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arXiv:quant-ph/0201150 · Physical Review A

Counterpropagating entangled photons from a waveguide with periodic nonlinearity

Mark C. Booth, Mete Atatüre, Giovanni Di Giuseppe, Bahaa E. A. Saleh, Alexander V. Sergienko, Malvin Carl Teich

Published Aug 26, 2002• 78 citations
arXivHTMLPDF

Abstract

The conditions required for spontaneous parametric down-conversion in a waveguide with periodic nonlinearity in the presence of an unguided pump field are established. Control of the periodic nonlinearity and the physical properties of the waveguide permits the quasiphase matching equations that describe counterpropagating guided signal and idler beams to be satisfied. We compare the tuning curves and spectral properties of such counterpropagating beams to those for copropagating beams under typical experimental conditions. We find that the counterpropagating beams exhibit a narrow bandwidth, permitting the generation of quantum states that possess discrete-frequency entanglement. Such states may be useful for experiments in quantum optics and technologies that benefit from frequency entanglement.

DOI
10.1103/physreva.66.023815

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The conditions required for spontaneous parametric down-conversion in a waveguide with periodic nonlinearity in the presence of an unguided pump field are established. Control of the periodic nonlinearity and the physical properties of the waveguide permits the quasiphase matching equations that describe counterpropagating guided signal and idler beams to be satisfied. We compare the tuning curves and spectral properties of such counterpropagating beams to those for copropagating beams under typical experimental conditions. We find that the counterpropagating beams exhibit a narrow bandwidth, permitting the generation of quantum states that possess discrete-frequency entanglement. Such states may be useful for experiments in quantum optics and technologies that benefit from frequency entanglement.
Entangled photons, which may be generated through the process of spontaneous parametric down-conversion (SPDC) in a crystal with /spl chi//sup (2)/ nonlinearity, have long been in the spotlight for quantum-optics experiments. The generation of entangled photons by quasi-phase matching (QPM) in lithium niobate offers the promise of increased photon-pair production and, with the integration of a waveguide structure, control of the spatial characteristics of the down-converted photons. It turns out that the use of a waveguide structure, in conjunction with periodic poling to achieve quasi-phase matching, offers another critically important feature: the possibility of generating counterpropagating signal and idler photons. We consider the conditions required for generating counterpropagating photon beams and explore some of the unique properties of this source of light using a periodically poled LiNbO/sub 3/ waveguide.
We propose the use of nonlinear periodic waveguides for direct and fully integrated generation of counterpropagating photon pairs by spontaneous parametric down-conversion. Using the unique properties of Bloch modes in such periodic structures, we furthermore show that two counterpropagating phase-matching conditions can be fulfilled simultaneously, allowing for the generation of path-entangled Bell states in a single periodic waveguide. To demonstrate the feasibility of our proposal, we design a photonic crystal slab waveguide made of lithium niobate and numerically demonstrate Bell-state generation.
Ultra-bright source of entangled photons is an essential component in optical quantum information processing. Here we propose a counterpropagating path-entangled photon pair sources using a quasi-periodic modulated lithium niobate crystal. The nonlinear crystal designed by a dual-grid method, simultaneously phase-matched two spontaneous parametric down-conversion processes. Signal and idler modes have opposite propagation directions in the two spontaneous parametric down-conversion processes, which is the key to generating path-entangled photon pairs. Compared to copropagating entangled sources, the counterpropagating path-entangled sources result in a much narrower spectrum. The quantum state of the path-entanglement source is not only suited for quantum coding, but also to allow the implementation of complex quantum algorithms on a photonic chip.
Summary form only given. Correlated photons are a key ingredient of many experiments testing the foundations of quantum mechanics and in quantum information processing. Many of these experiments harness entanglement by means of the nonclassical interference of photon pairs. A critical issue for such experiments is the mode matching of the photonic wave packets. Spontaneous parametric down-conversion is a well-established and practical method for generating pairs of correlated photons. High visibility interference of photon pairs generated by down-conversion in bulk crystals, a standard source for this type of experiments, can be achieved only by significant spatial filtering, which dramatically reduces the useful fraction of photon pairs. It also reduces the correlations between the presence of photons, thus opening for example the efficiency loophole in tests of Bell's inequalities. Nonlinear waveguides, compared to bulk crystals, offer several advantages as a source of correlated photon pairs. Most importantly, the waveguide structure provides a means to control precisely the spatial characteristics of generated photons, because of the well-defined transverse modes of the guide. in addition, nonlinear waveguides offer both higher pair production rates by utilizing the technique of quasiphase matching, and possibilities for spectral mode engineering.
Spontaneous parametric downconversion (SPDC) using periodically poled nonlinear optical crystals under the quasiphase- matching condition has found wide use in quantum optics. High efficiencies and good coupling to single-mode fibers resulted from using channel waveguides in crystals. It is often desirable to have a very narrow bandwidth for the signal and idler photons, but under the typical operating conditions, phase matching dictates the bandwidth of the SPDC to be of the order of <1 nm. This occurs because the co-propagating signal and idler photons are entangled, and an increase of the signal wave-vector is compensated by a decrease of the idler wave-vector. One way to reduce the bandwidth is by forming either external or internal cavities. Additionally, bandwidth reduction is possible without cavities when the signal and idler are counter-propagating, and the changes in the wave-vector with frequency are additive. To accomplish this a domain inversion on the wavelength scale is required. In this work, we experimentally demonstrate SPDC in one-dimensional KTP-based waveguides with sub-micron poling for forward and backward interactions. Some of the spectral features of the generated light are accounted for by mode coupling theory in periodically poled waveguides but other features are as yet not explained.