The Hamiltonian Structure of Soliton Equations and Deformed W-Algebras

The Poisson bracket algebra corresponding to the second Hamiltonian structure of a large class of generalized KdV and mKdV integrable hierarchies is carefully analysed. These algebras are known to have conformal properties, and their relation to $\cal W$-algebras has been previously investigated in some particular cases. The class of equations that is considered includes practically all the generalizations of the Drinfel'd-Sokolov hierarchies constructed in the literature. In particular, it has been recently shown that it includes matrix generalizations of the Gelfand-Dickey and the constrained KP hierarchies. Therefore, our results provide a unified description of the relation between the Hamiltonian structure of soliton equations and $\cal W$-algebras, and it comprises almost all the results formerly obtained by other authors. The main result of this paper is an explicit general equation showing that the second Poisson bracket algebra is a deformation of the Dirac bracket algebra corresponding to the $\cal W$-algebras obtained through Hamiltonian reduction.Comment: 41 pages, plain TeX, no figures. New introduction and references added. Version to be published in Annals of Physics (N.Y.

All-Optical Fiber Hanbury Brown & Twiss Interferometer to study 1300 nm single photon emission of a metamorphic InAs Quantum Dot

[EN] New optical fiber based spectroscopic tools open the possibility to develop more robust and efficient characterization experiments. Spectral filtering and light reflection have been used to produce compact and versatile fiber based optical cavities and sensors. Moreover, these technologies would be also suitable to study N-photon correlations, where high collection efficiency and frequency tunability is desirable. We demonstrated single photon emission of a single quantum dot emitting at 1300 nm, using a Fiber Bragg Grating for wavelength filtering and InGaAs Avalanche Photodiodes operated in Geiger mode for single photon detection. As we do not observe any significant fine structure splitting for the neutral exciton transition within our spectral resolution (46 mu eV), metamorphic QD single photon emission studied with our all-fiber Hanbury Brown & Twiss interferometer could lead to a more efficient analysis of entangled photon sources at telecom wavelength. This all-optical fiber scheme opens the door to new first and second order interferometers to study photon indistinguishability, entangled photon and photon cross correlation in the more interesting telecom wavelengths.G Munoz-Matutano thanks the Spanish Juan de la Cierva program (JCI-2011-10686). We acknowledge the support of the Spanish MINECO through projects TEC2014-53727-C2-1-R & TEC2014-60378-C2-1-R, the Research Excellency Award Program GVA PROMETEO 2013/012 PROMETEOII/2014/059 and the Explora Ciencia Tecnologia TEC2013-50552-EXP MULTIFUN project, and the Nanoscale Quantum Optics MPNS COST Action MP1403.Muñoz Matutano, G.; Barrera Vilar, D.; Fernandez-Pousa, CR.; Chulia-Jordan, R.; Seravalli. L.; Trevisi, G.; Frigeri, P.... (2016). All-Optical Fiber Hanbury Brown & Twiss Interferometer to study 1300 nm single photon emission of a metamorphic InAs Quantum Dot. Scientific Reports. 6(2721):1-9. https://doi.org/10.1038/srep27214S1962721Walmsley, I. A. 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Excitation spectroscopy of single quantum dots at tunable positive, neutral and negative charge states. Phys. Rev. B 86, 085306 (2012).Muñoz-Matutano, G. et al. Selective optical pumping of charged excitons in unintentionally doped InAs quantum dots. Nanotechnology 19, 145711 (2008).Ha, N. et al. Size-dependent line broadening in the emission spectra of single GaAs quantum dots: Impact of surface charge on spectral diffusion. Phys. Rev. B 92, 075306 (2015).Moskalenko, E. S. et al. Influence of excitation energy on charged exciton formation in self-assembled InAs single quantum dots. Phys. Rev. B 64, 085302 (2001).Rivas, D. et al. Two-color single-photon emission from InAs quantum dots: toward logic information management using quantum light. Nano Lett. 14, 456–463 (2014).Dekel, E. et al. Cascade evolution and radiative recombination of quantum dot multiexcitons studied by time-resolved spectroscopy. Phys. Rev. B 62, 11038 (2000).Wimmer, M., Nair, S. & Shumway, J. 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Parallel Recording of Single Quantum Dot Optical Emission Using Multicore Fibers

