Experimental Research On Coherent Hole-burning In Atomic Rubidium Vapor

This thesis is mainly discussing the experimental research work onlambda mode Coherent Hole-burning (CHB) in atomic rubidium vapor. Inorder to explain and illustrate the phenomena better, we add the related theory,which not only enriches the substances but also makes the demonstrationmore precise and experiment more convincing. In the first part, we investigate the optical hole-burning and atomiccoherence phenomena, and analyze them theoretically. Then we combinethese two theories and bring forward a new theory called CoherentHole-burning. We demonstrate the lambda mode Coherent Hole-burning in athree-level atomic system, and illustrate it in detail. A certain laser can saturate a group of resonant atoms in the populationdistribution when passing through a Doppler-broadened media. A "hole" willbe burned in the absorbing spectrum if another probe beam scans in thevicinal frequency, which is usually called "Bonnet hole" or "Lamb hole".We analyze theElectromagneticallyInduced Transparency(EIT) theoretically. EITis a kind of phenomenaof atomic coherence,which utilizes quantumcoherence generated bya coupling field to makean otherwise opaquemedium transparent to aresonant probe field in a narrow spectral window. FIG II-1 illustrates thephenomenon by theoretical curve, with Doppler Effect considered;EITwindow can beseen clearly.FIG II-1 Theoretical EIT Window,with Doppler Effect Considered-200 -100 0 100 2000123456Ωc=20.0Ωc=40.0αΔpΩc=40.Now we ΔΔΔ3calculate theCoherentHole-burning in athree-levellambda modeatomic system.FIG II-2 showsthe related energylevels.spcFIG II-2 Three-level LambdaMode Atomic Systemω s ,Esωc ,Ecωp ,EpΓ31Γ3212The Hamilton of interaction picture in the atomic system is,H I eiHatHbeiHat( sc)22s33[Gs13Gc23c.c]= ? =Δ?Δ+Δ?++ (II.1)We use the equation of density operator,??ρ t =?hi [H I,ρ] ?12{Γ ,ρ} +Λρ (II.2)The following equations can be concluded,ρ? 11 =iG s( ρ31?ρ13)+Γ31ρ33+Γs(ρ22?ρ11) (II.3a)ρ? 22 =iG c( ρ32?ρ23)+Γ32ρ33+Γs(ρ11?ρ22) (II.3b)ρ? 12 =[ i (Δs ?Δc)?γ12]ρ12+iGsρ32?iGcρ13 (II.3c)ρ? 13 =(i Δs ?γ13)ρ13+iGs(ρ33?ρ11)?iGcρ12 (II.3d)ρ? 23 =( i Δc ?γ23)ρ23+iGc(ρ33?ρ22)?iGsρ21 (II.3e)ρ11 + ρ22+ρ33=1 (II.3f)*ρ ij = ρji (II.3g)Where Γs represents the population transfer rate between levels 1and2 due to interatomic collisions, and γij refers to the coherence decay ratebetween level i and j . Γ3 1 and Γ32 designate the spontaneous decayrates from level 3 to levels 1 and 2 respectively. ( ) is the Rabifrequency of the saturating (coupling) laser.Gs GcBy utilizing Laplace transform and quantum regression theory, we furtherobtain the absorption spectrum of probe beam as,A( Δ p )=????? μ1 3 2???? +M M31 (3Δ3 ( Δp)pρ )3(11(?∞2)ρ+1 M1(∞32)(?Δρp)2ρ2(3∞2()∞))?M36(Δp)ρ21(∞)???????? (II.4)where M = (i Δp ?iΔs?L)?1 and ρ ij( ∞ )i,j=1→8 are the steady state solutionsof equations(II.3).To consider Doppler effect, we get,AAυ NυdυAυυNπeυ υdυppppp22( )(,)()∞(,)0??∞∞?∞Δ =∫ Δ=∫Δ (II.5)FIG II-3 Absorption Spectrum under Four Arrangements of Light Propagation(a) Coherent Light Forwards, Saturating Light Backwards, Probe Light Forwards(b) Coherent Light Forwards, Saturating Light Backwards, Probe Light Backwards(c) Coherent Light Forwards, Saturating Light Forwards, Probe Light Backwards(d) Coherent Light Forwards, Saturating Light Forwards, Probe Light Forwards-600 -400 -200 0 200 400 6000.00.51.01.52.02.5(a)Absorption (arb.units)Probe detuning (MHz)-600 -400 -200 0 200 400 6000.00.51.01.52.02.5(b)Absorption (arb.units)Probe detuning (MHz)-600 -400 -200 0 200 400 6000.00.51.01.52.02.5 (c)Absorption (arb.units)Probe detuning (MHz)-600 -400 -200 0 200 400 6000.00.51.01.52.02.5 (d)Absorption (arb.units)Probe detuning (MHz)where N 0 is the total number of atoms, andυp =2 kT/m=2RT/Mrepresents the most probable atomic velocity. k is the boltzmanns constant,and T means the temperature of the atomic system. m is the mass of a singleatom. M = NAm shows the atom molar mass, and R = NAkshows the gasconstant.Coherent light acts on the atom system together with saturating light.When utilizing another probe light to scan, four kinds of arrangements of lightpropagation direction are available. FIG II-3 shows the total fourarrangements. We can see clearly, only in the conditions of (a) and (b),Coherent Hole-burnings appear. So we will only consider the above twoarrangements in our experiment.The second part is our experiment on Coherent Hole-burning. We choose87Rb atomic vapor as the media. Four energy levels are concerned. The bottomlevel is 5S1/2, which contains two