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arXiv:1403.0805 · Physical Review A

Creating and manipulating entangled optical qubits in the frequency domain

Laurent Olislager, Erik Woodhead, Kien Phan Huy, Jean-Marc Mérolla, Philippe Emplit, Serge Massar

Published May 22, 2014• 31 citations
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Abstract

Radio-frequency phase modulation of frequency-entangled photons leads to a two-photon interference pattern in the frequency domain. In recent experiments, the pattern was measured with narrow-band frequency filters which select photons belonging to a given frequency bin. Here we show how photons can be grouped into even and odd frequencies by using periodic frequency filters called interleavers. In our theoretical analysis we show how this reduces the high-dimensional photon state to an effective two-dimensional state. This is of interest for applications such as quantum cryptography or low-dimensional tests of quantum nonlocality. We then report an experimental realization of this proposal. The observed two-photon interference pattern and violation of the CHSH inequality---the simplest binary-outcome Bell inequality---are in good agreement with the theoretical predictions.

DOI
10.1103/physreva.89.052323

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Radio-frequency phase modulation of frequency-entangled photons leads to a two-photon interference pattern in the frequency domain. In recent experiments, the pattern was measured with narrow-band frequency filters which select photons belonging to a given frequency bin. Here we show how photons can be grouped into even and odd frequencies by using periodic frequency filters called interleavers. In our theoretical analysis we show how this reduces the high-dimensional photon state to an effective two-dimensional state. This is of interest for applications such as quantum cryptography or low-dimensional tests of quantum nonlocality. We then report an experimental realization of this proposal. The observed two-photon interference pattern and violation of the CHSH inequality---the simplest binary-outcome Bell inequality---are in good agreement with the theoretical predictions.
Frequency-entangled photons can be readily produced using parametric down-conversion. We have recently shown how such entanglement could be manipulated and measured using electro-optic phase modulators and narrow-band frequency filters, thereby leading to two-photon interference patterns in the frequency domain. Here we introduce new theoretical and experimental developments showing that this method is potentially a competitive platform for the realization of quantum communication protocols in standard telecommunication fibres. We derive a simple theoretical expression for the coincidence probabilities and use it to optimize a Bell inequality. Furthermore, we establish an equivalence between the entangled- photon scheme and a classical interference scheme. Our measurements of two-photon interference in the frequency domain yield raw visibilities in excess of 99%. We use our high quality setup to experimentally validate the theoretical predictions, and in particular we report a violation of the CH74 inequality by more than 18 standard deviations.
We report on the study of two-photon interference in the frequency domain. Bell and Hong-Ou-Mandel experiments are investigated. These experiments involve the manipulation of photons in the frequency domain, using off-the-shelf telecommunication components such as electro-optic phase modulators and narrow-band frequency filters. In the first experiment, photon pairs entangled in frequency are created and separated. Each photon is then directed through an independent electro-optic phase modulator. Variation of the radio-frequency parameters of the modulation gives rise to a well-controlled Bessel-shape two-photon interference pattern in the frequency domain. This is efficiently measured with narrow-band frequency filters and superconducting single photon detectors. Experimental measurements exhibit high visibilities (over 99 percent both for net and raw visibilities) and allow the (theoretically proven) optimal violation of a Bell inequality for our setup (by more than 18 standard deviations). The second experiment is a Hong-Ou-Mandel experiment in the frequency domain. We show that a grating (spatial domain) or a phase modulator (temporal domain) can be seen as a frequency beam splitter. A broadband spectrum of photon pairs is divided into two interleaved frequency combs, each one used as an independent input to this acting beam splitter. A theoretical calculation shows clear photon anti-bunching behavior.
A monochromatic laser pumping a parametric down-conversion crystal generates frequency-entangled photon pairs. We study this experimentally by addressing such frequency-entangled photons at telecommunication wavelengths (around 155015501550 nm) with fiber-optics components such as electro-optic phase modulators and narrow-band frequency filters. The theory underlying our approach uses the notion of frequency-bin entanglement. Our results show that the phase modulators address coherently up to eleven frequency bins, leading to an interference pattern which can violate by more than five standard deviations a Bell inequality adapted to our setup.
Abstract We demonstrate frequency-bin entanglement between ultra-narrowband photons generated by cavity enhanced spontaneous parametric down conversion. Our source generates photon pairs in widely non-degenerate discrete frequency modes, with one photon resonant with a quantum memory material based on praseodymium doped crystals and the other photon at telecom wavelengths. Correlations between the frequency modes are analyzed using phase modulators and narrowband filters before detection. We show high-visibility two photon interference between the frequency modes, allowing us to infer a coherent superposition of the modes. We develop a model describing the state that we create and use it to estimate optimal measurements to achieve a violation of the Clauser–Horne (CH) Bell inequality under realistic assumptions. With these settings we perform a Bell test and show a significant violation of the CH inequality, thus proving the entanglement of the photons. Finally we demonstrate the compatibility with a quantum memory material by using a spectral hole in the praseodymium (Pr) doped crystal as spectral filter for measuring high-visibility two-photon interference. This demonstrates the feasibility of combining frequency-bin entangled photon pairs with Pr-based solid state quantum memories.
A parametric down conversion source pumped by a monochromatic laser will produce frequency entangled photon pairs. We demonstrate this by an experiment in which five-dimensional frequency entanglement is manipulated at telecommunication wavelengths using commercially available components such as electro-optic phase modulators and narrowband frequency filters. A theoretical intuition for this approach is developed by introducing the notion of frequency bin entanglement. We conclude by showing that using this method one can in principle violate the CHSH, the CGLMP, and a new – as yet unnamed – Bell inequalities.