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Optics Express

Multicolor multipartite entanglement produced by vector four-wave mixing in a fiber

Colin J. McKinstrie, S. J. van Enk, Michael G. Raymer, Stojan Radic

Published Jan 1, 2008• 28 citations
Publisher

Abstract

Multipartite entanglement is a resource for quantum communication and computation. Vector four-wave mixing (FWM) in a fiber, driven by two strong optical pumps, couples the evolution of four weak optical sidebands (modes). Depending on the fiber dispersion and pump frequencies, the mode frequencies can be similar (separated by less than 1 THz) or dissimilar (separated by more than 10 THz). In this report, the discrete- and continuous-variable entanglement produced by vector FWM is studied in detail. Formulas are derived for the variances of, and correlations between, the mode quadratures and photon numbers. These formulas and related results show that the modes are four-partite entangled.

DOI
10.1364/oe.16.002720

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•Oct 25, 2022•0 citations
Multipartite entanglement is a resource for quantum communication and computation. Vector four-wave mixing (FWM) in a fiber, driven by two strong optical pumps, couples the evolution of four weak optical sidebands (modes). Depending on the fiber dispersion and pump frequencies, the mode frequencies can be similar (separated by less than 1 THz) or dissimilar (separated by more than 10 THz). In this report, the discrete- and continuous-variable entanglement produced by vector FWM is studied in detail. Formulas are derived for the variances of, and correlations between, the mode quadratures and photon numbers. These formulas and related results show that the modes are four-partite entangled.
Polarization analysis of vectorial four-wave mixing (FWM) in birefringent photonic-crystal fibers reveals physically significant tendencies in the behavior of FWM sideband correlations as a function of fiber birefringence, dispersion, and nonlinearity, as well as the pump intensity and bandwidth. Scanning over this parameter space is shown to steer vectorial FWM from largely decoupled sideband generation by individual polarization modes of the pump to FWM scenarios enabling multipartite entanglement generation.
We present a time-domain Schmidt-mode analysis of a broadband continuous-variable entanglement of photon pairs generated via a vectorial four-wave mixing (FWM) of ultrashort laser pulses in a highly nonlinear birefringent optical fiber. We demonstrate that the time-domain eigenmodes of high-purity two-photon states generated through vectorial FWM can be steered, by varying the pump wavelength and FWM polarization geometry, from a high-purity entangled ket to a high-entropy entangled state in a space of a very high dimensionality. Moreover, this pulse-mode analysis is shown to provide a clear physical perspective on how the entanglement structure of two-photon states builds up as a result of short-pulse FWM dynamics. This insight reveals a correspondence-type relation between the quantum and classical pictures of photon-pair generation. With an eye on practical applications, a clear understanding of the temporal profile of pulse modes representing high-purity two-photon states is central to a meaningful shaping of ultrashort photon-packet waveforms for super-resolving microscopy and multiphoton spectroscopy using quantum states of light.
In this paper, we investigate the generation of multimode entanglement and squeezing of an optical field via coupled four-wave mixing interactions in a Kerr nonlinear medium pumped at multiple well-separated frequencies. We show that genuine multimode entanglement can be obtained and this entanglement can be verified with the measurable multimode squeezing present in the system. This scheme may be used to achieve entangled frequency combs which are useful in continuous-variable quantum communication networks.
Cylindrical vector (CV) beams are a set of transverse spatial modes that exhibit a cylindrically symmetric intensity profile and a variable polarization about the beam axis. They are composed of a non-separable superposition of orbital and spin angular momenta. Critically, CV beams are also the eigenmodes of optical fiber and, as such, are of widespread practical importance in photonics and have the potential to increase communications bandwidth through spatial multiplexing. Here, we derive the coupled amplitude equations that describe the four-wave mixing (FWM) of CV beams in optical fibers. These equations allow us to determine the selection rules that govern the interconversion of CV modes in FWM processes. With these selection rules, we show that FWM conserves the total angular momentum, the sum of orbital and spin angular momenta, in the conversion of two input photons to two output photons. When applied to spontaneous FWM, the selection rules show that photon pairs can be generated in CV modes directly and can be entangled in those modes. Such quantum states of light in CV modes could benefit technologies such as quantum key distribution with satellites.
We present a detailed characterization of the entanglement in a stimulated Fourwave mixing process.This process is widely studied by the homodyne detection, a technique insensitive to the details of the sideband modes of the involved beams.The emission profile of the FWM process in atomic media shows an imbalance in the amplification of the sidebands, which suggest an asymmetry in the entanglement of the generated states, that can not be observed by the homodyne detection.The stimulated FWM consists on a single frequency pump and a seed beam interacting with the hot rubidium atoms, generating a pair of entangled states, the probe and the conjugated.By the implementation of the resonantor detection, we revealed the hidden entanglement structure of the generated beams.We found that the usual characterization of the state through the homodyne detection is incomplete.On the contrary, the reconstruction of the covariance matrix from the resonant detection allows the full characterization of the quantum correlations and a more complete entanglement structure between the sideband frequency modes.Therefore, with the measurement using resonant detection over a Four-wave mixing process, we can demonstrate the advantage of the detection to reveal entanglement that would be hidden if the usual two-mode description is used.