Enhanced quantum correlations from joint pump and photon pair scattering

TL;DR

This work experimentally and theoretically demonstrates that entangled photon pairs generated inside a dynamic disordered medium maintain enhanced angular correlations after scattering, analogous to two-photon coherent backscattering (2p-CBS). By modeling the diffuser as a Gaussian random phase screen and using Green's-function propagation, the authors derive closed-form expressions for the two-photon coincidence function under two configurations: crystal after the diffuser ($z>0$) and crystal before the diffuser ($z<0$). The theory reveals that the correlation peak persists with a width that depends on geometry, distance, and diffuser properties, with explicit envelopes $\Delta\theta^{+}(z)$, $\Delta\theta_1^-(z)$, and $\Delta\theta_2^-(z)$, and that the results agree with numerical simulations. These findings advance understanding of quantum light generation in complex media and point toward practical schemes for exploiting scattering to control quantum correlations in photonic devices.

Abstract

Scattering of non-classical light is enabling new ways to study and control photon transport. However, advances in this field often rely on simplifying assumptions regarding the quantum light's generation and its source. In this work, we relax some of these assumptions and probe the behavior of entangled photon pairs passing through a disordered layer after being generated by a randomly scattered pump via spontaneous parametric down conversion. We experimentally demonstrate that, even when both the pump and the down-converted photons propagate through a dynamic scattering medium, the pairs maintain a sharp peak in their correlations. A comprehensive theoretical and numerical analysis shows that these correlations persist regardless of when the pairs are generated, whether immediately after the pump is scattered or under other conditions. More specifically, we detail how the shape of the angular correlation depends on the pump's scattering and how it varies with the distance between the pair-generation region and the entrance of the disordered medium. These findings represent a crucial step toward understanding quantum light generation in complex media, and potentially exploiting it for quantum technologies.

Figures (7)

• Figure 1: (a) Post-generation scattering: The entangled photon pairs enter a random medium after being generated via spontaneous down conversion (SPDC) from a typical plane-wave pump field. (b) Pre-generation scattering: The entangled pairs are generated from a scattered pump field. (c) Pre- and Post-generation scattering: Both the pump field and the entangled pairs generated are scattered. NLC, nonlinear crystal; RM, random medium.
• Figure 2: Simplified experimental setup. A pump beam passes through a rotating diffuser (RD), after which a nonlinear PPKTP crystal (NLC) generates entangled photon pairs via SPDC. The pairs propagate a distance $L$ toward a mirror (M), reflect back, and scatter again from the rotating diffuser. Coincidence events are collected using two single-photon detectors: a static detector $\text{D}_a$ and a scanning detector $\text{D}_b$, both positioned in the far-field of the diffuser. BS, beam splitter; $\theta_0$, scattering angle; CC, coincidence circuit.
• Figure 3: (a) The measured two-dimensional coincidence map at the far-field of the random medium. The coincidence distribution exhibits a clear peak in the backscattering direction. The transverse momenta are expressed in terms of angular positions such that $\theta_{x,y}$ denotes the transverse angular separation between the scanning ($D_b$) and static ($D_a$) detectors. Here, $L=3.5$ cm. (b) The single counts registered by the scanning detector $D_b$ exhibit a homogeneous distribution over the scanned region. Both the coincidence and single counts were acquired simultaneously using 100 $\mu$m core fiber-coupled detectors. (c) A one-dimensional scan of the peak for the same spacing $L$. Connected blue squares are the resultant coincidence counts, with the connected orange squares being the single counts. To better resolve the peak, we used 50 $\mu$m core fibers. Here, the data was averaged over two independent scans around the peak.
• Figure 4: (a) Simplified schematic of the experimental setup depicted in Fig. \ref{['fig:2']}, with an additional pump-propagation distance $z$ between the diffuser and nonlinear crystal. (b) Diagrammatic representation of the two-leading terms contributing to $\Gamma_{ba}^+$. Solid (dashed) lines represent the field (conjugate field). Open circles (squares) represent scattering events for the fields at frequency $\omega$ (2$\omega$), while correlated pairs are denoted by a red line connecting them. Each field line or its conjugate propagating carries a weight $H_\omega^z\left ( \textbf{q}\right )$ due to propagating a distance $z$ at frequency $\omega$, while each scattering vertex contributes $F_\omega\left(\Delta\textbf{q}\right)$ for a momentum transfer $\Delta\textbf{q}$. The weight of each diagram is obtained by assigning transverse momenta to the propagation lines, in accordance with the momentum conservation imposed by the correlators. A summation is then performed over all free transverse momenta. Inset depicts the fact that the correlator at $2\omega$ is a convolution of two correlators at $\omega$. (c) Solid lines: plot of Eq. (\ref{['EqGammaPlusExplicit']}), the theoretical prediction for the two-photon correlation function in the $z>0$ case, near the peak. Squares: the numerically obtained values for $\Gamma_{ba}^+$ for the parameters used in the theory. The transverse angular separation is defined as $\theta=\theta_b-\theta_a$. Both the theoretical expression and numerical data were first normalized to unit area, and then by the peak value in the resultant theoretical curve. Moreover, they are shown for $\theta_a=0$. The numerics were realized in the limit where the angular spread exceeds the transverse coherence length. i.e., when $kd\theta_0^2\gg1$. See text for more details.
• Figure 5: (a) Simplified schematic of the 2p-CBS setup with an additional $|z|$ propagation towards the medium. (b) Diagrammatic representation of the four-leading terms contributing to $\Gamma_{ba}^-$. The diagrammatic rules mentioned in the caption of Fig. (\ref{['fig:4']}) can be implemented here as well to arrive at a closed form for $\Gamma_{ba}^-$. (c) Solid lines: Plot of $\Gamma_{ba}^-$, which is a summation of Eq. (\ref{['EqGammaMinusExplicit1']}) and Eq. (\ref{['EqGammaMinusExplicit2']}). Squares: the numerically obtained values for $\Gamma_{ba}^-$ for the parameters used in the theory. The normalization procedure here is identical to the one mentioned in the caption of Fig. (\ref{['fig:4']}). Furthermore, the numerical parameters used here are also identical to the ones shown there.