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Emaranhamento eletrônico em moléculas de pontos quânticos semicondutores

Patrícia Oliveira

Published Feb 20, 2015• 0 citations
Publisher

Abstract

In this work, we study the dynamics of entanglement between two eletronic qubits inside two coupled quantum molecules, where each molecule is consisting of two semiconductor quantum dots.Our first interest is to explore the production of maximally entangled states in the two level system not considering dissipation.Using the Bell states, we define a new basis for the system of interest, which allows to obtain a new Hamiltonian for the quantum molecules.To analyze the characteristics of eigenstates of the Hamiltonian which describes the quantum molecules, we use a measure of entanglement called concurrence.From the new base, we verify the behavior the dynamics of entanglement by manipulating the physical parameters of the system as the detuning and the tunneling between the quantum dots contained in molecules and the Coulomb interaction.We identified a set of physical parameters which are linked to the creation of maximally entangled states and other conditions where it is not possible to entangle the subsystems.

DOI
10.14393/ufu.di.2015.77

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In this work, we study the dynamics of entanglement between two eletronic qubits inside two coupled quantum molecules, where each molecule is consisting of two semiconductor quantum dots.Our first interest is to explore the production of maximally entangled states in the two level system not considering dissipation.Using the Bell states, we define a new basis for the system of interest, which allows to obtain a new Hamiltonian for the quantum molecules.To analyze the characteristics of eigenstates of the Hamiltonian which describes the quantum molecules, we use a measure of entanglement called concurrence.From the new base, we verify the behavior the dynamics of entanglement by manipulating the physical parameters of the system as the detuning and the tunneling between the quantum dots contained in molecules and the Coulomb interaction.We identified a set of physical parameters which are linked to the creation of maximally entangled states and other conditions where it is not possible to entangle the subsystems.
In this thesis, we will analyze quantum entanglement phenomena in systems composed of quantum molecules, considering two different models. In the first, N molecules, each with a single excess electron, interact via Coulomb coupling. This interaction is restricted to the first neighbors. In the second system, electrons from distinct molecules interact with each other through the electron-phonon coupling. Considering the N-molecule system, we broadened our studies started in the master’s degree to verify the characteristics of the energy spectrum and eigenstates for the molecule system. We focus on the scalability of the system and its effect on entanglement, showing that some specific eigenstates are systematically associated with the maximally entangled GHZ states, regardless of the number of molecules. In the second part of the work, we explore the entanglement of both the electronic subsystem and the phonon subsystem, defining a new base composed of Bell’s electronic states associated with the excitation states in vibrational modes, which allows rewriting the Hamiltonian to the composite system. From this point of view, it is possible to determine a set of 4 ⊗ 4 matrix subspaces that elucidated the study of the entanglement behavior in both subsystems, allowing the determination of distinct sets of parameters effective in generating highly entangled states in the electronic subsystem and now in the phononic subsystem.
The effects of electronic initialization of quantum states on the entanglement in electronic systems remain an open question. Our research focuses on a system model comprising of quantum dot molecules attached to electronic reservoirs. Two electronic qubits interact with each other via Coulomb repulsion. The interplay between Coulomb and hopping process results on the formation of entangled states. Here we analyse how a Gaussian gate voltage pulse, that injects electrons into the qubits in a time controlled way, can interfere on the entanglement degree. To this aim we calculate different quantities such as fidelity, Von Neumann entropy and negativity . Ours results show that the proper adjustment of the initialization pulse width is crucial to the formation of highly entangled states, thus shining light on possible future experimental implementation of electronic qubits.
In this work, we show how electron-vibrational mode coupling can be used to drive maximally entangled states. The physical system consists of two pairs of quantum dots, each pair with a single electron able to tunnel between the dots, thus encoding a qubit. The electron-vibrational mode coupling, described by the strength parameter ggg, yields to an effective electron-electron interaction, responsible for the formation of a maximally entangled quantum state. Both the formation time and the relative phase of the aforementioned state are strongly dependent on ggg. The quantum dynamics exhibits a nonmonotonic behavior as ggg increases, an effect explained through an effective Hamiltonian that takes into account high-order transition processes.
The generation of entanglement between two identical, interacting quantum dots---initially in ground states---by a coherent field and the subsequent time evolution of the entanglement are studied by calculating the concurrence between the two dots. The results predict that while it is possible to generate entanglement (or entanglement of formation, as defined for a mixed state) between the two dots, at no time do the dots become fully entangled to each other or is a maximally entangled Bell state ever achieved. We also observe that the degree of entanglement increases with an increase in the photon number inside the cavity and a decrease in the dot-photon coupling. The behavior of the two-dot system, initially prepared in an entangled state and interacting with thermal light, is also studied.
In the present work we investigated the physical properties of quantum systems of two [1], three [2] and four [3] levels formed by electrons, excitons and trions using the formalism of the density matrix. The unitary evolution of the systems is based on the Liouville-von Neumann [4] master equation and the decoherence e ects are included according to the Lindblad [5] formalism. We investigated the optical properties [6] of these systems, looking for favorable conditions to the regime of electromagnetically induced transparency [7]. We calculate the geometric phases associated with the two and three level systems for pure and mixed states according to the formalism de ned by Pancharatnan [8]. In the four-level system we manipulate Gaussian pulses of test and control, provoking temporal delays [9], chirps [10] and creating ultra-short pulse trains [11] to induce coherent population accumulation and investigate the soliton propagation of light in the regime of transparency associated with the quantum memory phenomenon. We investigated the e ciency of a photocell of quantum dots coupled by tunnels in the presence of an external source of radiation within the Markovian [12] approximation for the interaction between system and reservoir.
The dynamics of the entanglement for coherent excitonic states in the system of two, coupled, large semiconductor quantum dots ${(R/a}_{B}\ensuremath{\gg}1)$ mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is present in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of the excitons.