Two-Photon Bandwidth of Hyper-Entangled Photons in Complex Media

TL;DR

This work demonstrates analytically and numerically that hyper-entangled photon pairs, entangled in both spatial and spectral degrees of freedom, experience cancellation of first-order chromatic modal dispersion in complex media, yielding a two-photon bandwidth far larger than the classical limit. The authors show this effect across multimode fibers, thin diffusers, and blazed gratings, and they connect it to broadband quantum wavefront shaping. By analyzing mode correlations and phase accumulation, they reveal how two-photon interference cancels phase-wrapping while preserving geometric scaling, enabling high-contrast two-photon speckle patterns over wide bandwidths. The findings open avenues for broadband quantum imaging, communication, and sensing by enabling robust quantum correlations through complex media, contingent on maintaining spatial and spectral entanglement and appropriate placement of shaping elements.

Abstract

When light propagates through complex media, its output spatial distribution is highly sensitive to its wavelength. This fundamentally limits the bandwidth of applications ranging from imaging to communication. Here, we demonstrate analytically and numerically that the spatial correlations of hyper-entangled photon pairs, simultaneously entangled spatially and spectrally, remain stable across a broad bandwidth: The chromatic modal dispersion experienced by one photon is canceled to first order by its spectrally anti-correlated twin, defining a "two-photon bandwidth" that can far exceed its classical counterpart. We illustrate this modal dispersion cancellation in multimode fibers, thin diffusers and blazed gratings, and demonstrate its utility for broadband wavefront shaping of quantum states. These findings advance our fundamental understanding of quantum light in complex media with applications in quantum imaging, communication, and sensing.

Figures (6)

• Figure 1: Modal dispersion cancellation for hyper-entangled photons. Spatially entangled photons occupy correlated spatial modes of the multimode fiber (MMF), but their frequencies are not necessarily correlated. The frequencies of spectrally entangled photons sum to a fixed value, but may occupy different spatial modes. In both cases the resulting two-photon speckle pattern will have a low contrast. Hyper-entangled photons are correlated both spatially and spectrally, resulting in a modal dispersion cancellation effect, manifested by a high contrast two-photon speckle pattern at the fiber output.
• Figure 2: Modal dispersion cancellation for SPDC photons in a multimode fiber. (a) A sketch of the proposed setup. Photon pairs, hyper-entangled in the spatial and spectral degrees of freedom, are generated via SPDC and imaged on a multimode fiber (MMF). Coincidence measurements are performed at the distal end of the fiber. L - lens. (b) Numerical results for the Pearson correlation (PCC) between the output speckles of degenerate and non-degenerate photons in the SPDC case (separated by $\Delta\lambda$), and between light with different wavelengths in the classical case. The inset shows a wider wavelength range over which the SPDC patterns begin to decorrelate. (c), (d) The incoherent sums of intensities over all wavelengths up to $\Delta\lambda=5$ nm in the SPDC (c) and classical (d) cases, depicting the expected observation in an experimental scenario. The dashed white squares mark the area over which the Pearson correlations were calculated. The output ring structure visible in (d) is explained by the radial memory effect gokay2025radial, and the straight line with excess energy stems from the symmetry of the fiber modes $\beta_{\ell,p}=\beta_{-\ell,p}$, where $\ell$ is the orbital angular momentum, as discussed in gokay2025radial.
• Figure 3: Two types of spatio-temporal effects in thin diffusers. Simulated far-field intensity distribution of a broadband classical laser ($808\pm40$ nm) scattered by a thin diffuser. (a) Resulting exploding speckles in the regime where the roughness of the diffuser $\sigma_L$ is on the order of the wavelength. The contrast is high close to the optical axis, and is reduced farther away from it due to a geometrical scaling effect. (b) Resulting low-contrast speckle in the regime where the roughness of the diffuser is much larger than the wavelength. The contrast is low everywhere, due to the phase-wrapping effect.
• Figure 4: Dispersion cancellation for SPDC photons in thin diffusers. (a) A sketch of the proposed setup. Spatially and spectrally entangled photons are generated via SPDC, and are imaged to a thin diffuser, after which coincidence measurements are performed in the far-field. L - lens. (b) Numerical results for the Pearson correlation (PCC) between the output speckle patterns of degenerate and non-degenerate photons in the SPDC case, and between light with different wavelengths in the classical case. In both cases, we compare only the region close to the optical axis, as depicted by the dashed white squares. (c), (d) The incoherent sums of intensities over all wavelengths up to $\Delta\lambda=80$ nm in the SPDC (c) and classical (d) cases. For SPDC, the phase-wrapping effect is canceled, and the geometric scaling effect remains, resulting in exploding speckles. See also supplemental movies 1 and 2.
• Figure 5: Dispersion cancellation for SPDC photons in blazed gratings. (a) A sketch of the proposed setup. Spatially and spectrally entangled photons are generated via SPDC, and are imaged on a blazed grating, after which coincidence measurements are performed, with one of the detectors on the optical axis (order $m=0$), and the other scanning the far field (plotted versus diffraction order $m$). L - lens. (b) The coincidence distribution for SPDC photons, and intensity for classical light at the far-field of the grating. Notably, in the SPDC case all the coincidence events occur in the $m=2$ order, with no leakage to other diffraction orders, due to the cancellation of the phase-wrapping effect. The bandwidth in this simulation is $808\pm40$nm.