Spatial Quantum Correlations in Multiple Scattered Light

We predict a new spatial quantum correlation in light propagating through a multiple scattering random medium. The correlation depends on the quantum state of the light illuminating the medium, is infinite in range, and dominates over classical mesoscopic intensity correlations. The spatial quantum correlation is revealed in the quantum fluctuations of the total transmission or reflection through the sample and should be readily observable experimentally.

Figure 1

Total transmission through a multiple scattering sample. A quantum state of light is coupled through mode $a$ and the total number of photons is collected with an integrating sphere. Vacuum fluctuations in all open channels $a^{\prime }\ne a$ and $b^{\prime }$ must be included in the quantum description.

Figure 2

Variance of the quantum fluctuations of the total reflection (upper plot) and total transmission (lower plot) for a coherent state (solid line), a thermal state with $⟨{\widehat{n}}_a^{\mathrm{in}}⟩=1$ (dashed-dotted line), and an arbitrary Fock state (dotted line) as a function of $\ell /L$. All correction terms of order $1/g$ have been neglected. In the reflection (transmission), pronounced variations in the photon statistics are found for decreasing (increasing) $\ell /L$.

Figure 3

Two-point correlation function $C_{b_0{b}_1}$ for three different quantum states of light as a function of the average number of photons in the incoming field. The correlation function exhibits either strong correlation (thermal state) or anticorrelation (Fock state) relative to the uncorrelated case (coherent state).

Figure 4

Fluctuations of the total transmission for a coherent state, a thermal state with $⟨{\widehat{n}}_a^{\mathrm{in}}⟩=1$, and an arbitrary Fock state as a function of the mesoscopic conductance $g$ and for a fixed amount of disorder: $\ell /L=1/3$ For decreasing $g$, the mesoscopic correlations either enhance or suppress quantum fluctuations for the thermal state and the Fock state, respectively. The fluctuations of the coherent state are unaltered for all values of $g$. When $g$ approaches unity, the localization regime is entered and the model is invalid.