梯型能級(jí)EIT透射峰.室溫原子的多普勒頻移大約在1 GHz左右,對(duì)鎖定于6S1/2→6P3/2(F′=5)的探測(cè)光,當(dāng)特定速度群原子運(yùn)動(dòng)方向與852 nm光束的傳播方向一致時(shí),由于多普勒效應(yīng),其感受到的探測(cè)光頻率共振于6S1/2→6P3/2(F′=3,4),當(dāng)509 nm耦合光掃描到對(duì)應(yīng)的頻率時(shí),可以實(shí)現(xiàn)雙光子共振,觀測(cè)到EIT透射峰.同樣地,對(duì)鎖定于6S1/2→6P3/2(F′=3,4)的探測(cè)光,當(dāng)特定速度群原子運(yùn)動(dòng)方向與852 nm光束的傳播方向相反時(shí),由于多普勒效應(yīng),其感受到的探測(cè)光頻率共振于6S1/2→6P3/2(F′=5),當(dāng)509 nm耦合光掃描到對(duì)應(yīng)的頻率實(shí)現(xiàn)雙光子共振,同樣可以觀測(cè)到EIT透射峰.

對(duì)于與852 nm探測(cè)光同向、速度為v的原子,其相應(yīng)的多普勒頻移為:?P=kPv;原子感受到反向的509 nm耦合光的頻移為:?C=?kCv,其中kP和kC分別為探測(cè)光和耦合光的波矢量.則在此三能級(jí)系統(tǒng)中總的頻移為?=?P+?C=(1?kC/kP)?P=?(λP/λC?1)?P=?0.67?P,(λP/λC?1)為多普勒因子［6］.當(dāng)掃描509 nm耦合光頻率時(shí),若將6S1/2→6P3/2(F′=5)→57S(D)峰作為參考頻率標(biāo)準(zhǔn),6S1/2→6P3/2(F′=3,4)→57S(D)透射峰的相對(duì)頻率移動(dòng)會(huì)受多普勒匹配的影響. 峰的強(qiáng)度依賴于探測(cè)光的失諧量和光強(qiáng),峰的間隔依賴于多普勒頻移、探測(cè)光和耦合光的頻率. 對(duì)于里德伯態(tài)的精細(xì)分裂譜線,其峰的間隔不依賴于多普勒效應(yīng)造成的能級(jí)移動(dòng).即對(duì)于6S1/2→6P3/2(F′)→57D3/2和6S1/2→6P3/2(F′)→57D5/2的EIT譜線間隔,只依賴于原子能級(jí)57D3/2和57D5/2的能級(jí)差.對(duì)于速度相關(guān)的EIT,在多普勒效應(yīng)范圍內(nèi),可以利用確定頻率(30 MHz)的射頻邊帶調(diào)制,獲得確定間隔的EIT信號(hào)作為頻率標(biāo)準(zhǔn),實(shí)現(xiàn)對(duì)原子低激發(fā)態(tài)能級(jí)(6P3/2)的超精細(xì)分裂和里德伯態(tài)(57D)的精細(xì)分裂測(cè)量.在～GHz多普勒效應(yīng)頻移范圍,這種速度選擇的射頻邊帶調(diào)制技術(shù)可以連續(xù)調(diào)諧射頻頻率,EIT頻譜的透射峰信號(hào)反映了里德伯態(tài)原子的能級(jí)間隔,依賴于多普勒匹配和雙光子共振,不敏感于單色激光頻率的絕對(duì)值.因此,這種射頻邊帶調(diào)制的方法不僅可以測(cè)量原子里德伯態(tài)的能級(jí)間隔,同樣可以測(cè)量里德伯態(tài)相互作用造成的相對(duì)能級(jí)移動(dòng).

