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Reconstrução da matriz densidade via corrente spin polarizada

Midana Sambú

Published Mar 3, 2023• 0 citations
Publisher

Abstract

This present thesis araised as theorical proposal for the reconstruction of density matrix of a single electron spin qubit using spin polarized transport. This model consists in a composed system for quantum dot attached to the ferromagnetics reservoir with magnetic field along plane on the Bloch sphere. The aim is investigating tunneling events of polarized spin along ±, ± and ± direction that provide distribuition of probabilities along these axis-quantization, in which we relate, through Stokes parameters, with density matrix, allowing, thereby, the reconstruction of the density matrix. For this aim, we did experimental simulation using python in which we created code that allowed us making the simulation of the system. Being an open system, we used the Lindblad master equation to simulate the dynamics of the system that provide us the evolution of the system along time. After experimental simulation, we were able of reconstructing the density matrix from probabilities getting through of dynamics of the system, verifying, thereby, the predict results by our theorical model. The model offers a vision about density matrix of open quantum system, probability amplitudes and relative phases.

DOI
10.14393/ufu.di.2023.152

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This present thesis araised as theorical proposal for the reconstruction of density matrix of a single electron spin qubit using spin polarized transport. This model consists in a composed system for quantum dot attached to the ferromagnetics reservoir with magnetic field along plane on the Bloch sphere. The aim is investigating tunneling events of polarized spin along ±, ± and ± direction that provide distribuition of probabilities along these axis-quantization, in which we relate, through Stokes parameters, with density matrix, allowing, thereby, the reconstruction of the density matrix. For this aim, we did experimental simulation using python in which we created code that allowed us making the simulation of the system. Being an open system, we used the Lindblad master equation to simulate the dynamics of the system that provide us the evolution of the system along time. After experimental simulation, we were able of reconstructing the density matrix from probabilities getting through of dynamics of the system, verifying, thereby, the predict results by our theorical model. The model offers a vision about density matrix of open quantum system, probability amplitudes and relative phases.
We propose a theoretical protocol for reconstructing the density matrix of a single-electron spin qubit using spin-polarized transport. The system consists of a quantum dot coupled to ferromagnetic reservoirs and subject to a magnetic field lying in the xyxyxy plane of the Bloch sphere. Spin-dependent tunneling events measured along the x±x\pmx±, y±y\pmy±, and z±z\pmz± quantization axes give rise to probability distributions that encode the quantum state of the qubit. The open-system dynamics are described using a Lindblad master equation, which captures the time evolution of the spin under continuous coupling to the reservoirs. By counting tunneling events for four different magnetic alignments, we formulate a scheme for reconstructing the full density matrix of the qubit. The resulting simulation data are analyzed using machine-learning techniques to process the measured probability distributions and infer the corresponding density matrix elements. The proposed model enables complete access to the open-system density matrix, including both population probabilities and relative phase information. Successful state reconstruction demonstrates the validity and robustness of the approach, highlighting its applicability to experimentally accessible spin-transport platforms.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possibles paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possible paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
We consider a scenario where interacting electrons confined in quantum dots (QDs) are either too close to be resolved, or we do not wish to apply measurements that resolve them. Then, the physical observable is an electron spin only and the system state is fully described by the spin density matrix. Accounting for the spatial degrees of freedom, we examine to what extent a Hamiltonian description of the spin-only degrees of freedom is valid. We show that as long as there is no coupling between singlet and triplet states, this is indeed the case, but when there is such a coupling, there are open systems effects, i.e., the dynamics is nonunitary even without interaction with a true bath. Our primary focus is an investigation of nonunitary effects, based on exact master equations we derive for the spin density matrix in the Lindblad and time-convolutionless forms, and the implications for quantum computation. In particular, we demonstrate that the Heisenberg interaction does not affect the unitary part (apart from a Lamb shift) but does affect the nonunitary contributions to the time evolution of the spin density matrix. In a sequel paper, we present a detailed analysis of an example system of two quantum dots, including spin-orbit effects.
The density matrix is a useful concept which will allow one to deal with a large collection of spinors with a statistical distribution at time t = 0 and follow their time evolution by tracking the time evolution of a new operator (the density matrix). This will require the extension of the Bloch sphere to the Bloch ball concept, in which the vector representing the collection of spinors will be able to reach points in the interior of the Bloch sphere as a function of time. This requires the inclusion of damping and scattering mechanisms representing interactions among spinors, and also their interactions with the environment. The phenomenological equations allowing a description of these relaxation mechanisms are known as Bloch’s equations. They are introduced here through a connection to the Bloch sphere and Bloch ball concepts. The longitudinal and transverse relaxation times, T1 and T2, respectively, are also introduced and some numerical examples (results of Monte-Carlo simulations) are presented to illustrate their physical meaning.
The density matrix is a useful concept which will allow one to deal with a large collection of spinors with a statistical distribution at time t = 0 and follow their time evolution by tracking the time evolution of a new operator (the density matrix). This will require the extension of the Bloch sphere to the Bloch ball concept, in which the vector representing the collection of spinors will be able to reach points in the interior of the Bloch sphere as a function of time. This requires the inclusion of damping and scattering mechanisms representing interactions among spinors, and also their interactions with the environment. The phenomenological equations allowing a description of these relaxation mechanisms are known as Bloch’s equations. They are introduced here through a connection to the Bloch sphere and Bloch ball concepts. The longitudinal and transverse relaxation times, T1 and T2, respectively, are also introduced and some numerical examples (results of Monte-Carlo simulations) are presented to illustrate their physical meaning.