Entanglement of photons due to nonlinear optical response of quantum wells
Mikhail Erementchouk, Michael Niklaus Leuenberger · Physical Review B · 2010
We study photons entangling in the short-time response of a quantum well excited by a short intense pulse. At the time scales, where the biexciton effect is not yet pronounced, the Pauli principle is responsible for many-body correlations among excitons, giving rise to the production of entangled photons with a yield $\ensuremath{\sim}{10}^{\ensuremath{-}2}$. The quantum-field theoretical two-particle density matrix in second quantization is used to calculate the entanglement for arbitrary emission angles of the entangled pairs of photons. At the time scales, where the heavy-light hole splitting is resolved, the resonances corresponding to different two-exciton states develop, which allow for a simple kinematic theory relating the states of the outgoing photons with the respective two-exciton states. The resonant response can be expected at symmetric emission angles for resonances with the heavy-heavy and light-light two-exciton states with remarkably nontrivial dependence of entanglement on the emission angles and on the ellipticity parameters of the excitation. We show that the emitted entangled two-photon states are always in a triplet state.