3 實(shí)驗(yàn)測(cè)量

實(shí)驗(yàn)裝置如圖2所示,探測(cè)光和耦合光聚焦后在置于磁屏蔽筒中的銫原子氣室重合.原子氣室的長(zhǎng)度為20 mm,兩束光的聚焦腰斑直徑約為100μm.探測(cè)光光源為低噪聲的852 nm外腔半導(dǎo)體激光器(external-cavity diode laser,ECDL),典型線寬為MHz量級(jí).探測(cè)光經(jīng)過(guò)波導(dǎo)型的電光調(diào)制器(EOM)實(shí)現(xiàn)光信號(hào)的射頻調(diào)制,信號(hào)源鎖定于銣原子鐘.耦合光的種子源為1018 nm的半導(dǎo)體激光器,線寬為MHz量級(jí),波長(zhǎng)調(diào)諧范圍為1016—1020 nm;經(jīng)光纖放大器放大,最大輸出功率為5 W.1018 nm激光經(jīng)四鏡環(huán)形腔倍頻系統(tǒng)可獲得約1 W的509 nm倍頻激光.倍頻晶體為周期極化的PPKTP晶體(1 mm×2 mm×10 mm).探測(cè)光利用銫原子飽和吸收譜(SAS)實(shí)現(xiàn)頻率鎖定和頻率識(shí)別;509 nm倍頻腔利用Pound-Drever-Hall(PDH)射頻邊帶調(diào)制［26］鎖定于1018 nm激光.在實(shí)驗(yàn)中,調(diào)制信號(hào)(4.7 MHz)加載到1018 nm激光器的射頻調(diào)制端口,腔透射信號(hào)經(jīng)混頻低通濾波解調(diào)獲得誤差信號(hào),利用誤差信號(hào)反饋控制倍頻腔的壓電陶瓷,實(shí)現(xiàn)倍頻腔腔長(zhǎng)的鎖定.

圖2 (網(wǎng)刊彩色)實(shí)驗(yàn)裝置示意圖 OI為光隔離器,λ/2為半波片,λ/4為四分之一波片,EOM為波導(dǎo)型的電光調(diào)制器,PBS為偏振分光棱鏡,SAS為飽和吸收譜實(shí)驗(yàn)系統(tǒng),Lens為聚焦透鏡,DM為852 nm高透509 nm高反的雙色鏡,OFA為1018 nm光纖放大器,μ-metal為納特斯拉的磁屏蔽系統(tǒng),PPKTP為溫度匹配倍頻晶體,PZT為壓電陶瓷,PD為探測(cè)器,Servo system為PDH鎖頻系統(tǒng)Fig.2.(color online)The schematic diagram of experimental set-up:Where OI,optical isolator;λ/2,halfwave plate;λ/4,quarter-wave plate;EOM,waveguide electro-optic modulator;PBS,polarization prism;SAS,the experimental system of saturated absorption spectra;Lens,focusing lens;DM,dichroic mirror that has high transmittance at 852 nm while high re fl ectivity at 509 nm;OFA,optical fi ber ampli fi er of 1018 nm;μ-metal,magnetic shielding system;PPKTP,the crystal of second harmonic generation system;PZT,piezoelectric ceramic;PD,photoelectric detector;Servo system,the frequency locking system.

實(shí)驗(yàn)中,852 nm激光運(yùn)轉(zhuǎn)于6S1/2→6P3/2(F′=3,4,5)吸收峰附近;509 nm激光倍頻腔鎖定于1018 nm激光上,掃描1018 nm激光頻率,掃描頻率為12 Hz,相應(yīng)的509 nm倍頻光也跟隨掃描.509 nm耦合光的功率為200 mW,852 nm探測(cè)光的功率為0.3μW.圖3為6S1/2→6P3/2(F′)→57S的EIT信號(hào).調(diào)諧探測(cè)光共振于6S1/2→6P3/2(F′=4)躍遷,耦合光波長(zhǎng)為509.2943 nm(對(duì)應(yīng)6P3/2(F′)→57S的躍遷),PPKTP晶體匹配溫度66.48°C.掃描1018 nm激光,由于多普勒效應(yīng),可觀測(cè)到6S1/2→6P3/2(F′=3,4,5)→57S的三條譜線,譜線相對(duì)于6S1/2→6P3/2(F′=5)→57S的間隔分別為169.2 MHz和304.8 MHz,如圖3(a)所示.通過(guò)EOM對(duì)探測(cè)光進(jìn)行射頻調(diào)制,調(diào)制頻率為30 MHz,每個(gè)EIT透射峰出現(xiàn)兩個(gè)邊帶,考慮到509 nm和852 nm的多普勒匹配,邊帶到主峰的間隔約為50 MHz,如圖3(b)所示. 以邊帶到主峰之間的頻率間隔(50 MHz)作為頻率標(biāo)準(zhǔn)可以標(biāo)定光譜線的間隔.

