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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Intermodal-Vectorial Four-Wave Mixing in Few-Mode Fibers for Generation of Photon Pairs with Spatial-Polarization-Frequency Hybrid Entanglement

Andrzej Gawlik, Marta Bernaś, Kinga Żołnacz, Karol Tarnowski

Published Jun 23, 2025• 0 citations
Publisher

Abstract

Four-wave mixing (FWM) in optical fibers is a nonlinear optical process which can be used to generate photon pairs with hybrid entanglement in multiple degrees of freedom (DOFs), including frequency, polarization, spatial mode, or angular momentum [1]. Until now, the realizations of entanglements in the DOFs: energy-time, frequency, polarization, spatial-frequency, and polarization-frequency [1] have been proposed using specific FWM processes in different optical fibers.

DOI
10.1109/cleo/europe-eqec65582.2025.11111500

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Four-wave mixing (FWM) in optical fibers is a nonlinear optical process which can be used to generate photon pairs with hybrid entanglement in multiple degrees of freedom (DOFs), including frequency, polarization, spatial mode, or angular momentum [1]. Until now, the realizations of entanglements in the DOFs: energy-time, frequency, polarization, spatial-frequency, and polarization-frequency [1] have been proposed using specific FWM processes in different optical fibers.
Optical fiber-based sources of photon pairs with hybrid entanglement across multiple degrees of freedom are essential for a wide range of quantum technologies, while remaining compatible with existing communication networks. In this paper, we use a birefringent few-mode fiber to demonstrate an intermodal-vectorial four-wave mixing process that generates two pairs of spectrally overlapping signal-idler bands. Using phase-matching conditions, we show that the pairs of bands become spectrally indistinguishable when the group refractive indices of the signal and idler modes intersect at the pump wavelength. Our theoretical predictions are confirmed through experimental observations and corroborated by numerical simulations. Furthermore, we introduce the two-photon state associated with the overlapping bands, which simultaneously exhibits entanglement in a single degree of freedom and hybrid entanglement across multiple degrees of freedom. We also explain how the type and degree of entanglement can be controlled by tailoring the spectral overlap between the signal-idler bands. This study presents a promising scheme for a fiber-based source of photon pairs with entanglement spanning the spatial, polarization, and frequency degrees of freedom.
The purpose of this tutorial paper is to present a broad overview of photon-pair generation through the spontaneous four wave mixing (SFWM) process in optical fibers. Progress in optical fiber technology means that today we have at our disposal a wide variety of types of fiber, which, together with the fact that SFWM uses two pump fields, implies a truly remarkable versatility in the resulting possible photon-pair properties. We discuss how the interplay of frequency, transverse mode, and polarization degrees of freedom—the first linked to the latter two through fiber dispersion—leads to interesting entanglement properties both in individual degrees of freedom and also permitting hybrid and hyper entanglement in combinations of degrees of freedom. This tutorial covers methods for photon-pair factorability, frequency tunability, and SFWM bandwidth control, the effect of frequency non-degenerate and counterpropagating pumps, as well as methods for characterizing photon pairs generated in optical fibers.
The strong interest in space-division multiplexing of classical communication signals has resulted in development of optical fibers that support propagation of multiple modes. This has paved the way for progress in signal processing using multiple modes and four-wave mixing between these. More specifically, careful design and knowledge of optical properties of individual modes enables phase matching in four-wave mixing that is otherwise not possible with single-mode fibers. This enables signal processing using four-wave mixing between higher-order modes for e.g. frequency conversion over a wide bandwidth. In addition, processing and creation of quantum states has also been demonstrated using four-wave mixing, including generation of photon pairs. In this work we review recent progress in signal processing and generation of quantum states using four-wave mixing.
In this paper, we use a birefringent few-mode fiber to demonstrate an intermodal-vectorial four-wave mixing process that generates two pairs of spectrally overlapping signal-idler bands. Using phase-matching conditions, we show that the pairs of bands become spectrally indistinguishable when the group refractive indices of the signal and idler modes intersect at the pump wavelength. Our theoretical predictions are confirmed through experimental observations corroborated by numerical simulations. Furthermore, we introduce the two-photon state associated with the overlapping bands, which exhibits hybrid entanglement in spatial-polarization-frequency degrees of freedom. We explain that its degree of entanglement can be manipulated by tailoring the spectral position of the overlapping pairs of bands with respect to the Raman band and varying the excitation ratio of the pump modes. This study introduces a scheme for a fiber-based source of photon pairs with spatial-polarization-frequency entanglement.
Intermodal four-wave mixing (FWM) process in few-mode fibers (FMFs) could be utilized for entangled photon-pair generation. Previous studies mainly performed in single-mode fibers suffered from the significant Raman scattering background from the glass fiber. Therefore, the instantaneous Raman and FWM effects would compete; this could be avoided in FMFs if the modal dispersion is larger than the Raman gain spectra. Utilizing two pumps in different modes in FMFs will generate photon pairs in various modes. Here, we study the effect of pump spectral separation on the intermodal FWM power and bandwidth using a seeding technique. It is concluded that the further the pumps and intermodal FWM idler and signal are from each other spectrally, the smaller the photon efficiency and larger the bandwidth. Experimental results for two FMFs of different differential mode group delay values are presented.
In this paper, a generation scheme for telecom band hyper-entanglement is proposed and demonstrated based on the vector spontaneous four wave mixing (SFWM) processes in optical fibers. Two kinds of two-photon states are generated, one is hyper-entangled in the degree of freedoms (DOFs) of energy-time and polarization, the other is hyper-entangled in DOFs of energy-time and discrete-frequency. Experiments of Franson-type interference, two-photon interference under non-orthogonal polarization bases and spatial quantum beating are realized to demonstrate the entanglement in energy-time, polarization and frequency, respectively. This scheme provides a simple way to realize telecom band hyper-entanglement, which has potential for large geographic-scale applications of quantum communication and quantum information over optical fibers.