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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Exploitation of transverse spatial modes in spontaneous four wave mixing photon-pair sources

Héctor Cruz-Ramírez, Roberto Ramírez-Alarcón, Daniel Cruz-Delgado, Jorge Monroy-Ruz, Erasto Ortiz-Ricardo, Francisco A. Domínguez-Serna, Karina Garay-Palmett, Alfred B. U’Ren

Published Sep 13, 2016• 1 citation
Publisher

Abstract

We present a source for which multiple spontaneous four-wave mixing (SFWM) processes are supported in a few mode birefringent fiber, each process associated with a particular combination of transverse modes for the four participating waves. Within the weakly guiding regime, for which the propagation modes may be well approximated by linearly polarized (LP) modes, the departure from circular symmetry due to the fiber birefringence translates into orbital angular momentum (OAM) and parity conservation rules, i.e. reflecting elements from both azimuthal and rectangular symmetries. In our source: i) each process is group-velocity-matched so that it is, by design, nearly-factorable, and ii) the spectral separation between neighboring processes is greater than the marginal spectral width of each process. Consequently, there is a direct correspondence between the joint amplitude of each process and each of the Schmidt mode pairs of the overall two-photon state. The present paper covers work presented in Refs.1 and.2

DOI
10.1117/12.2238544

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We present a source for which multiple spontaneous four-wave mixing (SFWM) processes are supported in a few mode birefringent fiber, each process associated with a particular combination of transverse modes for the four participating waves. Within the weakly guiding regime, for which the propagation modes may be well approximated by linearly polarized (LP) modes, the departure from circular symmetry due to the fiber birefringence translates into orbital angular momentum (OAM) and parity conservation rules, i.e. reflecting elements from both azimuthal and rectangular symmetries. In our source: i) each process is group-velocity-matched so that it is, by design, nearly-factorable, and ii) the spectral separation between neighboring processes is greater than the marginal spectral width of each process. Consequently, there is a direct correspondence between the joint amplitude of each process and each of the Schmidt mode pairs of the overall two-photon state. The present paper covers work presented in Refs.1 and.2
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 have designed and implemented a photon-pair source, based on the spontaneous four wave mixing (SFWM) process in a few-mode fiber, in a geometry which permits multiple, simultaneous SFWM processes, each associated with a distinct combination of transverse modes for the four participating waves. In our source: i) each process is group-velocity-matched so that it is, by design, nearly-factorable, and ii) the spectral separation between neighboring processes is greater than the marginal spectral width of each process. Consequently, there is a direct correspondence between the joint amplitude of each process and each of the Schmidt mode pairs of the overall two-photon state. Our approach permits hybrid entanglement in discrete frequency and in transverse mode, whereby control of the number of supported fiber transverse modes allows scalability to higher dimensions while spectral filtering may be used for straightforward Schmidt mode discrimination.
We have designed and implemented a photon-pair source, based on the spontaneous four wave mixing (SFWM) process in a few-mode fiber, in a geometry which permits multiple, simultaneous SFWM processes, each associated with a distinct combination of transverse modes for the four participating waves. In our source: i) each process is group-velocity-matched so that it is, by design, nearly-factorable, and ii) the spectral separation between neighboring processes is greater than the marginal spectral width of each process. Consequently, there is a direct correspondence between the joint amplitude of each process and each of the Schmidt mode pairs of the overall two-photon state. Our approach permits hybrid entanglement in discrete frequency and in transverse mode, whereby control of the number of supported fiber transverse modes allows scalability to higher dimensions while spectral filtering may be used for straightforward Schmidt mode discrimination.
We introduce a new kind of spontaneous four wave mixing process for the generation of photon pairs, in which the four waves involved counter-propagate in a guided-wave medium; we refer to this process as counter-propagating spontaneous four wave mixing (CP-SFWM). We show that for the simplest CP-SFWM source, in which all waves propagate in the same polarization and transverse mode and in which self- and cross-phase modulation effects are negligible, phasematching is attained automatically regardless of dispersion in the fiber or waveguide. Furthermore, we show that in two distinct versions of this source (both pumps pulsed, or one pump pulsed and the remaining one monochromatic), the two-photon state is automatically factorable provided that the length of the nonlinear medium exceeds a certain threshold, easily achievable in practice since this threshold length tends to be in the range of mm to cm. We also show that if one of the pumps approaches the monochromatic limit, and for a sufficient nonlinear medium length, the bandwidth of one of the two photons in a given pair may be reduced to the level of MHz, compatible with electronic transitions for the implementation of atom–photon interfaces, without the use of optical cavities.