Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems

Abstract

We perform the quantitative evaluation of the entanglement dynamics in scattering events between two insistinguishable electrons interacting via Coulomb potential in 1D and 2D semiconductor nanostructures. We apply a criterion based on the von Neumann entropy and the Schmidt decomposition of the global state vector suitable for systems of identical particles. From the time-dependent numerical solution of the two-particle wavefunction of the scattering carriers we compute their entanglement evolution for different spin configurations: two electrons with the same spin, with different spin, singlet, and triplet spin state. The procedure allows to evaluate the mechanisms that govern entanglement creation and their connection with the characteristic physical parameters and initial conditions of the system. The cases in which the evolution of entanglement is similar to the one obtained for distinguishable particles are discussed.

Linear entropy as an entanglement measure in two-fermion systems

“…(24) we observe that the minimum value of the LE of |Ξ is 3 4 , greater than the value of an offset is related to the lack of knowledge about the spin of the particles. The behavior shown by the triplet and singlet states is in agreement with the one obtained in previous works where the entanglement formation is evaluated in terms of the vNE for the case of one-dimensional and two-dimensional scattering [15,24], as we show in the following.…”

“…In order to get a better understanding of this criterion, we first apply it to study a simple prototype theoretical model, then we analyze a system of physical interest, namely a two-electron scattering event in a 2D semiconductor structure. The entanglement dynamics in such a system has been recently investigated in terms of the vNE [15,24] and a comparison with previous results lead to the conclusion that the LE can be an efficient and still valid entanglement measure for binary collisions, as for other physical phenomena of interest in quantum-information processing where identical particles are involved.…”

Two-electron entanglement in elliptically deformed quantum dots

“…In this work we consider the von Neumann (vN) entropy and the linear entropy that are the most popular measures of entanglement in pure states. The vN entropy [25,26,21] is defined as…”

Зацепление Электронов Во Взаимодействующих Молекулах

“…Покажем, как можно вычислить редуцированную матрицу плотности (9). Для упрощения вычислений рассмотрим случай двух электронов в двухуровневой систе-ме.…”

“…Хе с соавторами нашли в ра-боте [8] спектр энергий, парные корреляционные функции и степень зацепления двуэлектронных состояний в самоконцентрирующихся молекулах квантовой точки в сплаве InAs/GaAs, учитывая конфигурацию, в которой связанные состояния вза-имодействуют между собой, и сравнили величины, найденные при различных при-ближениях. Бускеми с соавторами произвели численные расчеты динамики зацеп-ления в процессах рассеяния двух неразличимых электронов, взаимодействующих посредством кулоновского потенциала в одно-и двумерных полупроводниковых на-ноструктурах [9]. Авторы при этом следовали идее Шлимана [10], развитой другими авторами [11], [12], согласно которой матрицу плотности в представлении простран-ственных координат можно использовать для вычисления энтропии фон Неймана.…”