圖3 (網(wǎng)刊彩色)6S1/2→6P3/2(F′)→57S的EIT信號(hào) (a)6P3/2態(tài)的超精細(xì)分裂,圖中紅線為信號(hào)發(fā)生器掃描信號(hào),通過(guò)(b)中的標(biāo)定方式可將頻率標(biāo)定,圖中以6S1/2→6P3/2(F′=4)→57S為零頻參考點(diǎn);(b)透射峰頻率間隔的標(biāo)定,在852 nm的探測(cè)光上施加30 MHz射頻調(diào)制,每個(gè)EIT透射峰出現(xiàn)兩個(gè)邊帶,由于坐標(biāo)橫軸為509 nm耦合光的頻率變化,考慮多普勒匹配,邊帶到主峰的間隔約為50 MHz,由此標(biāo)定透射峰之間的頻率間隔Fig.3.(color online)The EIT signal of the transition 6S1/2→ 6P3/2(F′)→ 57S:(a)The hyper fi ne splitting of 6P3/2,the red line shows the scanning signal of the function generator,the zero point frequency responds to the transition 6S1/2→ 6P3/2(F′=4)→ 57S;(b)the frequency calibration to the interval of transmission peaks,with a 30 MHz modulation to the probe laser,the peak of the EIT signal generated two sidebands,considering the Doppler matching,the interval from the main peak to its sidebands is 50 MHz;thereby we can calibrate the frequency interval between the transmission peaks.

圖4 (網(wǎng)刊彩色)6S1/2→6P3/2(F′)→57D的EIT信號(hào) (a)6P3/2的超精細(xì)分裂和57D態(tài)的精細(xì)分裂.圖中紅線為信號(hào)發(fā)生器掃描信號(hào),由于多普勒效應(yīng),掃描耦合光會(huì)產(chǎn)生6S1/2→6P3/2(F′=3,4,5)→57D5/2(圖中透射峰4,5,6)和6S1/2→6P3/2(F′=3,4,5)→57D3/2(圖中1,2,3)的透射峰,圖中透射峰3和6(或1和4,2和5)的間隔即為57D3/2和57D5/2的能級(jí)間隔;(b)透射峰間隔的標(biāo)定,如圖3(b)中所示,在852 nm探測(cè)光上施加30 MHz的頻率調(diào)制,通過(guò)EIT標(biāo)定了耦合光掃描的相對(duì)頻率及透射峰的間隔Fig.4.(color online)The EIT signal of the transition 6S1/2→ 6P3/2(F′)→ 57D:(a)The hyper fi ne splitting of the state 6P3/2and the fi ne splitting of the Rydberg state 57D,the red line shows the scanning signal of the function generator,because of Doppler e ff ect,the spectra of 6S1/2→ 6P3/2(F′)→ 57D transition can be observed,the transmission peaks 1,2,3 corresponding to the transition 6S1/2→ 6P3/2(F′)→ 57D3/2 and 4,5,6 corresponding to the transition 6S1/2→ 6P3/2(F′)→ 57D5/2,the interval between transmission 3 and 6(1 and 4 or 2 and 5)is the splitting of 57D3/2and 57D5/2;(b)the frequency calibration to the interval of transmission peaks.

表1 57D態(tài)精細(xì)分裂實(shí)驗(yàn)結(jié)果Table 1.The experimental results of the 57D fi ne splitting.

調(diào)諧耦合光波長(zhǎng)至509.23625nm或509.23655 nm,對(duì)應(yīng)于6P3/2(F′)→57D5/2(D3/2)躍遷,晶體匹配溫度為63.85°,觀察到6S1/2→6P3/2(F′)→57D的光譜,如圖4所示.圖4(a)為中間態(tài)的超精細(xì)分裂和里德伯態(tài)的精細(xì)分裂.峰1,2,3和4,5,6分別為6S1/2→6P3/2(F′)→57D3/2和6S1/2→6P3/2(F′)→57D5/2的EIT透射峰.對(duì)于每個(gè)里德伯態(tài)的精細(xì)結(jié)構(gòu),由于多普勒效應(yīng),可觀測(cè)到6S1/2→6P3/2(F′=3,4,5)→57D三條譜線,譜線相對(duì)于6S1/2→6P3/2(F′=5)→57D的間隔分別為169.2 MHz(F′=4)和304.8 MHz(F′=3).圖4(b)為射頻調(diào)制的EIT譜線,852 nm激光所加調(diào)制頻率為30 MHz.

