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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Two-photon experiments in the frequency domain

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

Published Apr 11, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.923241

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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.
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.
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.
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.
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.
We report on two-photon quantum interference experiments in the standard telecommunication band. Two identical photons in the 1.5 mm wavelength band were generated in spatially separated modes by a type-I spontaneous parametric down-conversion process, and injected into a fiber-optic Hong-Ou-Mandel interferometer. Two-photon interference patterns of dip and spatial beating in the coincidence counting rate were observed by varying the difference in optical path lengths. The visibilities obtained in the net coincidences were close to the theoretical value of 100%. The raw visibilities were also well above the classical limit.
The Hong-Ou-Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.