Optical manipulation of collective spin correlations in semiconductors with a squeezed vacuum of polarized photons

We calculate the transfer rate of correlations from polarization entangled photons to the collective spin of a many-electron state in a two-band system. It is shown that when a semiconductor absorbs pairs of photons from a two-mode squeezed vacuum, certain fourth-order electron-photon processes correlate the spins of the excited electron pairs of different quasimomenta. Different distributions of the quantum Stokes vector of the light lead to either enhancement or reduction of the collective spin correlations, depending on the symmetry of the distribution. We find that as the squeezing of the light becomes nonclassical, the spin correlations exhibit a crossover from being positive with an $\ensuremath{\sim}{N}^{2}$ ($N$ is the average photon number) scaling to being negative with $\ensuremath{\sim}N$ scaling, even when $N$ is not small. Negative spin correlations mean a preponderance of spin singlets in the optically generated state. We discuss the possibility to measure the collective spin correlations through the measurement of the Faraday rotation fluctuation spectrum in a steady-state configuration.