利用邊帶標(biāo)定的方法測(cè)量了6P3/2態(tài)的超精細(xì)分裂(譜線間隔與多普勒效應(yīng)有關(guān))和57D態(tài)的精細(xì)分裂(譜線間隔與多普勒效應(yīng)無(wú)關(guān)),結(jié)果如表1所列.其中躍遷能級(jí)為EIT譜線各透射峰對(duì)應(yīng)的躍遷線;?P為各EIT透射峰對(duì)應(yīng)探測(cè)光相對(duì)于6S1/2(F=4)→6P3/2(F′=5)失諧量的理論值;?C為對(duì)應(yīng)的耦合光失諧量,由?C=?kCv=?(kC/kP)?P=?(λP/λC)?P式得出;EIT譜線分裂計(jì)算值為計(jì)算得到的EIT透射峰的間隔,其中6S1/2(F=4)→6P3/2(F′=5)→57D3/2的計(jì)算值為由量子虧損理論計(jì)算得出的57D5/2和57D3/2態(tài)的能級(jí)差,即57D5/2和57D3/2的精細(xì)分裂間隔,具體計(jì)算由Rydberg-Ritz方程［27,28］:

給出,其中n,l,j分別為主量子數(shù)、軌道角動(dòng)量量子數(shù)和總角動(dòng)量量子數(shù);E∞和E(n,l,j)分別為銫原子的電離能和相應(yīng)能級(jí)的能量;δn,l,j為量子虧損數(shù);數(shù)據(jù)參考文獻(xiàn)［27,28］,計(jì)算可得57D態(tài)的精細(xì)分裂為346.8 MHz,其他值根據(jù)?=?P+?C=(1?kC/kP)?P及57D5/2和57D3/2態(tài)的能級(jí)差計(jì)算得出各EIT譜線對(duì)應(yīng)于6S1/2(F=4)→6P3/2(F′=5)→57D3/2躍遷的頻率間隔;測(cè)量值為實(shí)驗(yàn)標(biāo)定后得到的各EIT譜線間隔,最終給出了各譜線間隔測(cè)量值與理論計(jì)算值的偏差.測(cè)量得到的57D5/2和57D3/2的EIT光譜間隔為(354.7±2.5)MHz,與理論計(jì)算的結(jié)果346.8 MHz(由6P3/2(F′)→57D5/2和6P3/2(F′)→57D3/2躍遷的激光頻率差給出)基本一致,測(cè)量精度主要受EIT的線寬和耦合光頻率掃描的非線性影響.如圖3和圖4中所示,6S1/2→6P3/2(F′=5)→57D躍遷對(duì)應(yīng)的EIT譜線線寬約為13 MHz,這主要是由于其自然線寬(5.2 MHz)受多普勒效應(yīng)影響加寬,探測(cè)光和耦合光的功率展寬及原子的碰撞展寬.EIT透射峰的線寬加寬會(huì)導(dǎo)致峰值處的測(cè)量精度降低.耦合光頻率掃描的非線性會(huì)使頻率標(biāo)定產(chǎn)生偏差,從而影響測(cè)量的精度.測(cè)量誤差主要來(lái)源于1018 nm激光器壓電陶瓷電致伸縮的非線性導(dǎo)致的激光頻率的非線性掃描.

4 結(jié) 論

通過(guò)四鏡環(huán)形腔倍頻獲得了瓦級(jí)509 nm激光,基于509 nm激光和852 nm激光的雙光子激發(fā)過(guò)程實(shí)現(xiàn)了133Cs里德伯態(tài)制備,基于階梯型能級(jí)的EIT獲得了里德伯態(tài)光譜.基于速度選擇的射頻邊帶調(diào)制技術(shù),我們測(cè)得主量子數(shù)n=57的里德伯態(tài)原子的57D5/2和57D3/2的精細(xì)結(jié)構(gòu)分裂為(354.7±2.5)MHz,與理論計(jì)算值的偏差為2.3%.基于該實(shí)驗(yàn)技術(shù)的光譜間隔測(cè)量,目前的測(cè)量精度主要受EIT的線寬和耦合光頻率掃描的非線性影響.該方案不僅可以用于里德伯態(tài)能級(jí)的精密測(cè)量,也可以用來(lái)測(cè)量里德伯原子之間的強(qiáng)相互作用導(dǎo)致的相對(duì)能級(jí)移動(dòng).

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Measurement of the fi ne structure of cesium Rydberg state?

