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Analysis of elliptically polarized, maximally entangled states

Anthony Martin, Jean-Loup Smirr, Florian Kaiser, Amandine Issautier, Virginia D’Auria, Robert Frey, Olivier Alibart, Isabelle Zaquine, Sébastien Tanzilli

Published Jul 11, 2011• 0 citations
OpenAlex

Abstract

We demonstrate high quality polarization entanglement at telecom wavelength, based on guided-wave technology. The fully fibered setup relies on a type-II periodically poled Lithium Niobate waveguide (PPLN/W) emitting pairs of cross-polarized photons (H,V) at 1310 nm. These photon pairs are sent onto a simple 50/50 fiber-optic coupler, leading to an entangled state of the form |Ψ>=(1/21/2)*(|Ha,Vb>+|Va,Hb>) in the coincidence basis, which is eventually distributed to "users" (a,b) through standard optical fibers. Along these distribution channels, the entangled state acquires an unknown phase between its two components leading to an "elliptically polarized" maximally entangled states |Ψ>=(1/21/2)*(| Ha,Vb>+eiφ|Va,Hb>), in which φ is a non random phase, and (a,b) represent the two channels at the output of the emitting source. For such a state, the usual settings used for optimal violation of the Bell inequality are no longer adapted. Thanks to the use of a phase compensator, namely a Soleil-Babinet birefringent system, we demonstrate experimentally that any phase can be compensated, leading to a maximal violation of the Bell inequality when the standard settings are used. Alternatively, we propose here a theoretical approach that allows, when applied to those particular states, determining the phase, and finding new analysis parameters towards optimizing the Bell inequality violation. After introducing our formalism in its generic form, we will show that it can be applied to several existing systems capable of either compensating or analyzing the phase.

