I(ΔL) I(Δ0) τ(δ) α(δ) [1] (1) [2-5] α(δ) Δ [12] α(δ)= 3λ2 N a -N b [6] 2π 1+4(Δ/Γ) 2 ( 2) λ Γ N a N b N=N a+n b [7] 60 3 [8] 70 ( 25) 40% [9] [1

33 10 Vol.33No.10 2013 10 ACTA OPTICASINICA October2013 ( 030006) - ; ; O431.2 A doi:10.3788/aos201333.1002001 ExperimentalMeasurementsandAccurateSimulationoftheOptical ThicknessoftheCesium Atom Vapor Guo Miaojun WuJinze HuangJingbo WangHongli ZhouHaitao GaoJiangrui ZhangJunxiang (State KeyLaboratoryof Quantum Opticsand Quantum OpticsDevicesInstituteof Opto-Electronics Shanxi University TaiyuanShanxi030006China) Abstract Theexperimentalmeasurementsoftheopticalthicknesofthecesiumatomvaporinteractingwiththelights ofdifferentintensitiesand polarizationsatdifferentenergylevelsandtemperaturesaredemonstrated.therate equationsof each Zeeman sublevelsare established theoreticaly and the numericalsolution oftime-dependent absorptioncoefficientsisobtainedbysolvingtherateequationswithrunge-kutamethods.theaverageabsorption coefficientsatresonantfrequencycanbecalculatedbynumericalintegrationbecauseoftheeffectsofthethermal motionofatomsand beam width.thefitingoftransmisionspectrum ofthecesium vaporceliscarried out accuratelybyusingthebeer slawandthentheaccuratevaluesoftheopticalthicknesofthecesiumatom vaporare obtainedfinaly.theoreticalanalysisandexperimentalresultshow thathighertemperaturesleadtolargeroptical thickneswhilehigheropticalintensitiesresultinsmaleropticalthicknes. Key words atomicandmolecularphysics;opticalthicknes;absorptioncoefficients;transmision;beer slaw OCIScodes 020.1335;020.2930;300.1030 1 :2013-05-07; :2013-05-24 : (1127421061108003) (2010CB923102) (61121064) : (1985 ) E-mail:guomiaojun85@sina.com : (1966 ) E-mail:junxiang@sxu.edu.cn( ) www.opticsjournal.net 1002001-1

I(ΔL) I(Δ0) τ(δ) α(δ) [1] (1) [2-5] α(δ) Δ [12] α(δ)= 3λ2 N a -N b [6] 2π 1+4(Δ/Γ) 2 ( 2) λ Γ N a N b N=N a+n b 100 1 [7] 60 3 [8] 70 ( 25) 40% [9] [10-11] [12] 1 (a) D1 ;(b) ig.1 (a)energylevelsofcesium D1line; (Zeeman) (b)polarizationconfigurationsandthequantizationaxis 1(a) 133 CsD1 =3 =4 m ; =3 =4 m 32 m = m π ; 2 m =m +1 σ + ; m =m -1 σ - 1(b) Δ (QA) [12] L QA : 1(a) π I(ΔL)=I(Δ0)exp[-τ(Δ)]= I(Δ0)exp[-α(Δ)L] (1) ; QA 1(a) σ + ; 1002001-2

: 1(a) σ - q=1-1 =3 Δ =Δ; =4 Δ = Δ-Δ43 hδ43 珔 (3) α(δ) Δ α(δ)= 3λ2 2π N m =-1 m = m =- N m - N m +q 1+4(Δ /Γ) ( 3) 2 N m P m Q m m = ρ N m + N m = N;q=0±1; m m ρ m m m =- = 4 9 =-1 π q=0; σ + σ - N [13] dp m dt =- =-1 R m m +q Ω 2 P m -Q m +q + Γ 1+4[(Δ +kv)/γ] 2 =3 7 dp m dt = m =m +1 m =m R m -1 =-1 m =m +1 m =m -1 =-1 R m m ΓQ m. (4) m ΓQ m. (5) (5) (4) ( 133 Cs6 2 S 1/2 2π 9.2GHz) 16 dq m dt = R m m -q =-1 P m -q -Q m - Γ 1+4[(Δ +kv)/γ] 2 Ω 2 m = m +1 m = m -1 = +1 R m m ΓQ m = = -1 R m Ω 2 P m -q -Q m m -q -ΓQ =-1 Γ 1+4[(Δ +kv)/γ] 2 m. (6) (4)~(6) k v Ω R m [14-15] R m m = m d q er m 2 J d er J = (2J+1)(2 +1)(2+1) J J 1 2 I 133 CsD1 J d er J = J =1/2 m 1 { }( m q -m ) 2 [ ] (7) d er J =1/2 =2.702 10 29 C md er d er q d q (3) J I α(δt)= 3λ2 =I+Jm ; 6-j 3-j R m m [14] 15 ~20 fd(v)= 1 133 CsD1 32 槡 πu exp [ - v 2 (9) u ] (4)~(6) 32 u = 槡 2k BT/ m (10) fd(v) u 0 16 k B T m t = 0 P m (0) = 1/16 Q m (0)=0 1002001-3! 2π -! R m m +q dvfd(v)n =-1 m =- P m -Q m +q 1+4[(Δ +kv)/γ] 2 ( 8) ( )