Pei Dong-Liang1)2)He Jun1)2)3)?Wang Jie-Ying1)2)Wang Jia-Chao1)2)Wang Jun-Min1)2)3)?
1)(Institute of Opto-Electronics,Shanxi University,Taiyuan 030006,China)
2)(State Key Laboratory of Quantum Optics and Quantum Optics Devices,Shanxi University,Taiyuan 030006,China)
3)(Collaborative Innovation Center of Extreme Optics,Taiyuan 030006,China)

The spectra of Rydberg atoms are of great signi fi cance for studying the energy levels of Rydberg atoms and the interaction between neutral atoms,especially,the high-precision spectra of Rydberg atoms can be used to measure the energy level shifts of Rydberg atoms resulting from the dipole-dipole interactions in room-temperature vapor cells.In this paper we report the preparation of cesium Rydberg states based on the cascaded two-photon excitation of 509 nm laser and 852 nm laser in opposite,and the measurements of the fi ne structure of cesium Rydberg states.In this experiment,the 509 nm laser is generated by the cavity-enhanced second-harmonic generation from 1018 nm laser with a periodicallypoled KTP crystal and has a maximum power of about 1 W,and the 852 nm probe laser is provided by an external-cavity diode laser with a maximum output power of 5 mW and a typical linewidth of 1 MHz.By scanning the frequency of 509 nm coupling laser,it is presented that the Doppler-free spectra based on electromagnetically-induced transparency(EIT)of 509 nm coupling laser and 852 nm probe laser.The velocity-selective EIT spectra are used to study the spectral splitting of 6S1/2—6P3/2—57S(D)ladder-type system of cesium Rydberg atoms in a room-temperature vapor cell.The powers of 852 nm probe laser and 509 nm coupling laser are 0.3μW and 200 mW,respectively.Their waist radii are both approximately 50 μm.The intervals of hyper fi ne splitting of the intermediate state 6P3/2(F′=3,4,5)and fi ne splitting of 57D3/2and 57D5/2Rydberg states are measured by a frequency calibrating.Concretely,the velocity-selective spectrum with a radio frequency(RF)modulation of 30 MHz is used as a reference to calibrate the Rydberg fi ne-structure states in the hot vapor cell,where the RF frequency precision is smaller than a hertz on long time scales and the EIT linewidth is smaller than 13 MHz.The experimental value of the fi ne structure splitting of 57D3/2and 57D5/2Rydberg states is(354.7±2.5)MHz,that is in consistence with the value of 346.8 MHz calculated by Rydberg-Ritz equation and quantum defects of 57D3/2and 57D5/2Rydberg states.The experimental values of hyper fi ne splitting of intermediate state 6P3/2(F′=3,4,5)are also coincident with the theoretical calculated values.The dominant discrepancy existing between the experimental and calculated results may arise from the nonlinear correspondence of the PZT while the 509 nm wavelength cavity is scanned,and the measurement accuracy in fl uenced by the spectral linewidth.The velocityselective spectroscopy technique can also be used to measure the energy level shifts caused by the interactions of Rydberg atoms.

Rydberg state,electromagnetically induced transparency, fi ne structure,hyper fi ne structure

20 April 2017;revised manuscript

6 July 2017)

(2017年4月20日收到;2017年7月6日收到修改稿)

10.7498/aps.66.193701

?國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):61475091,61227902)、國(guó)家重點(diǎn)研發(fā)計(jì)劃(批準(zhǔn)號(hào):2017YFA0304502)和山西省高等學(xué)?？萍紕?chuàng)新項(xiàng)目(批準(zhǔn)號(hào):2017101)資助的課題.

?通信作者.E-mail:hejun@sxu.edu.cn

?通信作者.E-mail:wwjjmm@sxu.edu.cn

?2017中國(guó)物理學(xué)會(huì)Chinese Physical Society

PACS:37.10.–x,32.80.–t,42.50.Hz

10.7498/aps.66.193701

*Project supported by the National Nature Science Foundation of China(Grant Nos.61475091,61227902),the National Key Research and Development Program of China(Grant No.2017YFA0304502),and the Scienti fi c and Technological Innovation Programs of Higher Education Institutions in Shanxi Province,China(Grant No.2017101).

?Corresponding author.E-mail:hejun@sxu.edu.cn

?Corresponding author.E-mail:wwjjmm@sxu.edu.cn