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arXiv:2212.13652 · Journal of the Optical Society of America B

Fiber-based photon-pair generation: tutorial

Karina Garay-Palmett, Dong Beom Kim, Yujie Zhang, Francisco A. Domínguez-Serna, Virginia O. Lorenz, Alfred B. U’Ren

Published Jan 5, 2023• 54 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/josab.478008

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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.
We present a theoretical and experimental study of the generation of photon pairs through the process of spontaneous four-wave mixing (SFWM) in a few-mode, birefringent fiber. Under these conditions, multiple SFWM processes are in fact possible, each associated with a different combination of transverse modes for the four waves involved. We show that in the weakly guiding regime, for which the propagation modes may be well approximated by linearly polarized modes, the departure from circular symmetry due to the fiber birefringence translates into conservation rules, which retain elements from azimuthal and rectangular symmetries: both OAM and parity must be conserved for a process to be viable. We have implemented a SFWM source based on a bowtie birefringent fiber, and have measured for a collection of pump wavelengths the SFWM spectra of each of the signal and idler photons in coincidence with its partner photon. We have used this information, together with knowledge of the transverse modes into which the signal and idler photons are emitted, as input for a genetic algorithm, which accomplishes two tasks: (i) the identification of the particular SFWM processes that are present in the source, and (ii) the characterization of the fiber used.
We study both experimentally and theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in standard birefringent optical fibers. The ability to produce a range of two-photon spectral states, from highly correlated (entangled) to completely factorable, by means of cross-polarized birefringent phase matching, is explored. A simple model is developed to predict the spectral state of the photon pair which shows how this can be adjusted by choosing the appropriate pump bandwidth, fiber length and birefringence. Spontaneous Raman scattering is modeled to determine the tradeoff between SFWM and background Raman noise, and the predicted results are shown to agree with experimental data.
Spontaneous four-wave mixing (SFWM) in optical fibers is an important way to generate correlated/entangled photon pairs. When the pulsed pump light passes through the optical fiber, two kinds of SFWM will take place simultaneously. One is scalar scattering processes, in which two annihilated pump photons and generated photon pair are all polarized along the same fiber polarization axis. The other is vector scattering processes, in which two annihilated pump photons are polarized along different fiber polarization axes, either to the two photons of the generated pair. If the fiber has large group birefringence, the intensity of vector scattering processes will be suppressed at the phase matching frequencies of the scalar scattering processes. On the other hand, the walk-off effect of the pump pulse components polarized along the two fiber polarization axes also suppresses the vector scattering processes. Hence, by proper pump polarization and signal/idle frequency selection, photon pairs can be generated only by the two independent scalar scattering processes in optical fibers with birefringence, which provide a simple way to realize polarization entangled photon pair generation. In this paper, related experiments based on the high nonlinearity microstructure fiber (HN-MSF) with group birefringence and polarization maintained dispersion shifted fiber (PM-DSF) are introduced, showing their potential on developing practical quantum light sources.
We present a study of the spectral properties of photon pairs generated through the process of spontaneous four-wave mixing (SFWM) in single mode fiber. Our analysis assumes narrowband pumps, which are allowed to be frequency degenerate or nondegenerate. Based on this analysis, we derive conditions on the pump frequencies and on the fiber dispersion parameters which guarantee the generation of ultrabroadband photon pairs. Such photon pairs are characterized by (i) a very large degree of entanglement, and (ii) a very high degree of temporal synchronization between the signal and idler photons. Through a numerical exercise, we find that the use of photonic crystal fiber (PCF) facilitates the fulfilment of the conditions for ultrabroadband photon pair generation; in particular, the spectral region in which emission occurs can be adjusted to particular needs through an appropriate choice of the PCF parameters. In addition, we present a quantum interference effect, resulting from indistinguishable pathways to the same outcome, which can occur when pumping a SFWM source with multiple spectral lines.
We report our recent progress in the generation and verification of a transverse-mode Bell state using spontaneous four-wave mixing in a few-mode polarization-maintaining fiber. Utilizing spatial light modulators, we show control over individual four-wave mixing processes through precise beam shaping of the pump transverse mode and verify entanglement via quantum state tomography. We discuss challenges in temporal and frequency distinguishability and illustrate how they can be resolved. This work represents a first step towards creating a versatile fiber-based transverse mode-entangled photon-pair source matched to fiber infrastructure.