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Single Indium Arsenide Quantum Dot emission spectra have been recorded using a four-core, crosstalk-free, multicore fiber placed at the collection arm of a confocal microscope. We developed two different measurement set-ups depending on the relative configuration of the excitation and collection spots. In the single-matched mode, the emission from the excited area is collected by a single core in the multicore fiber, whereas the three remaining cores capture the emission from neighboring, non-excited areas. This procedure allows for the recording of the Quantum Dot emission from carrier diffusion between sample positions separated by more than 6 μm. In the multiple-matched mode, the excitation spot overlaps the four cores emission area. This configuration permits the acquisition of the micro-photoluminescence spectra at different sample positions without scanning. These results show the possibilities offered by multicore fibers for the spectroscopic analysis of single semiconductor Quantum Dot optical emission.This work was supported in part by the Research Excellency Award Program GVA PROMETEO under Grant 2013/012, in part by the Explora Ciencia Tecnologia through the MULTIFUN Project under Grant TEC2013-50552-EXP, in part by the Research Excellency Award Program GVA PROMETEOII under Grant 2014/059, and in part by the Ministerio de Economia y Competitividad under Grant TEC2014-53727-C2-1-R and Grant TEC2014-60378-C2-1-R. The work of G. Munoz-Matutano was supported by the Spanish Ministerio de Economia y Competitividad through the Juan de la Cierva Program under Grant JCI-2011-10686. The work of I. Gasulla was supported by the Spanish Ministerio de Economia y Competitividad through the Ramon y Cajal Program under Grant RyC-2014-16247.Muñoz-Matutano, G.; Barrera Vilar, D.; Fernandez-Pousa, CR.; Chulia-Jordan, R.; Martinez-Pastor, J.; Gasulla Mestre, I.; Seravalli, L.... (2016). Parallel Recording of Single Quantum Dot Optical Emission Using Multicore Fibers. IEEE Photonics Technology Letters. 28(11):1257-1260. https://doi.org/10.1109/LPT.2016.2538302S12571260281

The Relativistic Avatars of Giant Magnons and their S-Matrix

The motion of strings on symmetric space target spaces underlies the integrability of the AdS/CFT correspondence. Although these theories, whose excitations are giant magnons, are non-relativistic they are classically equivalent, via the Polhmeyer reduction, to a relativistic integrable field theory known as a symmetric space sine-Gordon theory. These theories can be formulated as integrable deformations of gauged WZW models. In this work we consider the class of symmetric spaces CP^{n+1} and solve the corresponding generalized sine-Gordon theories at the quantum level by finding the exact spectrum of topological solitons, or kinks, and their S-matrix. The latter involves a trignometric solution of the Yang-Baxer equation which exhibits a quantum group symmetry with a tower of states that is bounded, unlike for magnons, as a result of the quantum group deformation parameter q being a root of unity. We test the S-matrix by taking the semi-classical limit and comparing with the time delays for the scattering of classical solitons. We argue that the internal CP^{n-1} moduli space of collective coordinates of the solitons in the classical theory can be interpreted as a q-deformed fuzzy space in the quantum theory. We analyse the n=1 case separately and provide a further test of the S-matrix conjecture in this case by calculating the central charge of the UV CFT using the thermodynamic Bethe Ansatz.Comment: 33 pages, important correction to S-matrix to ensure crossing symmetr

Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure

The Faddeev-Reshetikhin procedure corresponds to a removal of the non-ultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to alleviate in a similar way the non-ultralocality of symmetric space sigma models. The equivalence of the equations of motion holds only at the level of the Pohlmeyer reduction of these models, which corresponds to symmetric space sine-Gordon models. This work therefore shows indirectly that symmetric space sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an integrable potential, have a mild non-ultralocality. The first step needed to construct an integrable discretization of these models is performed by determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change

Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3

We study classical open string solutions with a null polygonal boundary in AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS_n and generalized parafermions.Comment: 25 pages, 4 figures, v2: a figure and references added, minor corrections, v3: references added, minor corrections, to appear in JHE

Manipulating spatial qudit states with programmable optical devices

The study of how to generate high-dimensional quantum states (qudits) is justified by the advantages that they can bring for the field of quantum information. However, to have some real practical potential for quantum communication, these states must be also of simple manipulation. Spatial qudits states, which are generated by engineering the transverse momentum of the parametric down-converted photons, have been until now considered of hard manipulation. Nevertheless, we show in this work a simple technique for modifying these states. This technique is based on the use of programmable diffractive optical devices, that can act as spatial light modulators, to define the Hilbert space of these photons instead of pre-fabricated multi-slits