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Engenharia de estados espaciais de dimensões híbridas

Paula Davila Machado

Published Mar 4, 2016• 0 citations
OpenAlex

Abstract

In recent decades, Parametric Down Conversion (PDC) has been the main method of production of entangled photonic quantum states, most often bipartite. Inaddition, the discretization (withinacertainrange) of transversal momentum of the photon pair generated by PDC is the main tool for producing entangled qudits. Such discretization, in conjunction with different methods of experimental manipulation of photon beamsproduced in PDC, constitutes the various methods of engineering of slit states, which are well established only to states with dimensionality of the kind n×n. Inthismasters thesis, a study is presented of each of those methods of production applied to states of the form 2×2. As the central point of the work, is also presented their extension to case 2×3, aiming the generalization to any dimensionality of the form NxM. These twoparty discrete quantum states with different dimensions in each party is called Hybrid Dimension Quantum State.

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J. G. L. Condé

In this work we present a method of preparing and operating on photonic quantum states. It consists in coding quantum states in parallel Gaussian beams, which are transformed by diffraction gratings. We show through experimental results that this technique is able to operate in high-dimentional systems (D > 2) and perform sequential operations, among other advantages. We also show that, using the phenomenon of parametric down conversion, we are able to prepare two systems encoded in parallel Gaussian beams entangled with each other. Finally, we show that we can add one extra degree of freedom, the polarization, to create hyper-entangled states, i. e., entangled in more than one degree of freedom, and states that have hybrid entanglement, i. e., which present entanglement between different degrees of freedom.

•Aug 17, 2018•0 citations
In recent decades, Parametric Down Conversion (PDC) has been the main method of production of entangled photonic quantum states, most often bipartite. Inaddition, the discretization (withinacertainrange) of transversal momentum of the photon pair generated by PDC is the main tool for producing entangled qudits. Such discretization, in conjunction with different methods of experimental manipulation of photon beamsproduced in PDC, constitutes the various methods of engineering of slit states, which are well established only to states with dimensionality of the kind n×n. Inthismasters thesis, a study is presented of each of those methods of production applied to states of the form 2×2. As the central point of the work, is also presented their extension to case 2×3, aiming the generalization to any dimensionality of the form NxM. These twoparty discrete quantum states with different dimensions in each party is called Hybrid Dimension Quantum State.
In this thesis, we explore the properties of photons generated by parametric down-conversion (PDC) and entangled in continuous variables of transverse momentum, with the aim of using this degree of freedom for developing a new method for generating en-tangled states in discrete and multidimensional spaces. Such states have a great potential for applications in fundamental problems of quantum mechanics as well as in quantum information protocols. Our study is based on the theory of angular spectrum transfer from the laser beam tothe two-photon state, proposed and demonstrated by Monken, Souto Ribeiro and P Ladua [Phys. Rev. A 57, 3123 (1998)]. Using it, we investigate theoretically the evolution of the quantum state of photon pairs when they propagate from the crystal and are transmitted through linear optical systems like lenses and apertures. The two-photon state is calculated when there is only one optical system in the path of each photon and we also discuss the generalization of the method employed in the calculation, for more complex experiments. With the two-photon state obtained, we propose a method for generating entangledstates of qubits (two-dimensional quantum systems) and qudits (D-dimensional quantum systems), using the transverse momentum of photons from PDC. The method is based on the selection of specific transverse spatial modes of each photon, by using an array of D-slits (D . 2) in the path of these photons. In this method we have the control of the dimension, D, of each qudit and also the degree of entanglement between them, by manipulating the transverse laser beam profile, which is due to the transfer of angular spectrum. In order to test the theory, we make an experiment for a specific case, which has a great interest in practical applications of entanglement: we demonstrate the generation of maximally entangled states of qudits with D = 4 and D = 8. The quantum character of the correlations is assured qualitatively by measuring two-photon interference patterns with conditional fringes. We also investigate the propagation of these entangled states of qudits through free space and with a simple experiment we show that they can be distributed for distant and spatially separated parts, keeping the correlations. Finally, we perform an experiment for quantifying entanglement in this type of state that we are producing. In this work, we restrict ourselves to the simplest case of two qubits. We prepare different states by manipulating the transverse laser beam profile and their degree of entanglement is measured in two ways: (i) through the degree ofconditionality of the two-photon interference patterns and (ii) through the measurement of marginal probability. We discuss the extension of the method (i) for two-qudit states.
Discretizing transverse linear momentum of photon pairs, generated by spontaneous parametric down conversion (SPDC), is one of the simplest methods for producing bipartite entangled states in high dimensions. So far, it has been employed only to prepare states in dimensions $m\ifmmode\times\else\texttimes\fi{}m$. In this work, we study the generalization for engineering entangled states in dimensions $m\ifmmode\times\else\texttimes\fi{}n$. Our approach relies on the manipulation of the pump beam transverse profile and the phase-matching function of the SPDC process to prepare, behind an mmm- and nnn-slit aperture, different $m\ifmmode\times\else\texttimes\fi{}n$ spatial entangled states. We demonstrate the technique experimentally for some $2\ifmmode\times\else\texttimes\fi{}3$ states. Compared to previous approaches in producing $2\ifmmode\times\else\texttimes\fi{}n$ photonic entanglement, which require either more than two photons or hybrid entanglement, our scheme is less demanding and simpler since we employ only two photons and a single degree of freedom to encode the states.
We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.
We propose a method for generation of entangled photonic states in high dimensions, the so-called qudits, by exploiting quantum correlations of Orbital Angular Momentum (OAM) entangled photons, produced via Spontaneous Parametric Down Conversion. Diffraction masks containing N angular slits placed in the path of twin photons define a qudit space of dimension N2, spanned by the alternative pathways of OAM-entangled photons. We quantify the high-dimensional entanglement of path-entangled photons by the Concurrence, using an analytic expression valid for pure states. We report numerical results for the Concurrence as a function of the angular aperture size for the case of high-dimensional OAM entanglement and for the case of high-dimensional path entanglement, produced by N × M angular slits. Our results provide additional means for preparation and characterization of entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.
We show that the quantum disentanglement eraser implemented on a two-photon system from parametric downconversion is a general method to create hybrid photonic entanglement, namely the entanglement between different degrees of freedom of the photon pair. To demonstrate this, we generate and characterize a source with tunable degree of hybrid entanglement between two qubits, one encoded in the transverse momentum and position of a photon, and the other in the polarization of its partner. In addition, we show that a simple extension of our setup enables the generation of two-photon qubit-qudit hybrid entangled states. Finally, we discuss the advantages that this type of entanglement can bring for an optical quantum network.
In this work we present a method of preparing and operating on photonic quantum states. It consists in coding quantum states in parallel Gaussian beams, which are transformed by diffraction gratings. We show through experimental results that this technique is able to operate in high-dimentional systems (D > 2) and perform sequential operations, among other advantages. We also show that, using the phenomenon of parametric down conversion, we are able to prepare two systems encoded in parallel Gaussian beams entangled with each other. Finally, we show that we can add one extra degree of freedom, the polarization, to create hyper-entangled states, i. e., entangled in more than one degree of freedom, and states that have hybrid entanglement, i. e., which present entanglement between different degrees of freedom.