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arXiv:1107.3257 · Optics Express

Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color

Hayden McGuinness, M. G. Raymer, C. J. McKinstrie

Published Aug 29, 2011• 38 citations
arXivHTMLPDF

Abstract

We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively. Also, for a particular case, the Schmidt mode set was found to be nearly equal to a Hermite-Gaussian function set. The methods and results also apply with little modification to frequency conversion by sum-frequency conversion in optical crystals.

DOI
10.1364/oe.19.017876

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arXiv:1006.4350•Physical Review Letters•Aug 27, 2010•254 citations
We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively. Also, for a particular case, the Schmidt mode set was found to be nearly equal to a Hermite-Gaussian function set. The methods and results also apply with little modification to frequency conversion by sum-frequency conversion in optical crystals.
In this paper we consider frequency translation enabled by Bragg scattering, a four-wave mixing process. First we introduce the theoretical background of the Green function formalism and the Schmidt decomposition. Next the Green functions for the low-conversion regime are derived perturbatively in the frequency domain, using the methods developed for three-wave mixing, then transformed to the time domain. These results are also derived and verified using an alternative time-domain method, the results of which are more general. For the first time we include the effects of convecting pumps, a more realistic assumption, and show that separability and arbitrary reshaping is possible. This is confirmed numerically for Gaussian pumps as well as higher-order Hermite-Gaussian pumps.
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.
We experimentally demonstrate frequency translation of a non-classical optical field by Bragg-scattering four-wave mixing, driven by orthogonally polarized pump pulses in a birefringent optical fiber. Heralded single photons are up- and down-translated by 6.8 THz between bands at 688.1 nm and 678.2 nm, each with efficiency > 97%. The input and output spectral shape and bandwidth show negligible modulation. Second-order auto-correlation measurements of the 678.2 nm and 688.1 nm fields at maximum conversion yield values of 0.0302 ± 0.0005 and 0.028 ± 0.001, respectively, compared with the input second-order correlation of 0.026 ± 0.001; this indicates that the frequency translation process preserves the non-classical nature of the field. The high efficiency, broad bandwidth, and low noise render this scheme useful for quantum networks and sources.
We explore the frequency translation of single-photon states of light and the creation of photon pairs by four-wave mixing in optical fiber. Frequency translation refers to changing the central frequency of a field, while photon pair creation refers to the creation of two individual photons at the same time. We demonstrate these effects in third-order nonlinear optical fiber. While both phenomena have previously been shown by three-wave mixing in second-order nonlinear media, there are compelling reasons to develop these tasks in third-order media. Most importantly, frequency translation in third-order material allows for the practical implementation of both small and large frequency shifts, while second-order material only practically allows for large shifts. Photon creation in third-order media often permits more flexible phase-matching conditions, allowing for the creation of a wider variety of quantum states than is often possible in second-order media. In our theoretical study of photon pair creation, we focus on the spectral correlations of the photon pairs. We pay particular attention to the creation of quantum states of high purity, where the photons are not spectrally correlated with one another. High purity photons are a requisite resource for several different quantum information processing applications, such as linear-optical quantum computing. We find that states with high purity can be realized with a minimal amount of spectral filtering. Experimentally, we study photon frequency translation in photonic crystal fiber. The central wavelength of the input photons was translated from 683 nm to 659 nm. We perform second-order intensity correlation measurements on both channels to demonstrate their quantum nature. This resulted in values of 0.21 ± 0.02 and 0.19 ± 0.05 for the 683-nm and 659-nm channels, respectively, demonstrating that those fields were dominated by their single-photon component. The efficiency at which the process occurred was 29 percent. Theoretically, we develop a Green function formalism to describe the translation process and develop a computational model to calculate the solution to the governing equations. Also, in a related experiment, we demonstrate classical frequency translation from 851 nm to 641 nm, a record translation in both wavelength and frequency, at an efficiency of 0.2 percent in a birefringent fiber.
We experimentally demonstrate frequency translation of a nonclassical optical field via four-wave mixing (Bragg-scattering process) in a photonic crystal fiber (PCF). The high nonlinearity and the ability to control dispersion in PCF enable efficient translation between nearby photon channels within the visible to-near-infrared spectral range, useful in quantum networks. Heralded single photons at 683 nm were translated to 659 nm with an efficiency of 28.6±2.2 percent. Second-order correlation measurements on the 683- and 659-nm fields yielded g(683)(2) (0)=0.21±0.02 and g(659)(2) (0)=0.19±0.05, respectively, showing the nonclassical nature of both fields.