Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light

We present the experimental realization of spatial quantum correlations of photons that are induced by multiple scattering of squeezed light. The quantum correlation relates photons propagating along two different light paths through the random medium and is infinite in range. Both positive and negative spatial quantum correlations are observed when varying the quantum state incident to the multiple scattering medium, and the strength of the correlations is controlled by the number of photons. The experimental results are in excellent agreement with recent theoretical proposals by implementing the full quantum model of multiple scattering.

Figure 1

(a) Sketch of the experimental setup. Vacuum squeezing is generated in an optical parametric oscillator with a periodically poled potassium titanyl phosphate (PPKTP) nonlinear crystal, overlapped with a displacement beam on a beam splitter (BS), and directed onto the sample (S). The flip mirror (FM) is used to choose between transmission and reflection measurements. The multiple scattered light is imaged onto a photodetector, and its photon fluctuations are recorded using an electronic spectrum analyzer (SA). (b) Measured spatial intensity distribution of light transmitted through a multiple scattering medium displaying a volume speckle pattern. (c) Measured photon fluctuations after multiple scattering recorded in reflection geometry ($L=20\mu \mathrm{m}$). The photon fluctuations of the total reflection for a squeezed light source (blue circles) and the classical limit (gray triangles). Depending on the phase of a displacement beam, photon fluctuations below or above the classical limit are detected. The detection frequency was 3.93 MHz and the resolution bandwidth 300 kHz.

Figure 2

Measured transmitted (red triangles) and reflected (blue circles) photon fluctuations scaled to $\eta$ after multiple scattering of light with (a)  classical ($F_a=4.6$) and (b) nonclassical ($F_a=0.52$) photon fluctuations versus sample thickness. The classical limit ($\Delta n_{T,R}^2/⟨{\widehat{n}}_{T,R}⟩=1$) marks the boundary between the classical regime and the quantum regime. Every data point is obtained after ensemble averaging over six different sample positions. The shaded areas correspond to the theoretical predictions and incorporate the uncertainties in $F_a$, $\ell$, and the extrapolation lengths. (c) Separately measured overall detection efficiency $\eta$ for each sample thickness in transmission (red triangles) and reflection geometry (blue circles). The error bars on the sample thicknesses are plotted only once and should be considered as upper boundaries since they were obtained by characterizing inhomogeneities of the whole sample rather than the small area used for optical characterization.

Figure 3

(a) Measured spatial quantum correlation function $\overline{C_{aba{b}^{\prime }}^Q}$ versus power of the incident light beam. For classical ($F_a=4.6$, black points) and nonclassical ($F_a=0.52$, red triangles) photon fluctuations, positive and negative spatial correlations are observed, respectively. Every data point represents an average over three different positions on the sample of thickness $L=6\mu \mathrm{m}$. The curves are the theoretical predictions, and the dashed line represents the uncorrelated case. (b) Spatial quantum correlation function versus sample thickness taken at an input power of $P=120\mu \mathrm{W}$. The spatial quantum correlation function is found to be independent of the sample thickness in agreement with theory (horizontal lines).