Polarization state tomography of Stokes–anti-Stokes photon pairs from degenerate four-wave mixing in diamond

Degenerate four-wave mixing in diamond generates a quantum state ${\ensuremath{\rho}}_{\mathrm{SaS}}$ composed of Stokes (S) and anti-Stokes (aS) time-correlated photon pairs (SaS). Here, polarization state tomography of ${\ensuremath{\rho}}_{\mathrm{SaS}}$ is performed in four pertinent scattering configurations: Raman shift in resonance and out of resonance with the phonon energy, and incident light polarized in the direction parallel to or $\ensuremath{\pi}/4$ rotated from a diamond crystallographic axis. We reconstruct the density matrix, calculate concurrence and purity for the four configurations, and directly measure and analyze the diagonal terms of ${\ensuremath{\rho}}_{\mathrm{SaS}}$ in different bases. We establish ${\ensuremath{\rho}}_{\mathrm{SaS}}$ as an entangled linear combination of electronic four-wave mixing and SaS Raman process, mixed with uncorrelated S and aS photons, with the weight constants depending on the scattering conditions, which can be engineered for future applications.