Theory of nonlinear optical spectroscopy of electron spin co(3)

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

matrixcanbeexpandedas

ρα,β( )=2πEj···EkEm···El

j,...,k;m,...,l

×ρα,β

(j···km¯···¯l)

δ j···km¯···¯l,

(2)

where j···km¯···¯l≡ j+···+ k ( m+···+ l).The

¯···¯l)

derivationofthedensitymatrixcomponentρ(j···kmuptothe fthorderislengthybutstraightforward.The nalresultisaveragedwiththeinhomogeneousbroadeningdistributiong( ).

III.

RESULTSANDDISCUSSIONS

Thelinearopticalsusceptibilityisgivenby

g( )(j)

ρ=