Manipulação e mapeamento de correlações quânticas em estados de quatro qudits espaciais

Abstract

During the past thirty years the field of Quantum Information has beenvery successful in proposing protocols and algorithms that involve two-level quantum systems known as qubits. It has been shown that cryptographic keys can be distributed securely using quantum resources and that quantum algorithms can solve tasks such as the factoring of large numbers with an exponential speedup over classical algorithms. Most implementations, however, are restricted to proof-of-concept experiments using few qubits, due to the difficulty of scaling the physical systems utilized. Quantum systems with more than two levels, called qudits, present themselves as an alternative way of obtaining a space with large dimensionality without recurring to a large number of qubits. This reduces the number of particles necessary for implementing protocols in a scale that is relevant for practical applications. Additionally, pairs of entangled qudits are more robust agains noise than their qubit counterparts and are also more adequate for experiments that test the non-local and contextual behavior of nature, as predicted by its description using Quantum Mechanics. In this thesis we present the construction and characterization of a source of states of four qudits. We used a pulsed laser as pump for type-II Spontaneous Parametric Down Conversion (SPDC) to occur on a PPKTP, a KTiOPO4 (KTP) crystal with a periodic ferroelectric domain inversion, a technique called periodic poling. In type-II SPDC a pair of photons, also called biphoton, is generated in which one has horizontal polarization while the other hasvertical polarization. Due to the use of a pulsed pump beam and the highdown-conversion efficiency of our PPKTP, the probability that a single pump pulse will originate two pairs of photons is high. In order to generate qudits we used the multiple-slit implementation, meaning that a multiple slit was placed between the PPKTP and the detectors, encoding discrete qudit states onto the continuous transverse mode of the biphoton. Using double, triple and quadruple slits we produced, respectively, qubit, qutrit and ququart states. A system of lenses placed between the PPKTP and the slits manipulated the amplitude of the transverse biphoton state impinging on the slits and, thus, the quantum correlations between qudits after the slits. By projecting either the near or far field of the crystal onto the slits, the lenses changed the characteristics of the biphoton amplitude function and allowed us to obtain either states with very high entanglement, in the case of the near field, or very low entanglement, in the case of the far field. A lens in the f-f configuration between the plane of the slits and the plane of the detectors projected the far field of the slits, so we could observe conditional interference patterns. We detected the photons in coincidence asa function of the position of two detectors These were used to generate maps of coincidences between two photons with different polarization and for two photons with the same polarization. The first case contains contributions from photons of a single pair and from photons from two different pairs, while the second case contains contributions from different pairs only. In order to isolate the single pair contribution on different-polarization coincidences, we removed the background component from photons of different pairs, given by the same-polarization coincidences. Besides serving to isolate the singlepair signal, same-polarization coincidences confirm the existence two-pair events and give us information about the purity of the reduced state of a single photon, which is related to the degree of entanglement in a biphoton. We conclude that manipulating the biphoton transverse amplitude is a promising technique for generating qudit states while controlling their entanglement and correlation properties, especially if more exotic transverse amplitudes are explored, such as Hermite-Gaussian pump beams or amplitudes engineered with a spatial light modulator. The use of high-efficiency SPDC sources allows for states of more than one biphoton, engineered using transverse amplitude manipulation, to be employed in many different protocolsin Quantum Information, serving as sources of heralded pure or mixedstates, or playing an important role in tests of the non-local and contextual nature of physical systems, as predicted by Quantum Mechanics.