Hierarchy of density matrices in coherent semiconductor optics

Signatures of the electromagnetic field quantization in the nonlinear optical response of excitons

“…As we have pointed out in the introduction, and as it is known from semiconductor nonlinear optics [9,26], the theory describing the dynamics of the semiconductor electrons interacting with a light field has the structure of an open hierarchy of dynamical variables. Whenever one is dealing with an open hierarchy of dynamical objects, one is facing the problem of finding an appropriate termination procedure.…”

“…Whenever one is dealing with an open hierarchy of dynamical objects, one is facing the problem of finding an appropriate termination procedure. Here we present an extension of the truncation procedure introduced by Axt and Stahl [9] to include the quantization of the light field and polariton effects. Such a truncation scheme is analogous to the classification scheme of nonlinear optical processes, where the coherent input light beam represents the expansion parameter.…”

“…Within this approach, once the perturbative order in the excitation strength has been fixed, the Coulomb correlation contributing to the optical response up to fixed order is included exactly. By applying the DCTS, it can be shown that the third order nonlinear reponse depends only on one eh-pair subspace (excitons) and the two eh-pair subspace (biexcitons) [9], hence the third order nonlinear response is intimately tied to the dynamics of two and four-particle (two electrons and two holes) states.Östreich et al [10], provided an exact numerical evaluation of the four particle correlation determining the third order nonlinear response.…”

Semiconductor polarization dynamics from the coherent to the incoherent regime: Theory and experiment

“…The approach was tested against experiment in the case of bulk three-dimensional ͑3D͒ GaAs in high magnetic field and it was found to describe well the transition from low to intermediate densities, i.e., for N eh ϭ1.5ϫ10 ϫ10 16 cm Ϫ3 . Clearly, it is interesting to probe the range of applicability of the theory.…”

“…The DCTS formalism has been developed for describing the coherently driven e-h pair system generated in the initial phase following laser excitation of the semiconductor in its ground state. [15][16][17][18][19][20] The NGF approach is well suited for treating the effects of incoherent scattering and has been successfully applied to describe the non-Markovian behavior of relaxation processes. 9,[21][22][23] To obtain a thorough understanding of the evolution of e-h pair systems from initial coherently driven states to relaxed ones it is important to have at hand a theoretical description that can bridge the two cases.…”