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arXiv:quant-ph/0611018 · Physical Review Letters

Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices

Alfred B. U’Ren, Reinhard K. Erdmann, Manuel de la Cruz Gutierrez, Ian A. Walmsley

Published Nov 29, 2006• 70 citations
arXivHTMLPDF

Abstract

We demonstrate a general method of engineering the joint quantum state of photon pairs produced in spontaneous parametric down-conversion. The method makes use of a superlattice structure of nonlinear and linear materials, in conjunction with a broadband pump, to manipulate the group delays of the signal and idler photons relative to the pump pulse, and realizes photon pairs described by a joint spectral amplitude with arbitrary degree of entanglement. This method of group-delay engineering has the potential of synthesizing a broad range of states including factorizable states crucial for quantum networking and states optimized for Hong-Ou-Mandel interferometry. Experimental results for the latter case are presented, illustrating the principles of this approach.

DOI
10.1103/physrevlett.97.223602

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We demonstrate a general method of engineering the joint quantum state of photon pairs produced in spontaneous parametric down-conversion. The method makes use of a superlattice structure of nonlinear and linear materials, in conjunction with a broadband pump, to manipulate the group delays of the signal and idler photons relative to the pump pulse, and realizes photon pairs described by a joint spectral amplitude with arbitrary degree of entanglement. This method of group-delay engineering has the potential of synthesizing a broad range of states including factorizable states crucial for quantum networking and states optimized for Hong-Ou-Mandel interferometry. Experimental results for the latter case are presented, illustrating the principles of this approach.
It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider a scheme that involves two parametric processes---${\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, ${\ensuremath{\omega}}_{2}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{1}$ under pulsed pump---and investigate the spontaneous creation of a photon triplet as well as the generation of high-intensity mode in intracavity three-photon splitting. We show the preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework of considering the dual-grid structure that involves two periodically poled crystals. We demonstrate the method of compensation of the dispersive effects in nonlinear segments by appropriately chosen linear dispersive segments of superlattice for preparation of the heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on the investigation of photon-number distributions, third-order photon-number correlation function, as well as the Wigner functions. These quantities are observed both for short interaction time intervals and the over-transient regime, when dissipative effects are essential.
The search for new methods to produce entangled photons is a subject of great interest in quantum optics. We show theoretically that two_photon entangled states may be generated through a cascaded nonlinear optical process in a quasiperiodic optical superlattice. When an idler photon ωi produced from spontaneous parametric down conversion (ωp=ωs+ωi) combines with a pum p photon to produce a sum frequency photon ωb(ωb=ωi+ω p), the latter is entangled with the remaining signal photon ωi. Both a pulsed and a cw 532nm laser have been used to pump a quasi_phase matched LiTaO 3 crystal to generate simultaneously 630nm signal photons through parametric d own conversion and 460nm sum frequency photons. The advantage of this method is that entangled photons of short wavelength may be produced.
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In the process of spontaneous parametric down-conversion, photons from a pump field are converted to signal and idler photon pairs in a nonlinear crystal. The reversed process, or up-conversion of these pairs back to single photons in a second crystal, is also possible. Here, we present experimental measurements of the up-conversion rate with a controlled time delay introduced between the signal and idler photons. As a function of delay, this rate presents a full width at half maximum of 27.9 fs under our experimental conditions, and we further demonstrate that group delay dispersion of the photon pairs broadens this width. These observations are in close agreement with our calculations, thus demonstrating an ultrafast, nonclassical correlation between the signal and idler waves.
We describe properties of entangled photon pairs generated by spontaneous parametric down-conversion in periodically poled nonlinear crystals. These materials can serve as a useful bright source of photon pairs which properties can be tailored on demand. Especially photon pairs with broad spectra and sharp temporal features can be observed. Both uniform and chirped poling are considered. Spectral properties of the generated photons, photon fluxes, coincidence-count patterns in a Hong-Ou-Mandel interferometer, entropy of entanglement, as well as transverse profiles of intensities of the generated photon fields are discussed. Also the correlation area of two photons comprising a photon pair has been studied as it depends on parameters of periodical poling. Attention is also paid to structures with randomly distributed boundaries.
We experimentally demonstrate an approach for manipulating the spectral profiles of entangled-photon pairs. The spectral properties are determined by selecting both the appropriate spatial profile of the pump laser radiation and the geometry of the noncollinear spontaneous parametric downconversion. Both spectra, the spectrum of the individual signal and idler photons, and the joint spectrum of the entangled-photon pairs, can be modified at will over a substantial range of values. This technique is therefore expected to be useful for an array of quantum-optics applications.