The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wave-function approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon-dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at nonzero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.

Bogoliubov's theory states that self-interaction effects in Bose-Einstein condensates produce a characteristic linear dispersion at low momenta. One of the curious features of Bogoliubov's theory is that the new quasiparticles in the system are linear combinations of creation and destruction operators of the bosons. In exciton-polariton condensates, this gives the possibility of directly observing the negative branch of the Bogoliubov dispersion in the photoluminescence (PL) emission.Here we theoretically examine the PL spectra of exciton-polariton condensates taking into account of reservoir effects. At sufficiently high excitation densities, the negative dispersion becomes visible. We also discuss the possibility for relaxation oscillations to occur under conditions of strong reservoir coupling. This is found to give a secondary mechanism for making the negative branch visible.

The second and third order coherence functions $g^{(n)}(0) (n=2 {\rm and} 3)$ of an exciton-polariton condensate is measured and compared to the theory. Contrary to an ideal photon laser, deviation from unity in the second and third order coherence functions is observed, thus showing a bunching effect, but not the characteristics of a standard thermal state with $g^{(n)}(0)=n!$. The increase of bunching with the order of the coherence function, $g^{(3)}(0) > g^{(2)}(0)>1$, indicates that the polariton condensate is different from coherent state, number state and thermal state. The experimental results are in agreement with the theoretical model where polariton-polariton and polariton-phonon interactions are responsible for the loss of temporal coherence.Comment: 4 pages, 4 figure

We report the generation of polarization-entangled photons by cavity-enhanced spontaneous parametric down-conversion. The bandwidth of entangled photons is reduced to that of the optical parometric oscillator and the conversion rate is enhanced by cavity. The time interval between the conjugate two photon is prolongated so that it can be directly measured by a common detector. The time correlation function of the entangledphotons pair shows a time-oscillatory characteristic. To demonstrate the entanglement, we experimentally obtain two-photon quantum interference for the polarization variable.