We perform the quantitative evaluation of the entanglement dynamics in scattering events between two indistinguishable electrons interacting via the Coulomb potential in one- and two-dimensional 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 wave function of the scattering carriers we compute their entanglement evolution for different spin configurations: two electrons with the same spin, with different spin, and singlet and triplet spin states. The procedure allows us 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.
We investigate the time evolution of pairwise entanglement between two Tavis–Cummings atoms for various entangled initial states, including pure and mixed states. We find that the phenomenon of entanglement sudden death behaviors is distinct in the evolution of entanglement for different initial states. What deserves mentioning here is that the initial portion of the excited state in the initial state is responsible for the sudden death of entanglement, and the degree of this effect also depends on the initial states.
We study the dynamics of quantum entanglement between two harmonically trapped electrons interacting via the electromagnetic force. Starting from two-mode Gaussian states at thermal equilibrium, we make use of the covariance matrix formalism in order to compute the logarithmic negativity of the evolved state as a quantitative measure of entanglement. We analyze two initial configurations: thermal single-mode and two-mode squeezed states, and describe the time evolution of entanglement in the system for different values of squeezing and temperature, while identifying the parameter regimes accessible to current and near-future single-electron trap experiments.
Based on the correlated ground-state wave function of an exactly solvable interacting one-dimensional two-electron model Hamiltonian we address the switch-off of confining and interparticle interactions to calculate the exact time-evolving wave function from a prescribed correlated initial state. Using this evolving wave function, the time-dependent pair probability function $\mathcal{R}({x}_{1},{x}_{2},t)\ensuremath{\equiv}{n}_{2}({x}_{1},{x}_{2},t)/[n({x}_{1},t)\phantom{\rule{0.16em}{0ex}}n({x}_{2},t)]$ is determined via the pair density
n2(x1,x2,t) and single-particle density
n(x,t). It is found that $\mathcal{R}(0,0,t=\ensuremath{\infty})=\mathcal{R}(0,0,t=0)>1$, and
R(x1,x2,t∗)=1 at a finite
t∗ for $\ensuremath{\Lambda}\ensuremath{\ne}0$ interparticle interaction strength in the initial two-electron model. By expanding
n(x,t) in an infinite sum of closed-shell products of time-dependent normalized single-particle states and time-dependent occupation numbers ${P}_{k}(\ensuremath{\Lambda},t)$, the von Neumann entropy $S(\ensuremath{\Lambda},t)=\ensuremath{-}{\ensuremath{\sum}}_{k=0}^{\ensuremath{\infty}}{P}_{k}(t)\mathrm{ln}{P}_{k}(t)$ is calculated as well. The such-defined information entropy is zero at ${t}^{*}(\ensuremath{\Lambda})$ and its maximum in time is $S(\ensuremath{\Lambda},t=\ensuremath{\infty})=S(\ensuremath{\Lambda},t=0)$.
The pairwise entanglement dynamics in a multipartite system consisting of three two-level atoms A, B, C and a single-mode cavity field a is studied via negativity. Three atoms are arranged in such a way that atoms BC are embedded in and locally interact with the cavity while atom A is located in a spatially separate place outside of the cavity. Initially, atom-pair AB is prepared in a Bell-like state while atom C in a superposition of ground and excited state, |gC〉 and |eC〉. It shall be shown that all the pairwise negativities of the total system including atoms and cavity undergo qualitatively different evolutions. The so-called entanglement sudden death is observed for atom-pair AB under certain conditions and the entanglement transfer among all the possible degrees of freedom of the whole system is also discussed.