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arXiv:1107.5519 · New Journal of Physics

Implementing two-photon interference in the frequency domain with electro-optic phase modulators

Laurent Olislager, I. Mbodji, Erik Woodhead, Johann Cussey, Luca Furfaro, Philippe Emplit, Serge Massar, Kien Phan Huy, Jean-Marc Mérolla

Published Apr 17, 2012• 30 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/14/4/043015

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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.
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.
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.
Entangled photons have appeared to be a promising way both for fundamental tests of physical principles and for quantum information applications such as Quantum Key Distribution. In particular, using entangled photons could potentially allow the realization of key distribution protocols over distances greater than a few hundreds of kilometers and security certification without a priori trust in the devices employed. Recently we reported experiments in which entanglement is manipulated in the frequency domain using electro-optic phase modulators driven by radio-frequency signals. Such method allows observation of an accurate and stable high-visibility (better than 99%) two-photon Bessel interference patterns. However in long distance fibre implementation this scheme remains sensitive to chromatic dispersion effect. We report a simple non local dispersion cancellation method built entirely from off-the-shelf components. The figure 1 a) depicts a setup allowing a realization of a non local dispersion cancellation in frequency domain. Pairs of photon are created by parametric down conversion in a Periodically Poled Lithium Niobate (PPLN) waveguide symmetrically around the 1550 nm wavelength (pulsation ω0). A 3dB coupler separates photon pairs. One of the photons is launched in a fibre spool. The second is launched in equivalent fibre spool following by a commercial programmable optical filter based on solid-state Liquid Crystal on Silicon switching element (Waveshaper 4000S). This equipment allows introducing a negative dispersion necessary to cancel the positive dispersion effect experienced by the photons propagating in the fiber spools. Both photons are then modulated by independent electro-optic phase modulators (EOPM) at 25 GHz. The relative phases between the 25 GHz signals are independently controlled by two phase shifters PS1 and PS2. After modulation, the photons are sent through narrowband tunable filters (F1,2) centred on angular frequency ω0. The photons are detected by two Avalanche Photodiodes (D1, 2). The phase modulators perform Bessel-type interference between photons separately detected on D1 and D2 (see [3] for details). The figure 1 b) and 1c) shows respectively the theoretical evolution of the interference patterns versus the distance when the phase shift is varying between 0 and 2π without (b) and with (c) negative dispersion (the normalized amplitude of modulation is 2.74). The introduction of negative dispersion allows cancelling the dispersion effect on the observed interference patterns.
We demonstrate a two-photon interference experiment for phase coherent biphoton frequency combs (BFCs), created through spectral amplitude filtering of biphotons with a continuous broadband spectrum. By using an electro-optic phase modulator, we project the BFC lines into sidebands that overlap in frequency. The resulting high-visibility interference patterns provide an approach to verify frequency-bin entanglement even with slow single-photon detectors; we show interference patterns with visibilities that surpass the classical threshold for qubit and qutrit states. Additionally, we show that with entangled qutrits, two-photon interference occurs even with projections onto different final frequency states. Finally, we show the versatility of this scheme for weak-light measurements by performing a series of two-dimensional experiments at different signal-idler frequency offsets to measure the dispersion of a single-mode fiber.