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•Nov 23, 2011•0 citations
We demonstrate high quality polarization entanglement at telecom wavelength, based on guided-wave technology. The fully fibered setup relies on a type-II periodically poled Lithium Niobate waveguide (PPLN/W) emitting pairs of cross-polarized photons (H,V) at 1310 nm. These photon pairs are sent onto a simple 50/50 fiber-optic coupler, leading to an entangled state of the form |Ψ>=(1/21/2)(|Ha,Vb>+|Va,Hb>) in the coincidence basis, which is eventually distributed to "users" (a,b) through standard optical fibers. Along these distribution channels, the entangled state acquires an unknown phase between its two components leading to an "elliptically polarized" maximally entangled states |Ψ>=(1/21/2)(| Ha,Vb>+eiφ|Va,Hb>), in which φ is a non random phase, and (a,b) represent the two channels at the output of the emitting source. For such a state, the usual settings used for optimal violation of the Bell inequality are no longer adapted. Thanks to the use of a phase compensator, namely a Soleil-Babinet birefringent system, we demonstrate experimentally that any phase can be compensated, leading to a maximal violation of the Bell inequality when the standard settings are used. Alternatively, we propose here a theoretical approach that allows, when applied to those particular states, determining the phase, and finding new analysis parameters towards optimizing the Bell inequality violation. After introducing our formalism in its generic form, we will show that it can be applied to several existing systems capable of either compensating or analyzing the phase.
When elliptically polarized maximally entangled states are considered, i.e., states having a non random phase factor between the two bipartite polarization components, the standard settings used for optimal violation of Bell inequalities are no longer adapted. One way to retrieve the maximal amount of violation is to compensate for this phase while keeping the standard Bell inequality analysis settings. We propose in this paper a general theoretical approach that allows determining and adjusting the phase of elliptically polarized maximally entangled states in order to optimize the violation of Bell inequalities. The formalism is also applied to several suggested experimental phase compensation schemes. In order to emphasize the simplicity and relevance of our approach, we also describe an experimental implementation using a standard Soleil-Babinet phase compensator. This device is employed to correct the phase that appears in the maximally entangled state generated from a type-II nonlinear photon-pair source after the photons are created and distributed over fiber channels.
Recent advances in guided-wave optics bring quantum key distribution (QKD) to a new level where less complex, yet more robust, schemes have been proposed. Through continuous research in this field, newer QKD systems achieve higher bit rate, distance, and reliability. Entanglement-based QKD receives enormous attention from the scientific community, in order to increase the communication distance and to go to device-independent systems. In this framework, photons are generally the preferred qubit carrier, taking advantage of low-loss fibre optical networks, and high-performance standard telecom components. Future QKD networks will demand sources exhibiting high brightness, reliability, and photons in the standard telecom ITU channels for compatibility and easy integration with current technology. One of the most exploited approaches towards genera- ting photonic entanglement is based on the process of spontaneous parametric down-conversion (SPDC) in non-linear crystals. Usually employed entanglement observables are energy-time and polarization. The latter one is, without doubt, the easiest to analyze thanks to interferometer-free setups. Polarization entanglement is conveniently generated via the so-called type-II SPDC interaction, possibly in a waveguide non-linear structure for increasing the efficiency. Nevertheless, with a type-II source, there are some precautions that must be taken for achieving high entanglement qualities. In particular, the generated paired photons need to be spectrally and temporally indistinguishable. Typically, this requires spectral filtering, and temporal walk-off compensation stages. So far, these issues have been addressed by using bulk optics arrangements. We demonstrate a fully fibred approach based on a type-II periodically poled lithium niobate waveguide (PPLN/W) generating paired photons at 1540 nm (telecom C-band wavelength). We highlight the use of a standard polarization maintaining fibre (PMF) as an essentially loss-free, guided-wave solution to the temporal walk-off problem. By using standard telecom DWDMs, we perform, at the same time, the tasks of spectral filtering and deterministic photon pair separation in two ITU channels. By the violation of the Bell's inequalities with more than 100 standard deviations, we demonstrate excellent entanglement qualities and high coincidence rates. Our fully fibred approach offers very low losses, high reliability, and would be ready for QKD field tests.
We report the realization of a fiber-coupled polarization entangled photon-pair source at 1310 nm based on a birefringent titanium in-diffused waveguide integrated into periodically poled lithium niobate. By making use of a dedicated and high-performance setup, we characterized the quantum properties of the pairs by measuring two-photon interference in both Hong–Ou–Mandel and standard Bell inequality configurations. For the two sets of measurements we obtained interference net visibilities reaching nearly 100%, which represent important and competitive results compared to those for the similar waveguide-based configurations already reported. These results prove the relevance of our approach as an enabling technology for long-distance quantum communication.
We report the realization of a fiber coupled polarization entangled photon-pair source at 1310 nm based on a birefringent titanium in-diffused waveguide integrated on periodically poled lithium niobate. By taking advantage of an original setup, we characterized the quantum properties of the pairs by measuring two-photon interference in both Hong-Ou-Mandel and standard Bell inequality configurations. We obtained, for the two sets of measurements, interference net visibilities reaching nearly 100%, which represent the best results ever reported for similar waveguide-based configurations. These results prove the relevance of our approach as an enabling technology for long-distance quantum communication.
We report the realization of a fiber coupled polarization entangled photon-pair source at 1310 nm based on a birefringent titanium in-diffused waveguide integrated on periodically poled lithium niobate. By taking advantage of an original setup, we characterized the quantum properties of the pairs by measuring two-photon interference in both Hong-Ou-Mandel and standard Bell inequality configurations. We obtained, for the two sets of measurements, interference net visibilities reaching nearly 100%, which represent the best results ever reported for similar waveguide-based configurations. These results prove the relevance of our approach as an enabling technology for long-distance quantum communication.
During the last decade, quantum entanglement has paved the way out to of the lab modern applications such as quantum computation and communication. Today, small scale quantum networks exist already, but they are limited to a few 100 km distance, due to intrinsic fiber transmission losses and non perfect detectors. These networks are typically established using photon pair sources based on spontaneous parametric down conversion (SPDC). Widely used entanglement observables are time-bin and polarization, where the latter one is undoubtedly simpler to analyze due to lack of interferometric devices. It was shown recently, that introducing quantum memories (QM) between the communication parties could increase both communication speed and distance. Such memories already exist, but their narrow absorption bandwidth does not match the broadband emission spectrum of SPDC sources. Our report is twofold. First, we introduce a new polarization entanglement scheme based on a birefringent delay line (BDL). A pair of incoming photons is projected on a polarizing beam splitter (PBS), where vertically polarized photons travel along a polarization maintaining fiber loop accumulating a delay δ compared to horizontally polarized photons, which exit the BDL directly upon reflection at the PBS. Via post selection of only simultaneously arriving photon pair events, we create entangled states of the form α|H>_1|H>_2 + e^(iφ)β|V>_1 |V>_2. The probability amplitudes α and β are simply tuned by controlling the input pair's polarization and the phase φ can be varied by piezo fiber stretcher (PZT) in the delay line. Therefore, any superposition of the polarization entangled Bell states can be created. The scheme may also be used for entanglement distillation of non maximally entangled states, e.g. emitted by quantum dots. We will introduce all requirements needed to create entanglement from such a BDL. Second, we show how to apply this scheme to produce polarization entanglement from one of the most efficient photon pair generators, namely a periodically poled Lithium Niobate waveguide structure (PPLN/W), where the quasi phase matching is optimized for the type-0 SPDC interaction. The pair's wavelength is chosen in the standardized ITU-21 channel of the low loss telecom C-band and a fiber Bragg grating is applied to reduce the initial spectral bandwidth from 5 THz to 540 MHz, which is suitable for some solid-state quantum memories. Using the BDL, we create the maximally entangled states, with near perfect quality, which is proven by a violation of the Bell's inequalities by more than 29 standard deviations. We achieve a source spectral brightness of 211 narrowband polarization entangled pairs created per second, mW of pump power, and MHz of spectral bandwidth, coupled into a single mode fiber. This is on the same level as the best time-bin entanglement sources reported to date. The source is very practical due to the use of standard telecom fiber components. Moreover the choice for polarization instead of time-bin entanglement allows for simple state analysis using only rotating PBSs. This is a non negligible advantage, especially for narrowband photons with long coherence times, where time-bin analysis requires interferometer path length differences on the order of a few meters stabilized to a few tens of nanometers. Non unit visibilities are solely explained by the nonlinear character of our photon pair source, giving rise to double pair contributions. Applying this scheme to deterministic photon pair sources should result in perfect quality entanglement. We believe that our scheme should play an important role for future quantum networking applications.