H(t) 2a H(t)= G(tl)(l)dl= 0 [ ] α(δt) H(t) [13] H(t) a 2 ig.2 Schematicdiagramofexperimentalarrangement l λ/2 l (l)= 2a 槡 4a 2 2 -l. (11) l t 4 : G(tl)= ml2 exp - ml2 k BTt ( 3 2k BTt ). (12) 2 λ/2 1 t -1+ 槡 π(1+2η 2 )exp(-η 2 )erfi( η 2η ) ( 13) η =2a/(ut)erfi( η )=erf(iη )/ ierf(iη ) α(δ) 珔! α(δ)= 珔 α(δt)h(t)dt. (14) 0 τ(δ)= α(δ)l. 珔 (15) 10 16 2.2 10 17 0.6 10 18 m -3 - (4)~(6) (8) 3(a) =4 =34 π (14) σ + 3(b) =3 = (1) (15) 34 π σ + 3 4 3 3 2 4(a) =4 (ECDL) λ/2 =34 π σ + 4(b) (PBS) L=75mm =3 =34 π σ + ( ) 4 (PD) λ/4 ; λ/4 4 1 Ω=0.32Γ 1 mm =4 =34 1.412μW PD T=50 λ/2 3 1.412μW ( 0.5mm) Ω=0.32Γ 25 50 70 N T 25 50 70 N 4.2 4 1 PBS 1002001-4

: =3 =3 =4 =3 =3 =4 3 Ω=0.32Γ (Γ=2π 4.6 MHz) (a)=4 =34 π σ + ;(b)=3 =34π σ + ig.3 TransmissionspectrumversuslightfrequencydetuningfordiferenttemperaturesatΩ=0.32Γ (Γ=2π 4.6 MHz). (a)πconfigurationandσ + configurationat=4 =34;(b)πconfigurationandσ + configurationat=3 =34 4 (a)=4 =34π σ + ; (b)=3 =34π σ + ig.4 Theoreticalcalculatedopticalthicknessversuslightfrequencydetuningfordiferenttemperatures.(a)π configurationandσ + configurationat=4 =34;(b)πconfigurationandσ + configurationat=3 =34 1 Ω=0.32Γ τ Table1 Opticalthicknessesofcesiumatomvaporwithdiferentatomvaportemperatures andlightpolarizationsatresonantfrequencywhenω=0.32γ T=25 T=50 T=70 π σ + π σ + π σ + 4 3 2.05 1.96 10.39 9.94 27.63 26.44 4 4 1.4 1.47 7.12 7.45 18.94 19.82 3 3 0.68 0.71 3.47 3.59 9.22 9.54 3 4 2.05 1.96 10.39 9.94 27.63 26.44 1002001-5

5 T=50 6 5 0.404 1.412 4.04μW Ω=0.17Γ0.32Γ0.54Γ 6(a) =4 = 5(a) 34 π σ + 6(b) =4 =34 π σ + =3 =34 π σ + 5(b) =3 =34 π σ + 6 5 5 T=50 Γ=2π 4.6 MHzN=2.2 10 17 m -3 (a)=4 =34π σ + ;(b)=3 =34π σ + ig.5 TransmissionspectrumversuslightfrequencydetuningfordiferentlightintensitiesandpolarizationsatT=50. Theparametersare:Γ=2π 4.6 MHzN =2.2 10 17 m -3.(a)πconfigurationandσ + configurationat= 4 =34;(b)πconfigurationandσ + configurationat=3 =34 6 (a)=4 =34π σ + ; (b)=3 =34π σ + ig.6 ResultsofcalculationsforopticalthicknessversuslightfrequencydetuningfordiferentRabifrequencies.(a)π configurationandσ + configurationat=4 =34;(b)πconfigurationandσ + configurationat=3 =34 1002001-6

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