Theory of nonlinear optical spectroscopy of electron spin co(2)

时间:2025-07-15

We study in theory the generation and detection of electron spin coherence in nonlinear optical spectroscopy of semiconductor quantum dots doped with single electrons. In third-order differential transmission spectra, the inverse width of the ultra-narrow

ispresentedinAppendixA.

g( )=e ( T2)

2

/2

√/(

II.MODELANDTHEORY

ThesystemtobestudiedisasemiconductorQDdopedwithasingleelectron.ThegeometryoftheQDun-deranexternalmagnetic eldandopticalexcitationisshowninFig.1(a)and(c).TheQDisassumedofashapewithsmallthicknessinthegrowthdirectionandrelativelylargeradiusinthelateraldirections,asintheusualcasesof uctuationQDsandself-assembledQDs.3,4,9,10,11Toenablethegenerationandmanipula-tionoftheelectronspincoherencethroughRamanpro-cesses,amagnetic eldisappliedalongalateraldirec-tion(x-axis).Thepropagationdirectionsofthepumpandprobelaserbeamsareclosetothegrowthdirection(z-axis).Thetwoelectronspinstates|± aresplitbythemagnetic eldwithZeemanenergyω0.Thestrongcon nementalongthez-axisinducesalargesplittingbe-tweentheheavyholeandthelightholestates,thustherelevantexcitonstatesarethegroundtrionstates|τ and|τ¯ whichconsistoftwoelectrons(includingthedopedoneandonecreatedbyopticalexcitation)inthesingletspinstateandoneheavyholeinthespinstate|+3/2 and| 3/2 (quantizedalongthez-axiswithnearlyzeroZeemansplitting),respectively.Similarly,wecanalsoneglecttheexcitationofhigherlyingtrions,bi-excitonandmulti-excitonstatessincetheenergyofaddinganexcitonineachcaseiswellseparatedfromenergyofthelowesttrionstates.Theselectionrulesfortheopticaltransitionsaredeterminedbythe(approximate)conser-vationoftheangularmomentumalongthegrowthdirec-tionsothatacircularlypolarizedlightwithpolarizationσ+orσ connectsthetwoelectronspinstatestothetrionstate|τ orτ¯ ,respectively[seeFig.1(b)].TherelaxationprocessesinthesystemareparameterizedbytheexcitonrecombinationrateΓ1,theexcitondephas- 1

ingrateΓ2,thespinrelaxationrateT1,andthespin

1

dephasingrateT2.Theinhomogeneousbroadeningleadstoarandomcomponent totheZeemansplitting:ωc=

FIG.dot,(b)op-tical

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