hyperfine levels (F=1,2) with the distance of6835MHz. The upper lever is 5P1/2 with the distance of 794.978nm to 5S1/2,and it also contains two hyperfine levels (F'=1,2) that both can transfer downto bottom level.The experimental arrangement is illustrated in FIG II-4.The 87Rb atomic vapor contained in a 3cm long cylindrical cell is heatedto the temperature of about 325K. The probe beam with linewidth of about4MHz is provided by an extended cavity diode laser (DL100) and attenuatedto less than 1μW by a Nd filter before it enters the atomic cell. TwoTi:Sapphire lasers (Coherent 899 ring laser) with linewidth of about 500KHz,Ti:Sapphire1 and Ti:Sapphire2, are used to provide the coupling andsaturating beams, respectively. The coupling and saturating beams areorthogonal in polarization and counter-propagate through the atomic cell withthe help of a λ/2 wave plate as well as a pair of polarization beam splitters(PBS). The probe beam, with its polarization parallel to the saturating beam,co-propagates with the coupling beam at a small angle of 0.01rad. The probebeam is always well contained by the other two collinear beams inside theatomic cell, which permits all probed atoms being coherently prepared. Apinhole is placed in front of the ECDL to block the saturating beam and thusprotect the ECDL against feedback. A photodiode is used to detect theabsorption spectrum of the probe beam passing through the atomic cell.1). The probe beam co-propagating with the saturating beam whilecounter-propagating with the coupling beam.FIG II-5 shows the Coherent Hole-burning under different light intensity.We can clearly see that a deep and narrow EIT hole locates in the middle withtwo coherent burning holes on either side of the shoulder. The width & depthof EIT window and the location & depth of the coherent burning hole can beeasily changed by adjusting the light intensity, that is , Rabi frequency. (a')-(c')illustrate the corresponding theoretical figures, and apparently, experimentsaccord with the theory well.2). coupling beam counter-propagating while the saturating beamco-propagating with the probe beam.FIG II-6 shows the Coherent Hole-burning under different detuning ofFIG II-4 Experiment SetupVI 吉 林 大 学 硕 士 论 文ABSTRACT-400 -200 0 200 4000.00.20.40.60.81.0Absorption(arb.units)(a)Probe detuning(MHz)-400 -200 0 200 4000.00.20.40.60.81.0(b)Probe detuning(MHz)-400 -200 0 200 4000.00.20.40.60.81.0(c)Probe detuning(MHz)-400 -200 0 200 4000.00.20.40.60.81.0(b')Probe detuning(MHz)-400 -200 0 200 4000.00.20.40.60.81.0(c')Probe detuning(MHz)-400 -200 0 200 4000.00.20.40.60.81.0(a')Absorption(arb.units)Probe detuning(MHz)FIG II-5 Coherent Hole-burning Under Different LightIntensity (Rabi Frequency)MHzMHzaIWcmIWcmascSC1060(')0.12/4.60/()22Ω=Ω===MHzMHzbIWcmIWcmbscSC1090(')0.12/8.55/()22Ω=Ω===MHzMHzcIWcmIWcmcscSC1560(')0.25/4.60/()22Ω=Ω===coherent light and saturating light. We can observe three coherent burningholes with the central one deepest due to degeneracy. While adjusting thedetuning of the saturating light, we can see the location of the central hole ischanging, together with the other twos. Meanwhile, the sideward CHBs areasymmetric both in position and in depth. (a')-(c') illustrate the correspondingtheoretical figures, and apparently, experiments accord with the theory well.0.-0400 -200 0 200 4000.20.40.60.81.0Absorption(arb.units)(a')Probe detuning(MHz)0.-0400 -200 0 200 4000.20.40.60.81.0(c')Probe detuning(MHz)0.-0400 -200 0 200 4000.20.40.60.81.0(b')Δc=-60MHzΔs=30MHzProbe detuning(MHz)0.-0400 -200 0 200 4000.20.40.60.81.0(a)Absorption(arb.units) Probe detuning(MHz)0.-0400 -200 0 200 4000.20.40.60.81.0(c)Probe detuning(MHz)0.-0400 -200 0 200 4000.20.40.60.81.0(b)Probe detuning(MHz)FIG II-6 Coherent Hole-burning under DifferentDetuning of Coherent and Saturating LightMHzMHzaaSC060()(')Δ=Δ =?MHzMHzbbSC3060()(')Δ=Δ =?MHzMHzccSC3060()(')Δ=?Δ =?In summary, we have experimentally demonstrated the interesting CHBphenomenon in two different propagation schemes of applied laser beams.Four controllable CHBs are observed in the probe absorption spectrum whenthe coupling (saturating) field co-or counter-propagates with the probe field.In the reverse case, however, we instead observe three controllable CHBs withthe middle one being much deeper. Our experimental results are shown to bein good agreement with corresponding numerical simulations (qualitativeanalysis) in the bare-state (dressed-state) representation. The CHB techniquedeveloped here are expected to have potential applications in opticalinformation storage as well as processing.