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

Quantum theory and applications of fiber-based parametric devices

Colin J. McKinstrie

Published Jun 1, 2009• 0 citations
Publisher

Abstract

Parametric devices based on four-wave mixing processes in fibers can amplify, frequency convert, phase conjugate, regenerate, sample and delay signals in conventional communication systems. They can also generate and frequency-convert photons used in quantum-information experiments. Photons can be frequency-converted by Bragg scattering in a fiber, which is the analog of sum-frequency generation in a crystal.

DOI
10.1109/cleoe-eqec.2009.5196237

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Parametric devices based on four-wave mixing processes in fibers can amplify, frequency convert, phase conjugate, regenerate, sample and delay signals in conventional communication systems. They can also generate and frequency-convert photons used in quantum-information experiments. Photons can be frequency-converted by Bragg scattering in a fiber, which is the analog of sum-frequency generation in a crystal.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.
Efficient frequency conversion is crucial for interfacing photons with a variety of quantum systems ranging from matter qubits (color centers, quantum dots, atoms), optical fibers, detectors, that often operate at widely different wavelengths. Frequency conversion is also a resource to process quantum information.1, 2 Parametric processes such as sum frequency generation (SFG) and Bragg scattering four wave mixing (BS-FWM) offer a good versatility for such frequency conversion. It is well understood that those nonlinear processes have to be strong enough and satisfy phase matching to achieve a high conversion efficiency. While it is enough to consider those two aspects for moderate conversion efficiency up to 50%, the analysis is a bit more complicated when targeting efficiencies closely approaching unity. We are reviewing the pitfall that must be avoided to indeed reach near unity frequency transduction.
In this tutorial, the optical field fluctuations produced by four-wave mixing processes in fibers are studied in detail. Modulation interaction and phase conjugation amplify input signals, whereas Bragg scattering frequency converts an input signal. If the input states are coherent, the quadrature fluctuations associated with the output states have Gaussian statistics. Formulas are derived for the output quadrature means, variances, and correlations, which are valid for arbitrary pump-induced coupling and dispersion- and pump-induced mismatch coefficients. These formulas allow one to determine the output Wigner distributions, which specify the output fields completely, and the effects of the aforementioned processes on the information carried by signals. The results of this paper are relevant to communication systems and quantum-information protocols based on continuous variables.
The authors consider, experimentally and theoretically, the quantum frequency translation (i.e., noiseless conversion) of quantum states of light, including single-photon states. This process is useful for allowing quantum optical systems (atoms, ions, cavities, fibers, detectors) operating at different wavelengths to communicate with each other. The authors recently developed the process of frequency translation in optical fiber through use of the Bragg scattering four-wave mixing process. The high nonlinearity and the ability to control dispersion in photonic crystal fiber (PCF) enable efficient translation between nearby photon channels within the visible to-near-infrared spectral range, useful in quantum networks. This offers an important advantage compared with frequency translation using second-order nonlinear optical crystals, which limits the translation process to widely separated frequencies only.