  A quantum dot strongly coupled to a photonic crystal has been recently
proposed as a source of entangled photon pairs [R. Johne et al., Phys. Rev.
Lett. 100, 240404 (2008)]. The biexction decay via intermediate polariton
states can be used to overcome the natural splitting between the exciton states
coupled to the horizontally and vertically polarized light modes, so that high
degrees of entanglement can be expected. We investigate theoretically the
features of realistic dot-cavity systems, including the effect of the different
oscillator strength of excitons resonances coupled to the different
polarizations of light. We show that in this case, an independent adjustment of
the cavity resonances is needed in order to keep a high entanglement degree. We
also consider the case when the biexciton-exciton transition is also strongly
coupled to a cavity mode. We show that a very fast emission rate can be
achieved allowing the repetition rates in the THz range. Such fast emission
should however be paid for by a very complex tuning of the many strongly
coupled resonances involved and by a loss of quantum efficiency. Altogether a
strongly coupled dot-cavity system seems to be very promising as a source of
entangled photon pairs.
