Suppression of quadrupole polariton generation due to large $\chi^{(3)}$ effect in Cu$_2$O

Cuprous oxide (Cu$_2$O) is a dipole-forbidden semiconductor exhibiting a vanishing second-order nonlinear susceptibility and a large third-order nonlinear response.$^1$ We employ resonant two-photon excitation to create quadrupole polaritons in this semiconductor aiming at the Bose-Einstein condensation of polaritons. Generally, to observe this quantum phase transition, high optical excitations at low temperature is essential. Using a Z-scan setup, we explore the resonant two- photon generation of polaritons in Cu$_2$O at 2K. Our results suggest that the third-harmonic generation of the incident light severely limits the polariton density at high excitation levels. Based on the measured nonlinear optical parameters, the experimentally achievable polariton density is estimated. \newline \newline [1] S. Mani, J. I. Jang, and J. B. Ketterson, Opt. Lett. {\bf 34}, 2817 (2009).