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\noi {\sc Excitonic quantum coherences and correlations in
semiconductor quantum wells
}
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\noi \hspace*{2.6cm} \begin{minipage}{12.5cm}
Rolf Binder\\
Optical Sciences Center  \\
University of Arizona \\
Tucson, Arizona 85721 \\
USA
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\noi {\sc Abstract}
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Semiconductor quantum wells offer unique and exciting possibilities
for the investigation of quantum correlations and quantum coherences. 
Existing advanced experimental methods in ultrafast nonlinear spectroscopy go hand 
in hand with advanced theoretical methods applied to quantum mechanical coherences 
and correlations. The main focus of this talk
will be on two-exciton correlations as well as radiative and non-radiative quantum 
coherences in quantum wells. These are examples of optically driven quantum coherences 
and non-equilibrium correlations. In the lowest-order nonlinear optical response 
(the so-called $\chi^{(3)}$ regime), the main issues are not related to problems such 
as screening of the Coulomb potential (which are usually important issues in Coulomb 
systems). Rather, in this regime the correlation between excitons (including the 
formation of coherent biexcitons and the role of two-exciton continuum states) are the 
central concerns. On the basis of a T-matrix analysis inolving an excitonic T-matrix 
we will elucidate, in this talk,  several nonlinear optical effects observed in recent 
experiments. After a brief discussion of the theoretical foundation, including the 
interface between conventional Green's functions techniques and the dynamics-controlled 
truncation formalism (a generalized density matrix approach), we discuss the excitonic 
T-matrix analysis of excitons in two dimensions and the ramifications of the spatial 
dimension being two in the case of quantum wells. The application and verification of 
the excitonic T-matrix description includes the system consisting of a semiconductor 
quantum well inside an optical microcavity as well as single quantum well systems. Clear 
signatures of quantum coherences and  two-exciton correlations can be identified in 
four-wave mixing signals as well as differential absorption spectra. In particular, we 
discuss evidence of  two-exciton continuum correlations that cannot be understood within 
the second Born approximation, and evidence for the formation of coherent biexcitons in 
single quantum wells.

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