The Exciton-Exciton Continuum and Its Contribution to Four-Wave Mixing Signals

Abstract

The combined influence of biexcitons and the two‐exciton scattering continuum is analyzed. The analysis is based on a density matrix description of a two‐band semiconductor accounting for mean‐field contributions, bound biexcitons and the correlated parts of the two‐exciton scattering continuum on a common footing. Consistent with the microscopic formulation, the influence of biexcitons as well as that of the two‐exciton continuum is represented by a correlation kernel which is obtained from an integral equation. For a one‐dimensional model four‐wave mixing signals are calculated solving numerically the resulting coupled nonlinear equations for excitation conditions in the vicinity of the 1s resonance. A strong compensation between the exciton–exciton continuum and the mean‐field contribution is found for all excitation conditions studied. Surprisingly, biexcitonic signatures turn out to be enhanced when continua are included in the description.

Polariton interactions in semiconductor microcavities

“…To this aim, we first rewrite the Hamiltonian of Eq. (2) using the lower polariton basis defined as p lp = Xx + Cĉ and neglect all terms that include upper polaritons [63] …”

“…Therefore, the inclusion of the biexciton state through the term g bx and a calculation beyond the Born approximation are necessary to explain the interactions between excitons with antiparallel spins [63,64]. For example, such a calculation has been performed in Refs.…”

Spin anisotropic interactions of lower polaritons in the vicinity of polaritonic Feshbach resonance

“…In the case of GaAs quantum well, it is known that the bare exciton-exciton interaction potentialW +− (q) includes one molecular bound state, which is nothing but the biexciton state considered in the main text. In addition to the biexciton, several calculations and experiments proved that the bare exciton-exciton interaction contains unbound continuum states, which is called "scattering continuum" [61,62]. Thus, we assume that the n = 1 state is the bound biexciton state and its energy Ω (1) 0 is written as ε B .…”

Coherent and incoherent aspects of polariton dynamics in semiconductor microcavities

“…This coherent term originates from the non-Markovian nature of the exciton-exciton interaction when going beyond the usual Hartree-Fock approximation and corresponds to four-particle correlations [22]. Lastly, several state of the art microscopic calculations show that the EID strength is highly energy dependent and becomes large when the energy of the two scattered polaritons exceeds twice the exciton energy [23][24][25][26][27]. This might also explain the onset of the lower polariton EID towards positive cavity detuning.…”