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Higher order coherence of exciton-polariton condensates

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.