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Efeitos da Inicialização na Formação de Emaranhamento Quântico em Qubits de Carga

Ellen Fernandes

Published Jul 31, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.14393/ufu.di.2024.5169

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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.
We examine the impact of time-dependent gate voltages on entanglement generation in two capacitively coupled charge qubits, with single-electron injection triggered on demand. The gate voltage modulates the tunnel coupling between the qubits and electronic reservoirs, initiating charge transport into the system. The formation of entangled states arises from the competition between interqubit Coulomb interactions and electron-hopping processes. Particular attention is paid to the temporal structure of the gate pulse, which plays a pivotal role in shaping the entanglement dynamics. By exploring a variety of pulse profiles, we uncover regimes of enhanced entanglement and identify optimal driving conditions. Additionally, we investigate how environmental dephasing deteriorates entanglement formation. Within the framework of the density-matrix formalism, we calculate fidelity, linear entropy, and negativity to identify robust operational windows. These results provide insights into controlling quantum correlations in mesoscopic systems and underscore the importance of error-mitigation strategies in realizing high-performance electronic quantum devices.
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.
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 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.
We propose schemes for generating spatially separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin entanglement is found in nonequilibrium situations with one extra electron on each dot, either in the transient state after rapid changes of the gate voltage or in the steady state with applied bias voltage. In both cases, so-called Werner states with spin-singlet fidelity exceeding 1∕21∕21∕2 are generated, which indicates entanglement.
The entanglement dynamics of spin–subband states for an electron in a 2D isotropic Rashba quantum dot, with an applied magnetic field of arbitrary strength, is studied. We explicitly include the confining (gate) effects as a two-dimensional isotropic harmonic oscillator. The von Neumann entropy, as a measure of entanglement, is calculated as a function of time, by going to the Fock–Darwin representation. Our results indicate that the period and amplitude of the collapse–revival behavior of the entanglement between the spin states and the structural subbands strongly depend upon the size of the quantum dot (confining length) and choice of heterostructural materials. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these factors.