Two-electron entanglement in quasi-one-dimensional systems: Role of resonances

Abstract

We analyze the role of resonances in two-fermion entanglement production for a quasi-one-dimensional two-channel scattering problem. We solve exactly for the problem of a two-fermion antisymmetric product state scattering off a double-␦-well potential. It is shown that the two-particle concurrence of the post-selected state has an oscillatory behavior where the concurrence vanishes at the values of momenta for virtual bound states in the double well. These concurrence zeros are interpreted in terms of the uncertainty in the knowledge of the state of the one-particle subspace-reduced one-particle density matrix. Our results suggest the manipulation of fermion entanglement production through the resonance structure of quantum dots.Entanglement production and quantification have been given much recent attention due to their importance as a resource for quantum information and quantum communication. 1,2 In this direction, there have been recent proposals for producing bipartite fermionic entangled states in the solid-state environment focusing on the role of the direct interaction between particles. Some of these approaches involve direct Coulomb interactions in quantum dots 3 and interference effects, 4 phonon-mediated interactions in superconductors, 5,6 and Kondo-like scattering of conduction electrons. 7 Nevertheless, it has been shown that fermion entanglement can be achieved in the absence of such interactions 8 in the form of particle-hole entanglement even when fermions are injected from thermal reservoirs. In such a setup the orbital degree of freedom is entangled. Other implementations based on the noninteracting scheme have been proposed that entangle the spin degree of freedom and are thus more robust to decoherence 9 because of the weaker coupling of the spin to the environment.In this work we address the problem of entanglement generation for electrons in the context of a two-channel quasione-dimensional conductor, 10 following the scattering matrix formalism of Ref. 8 For the scattering region, we choose a double-␦ potential, separated a distance d. Such a potential is the simplest potential that exhibits resonances and that can be analytically handled. The problem is solved for the concurrence 11,12 exactly for all values of the barrier heights and separation as a function of the incoming electron momenta. The concurrence of the entangled post-selected state is found to oscillate while its envelope decays as a function of electron momentum ͑k i ͒ difference ⌬k = k 2 − k 1 . We find that the concurrence is exactly zero when one or both of the k values hits the resonant states for the potential well. The concurrence zeros are then interpreted in terms of the uncertainty of the state in the one-particle subspace by obtaining the reduced density matrix. We thus determine the role of resonances in the entangling properties of the well, demonstrating new possibilities for fermion entanglement control. We consider in detail the independent channel scenario but quantitative changes due to channel mixing will ...

Carrier-carrier entanglement and transport resonances in semiconductor quantum dots

“…In fact, if noninteracting electrons are considered, only one transmission channel is active, and, as a consequence, the von Neumann entropy results to be zero. We stress that, unlike other works estimating the quantum correlation in QDs, 8,33 we are not considering the transmitted and reflected components of the scattering wave function as two different states that can be entangled with the QD. We estimate the entanglement between the dot and the transmitted electron.…”

“…In this spirit, various proposals for producing bipartite entangled fermionic systems have been advanced, on the basis of different physical mechanisms requiring a direct interaction between particles. 5,[7][8][9][10]33 In this paper, we have investigated the quantum correlations appearing, as a consequence of a Coulomb scattering, between two electrons having the same spin, in a system of physical interest, where the degree of the entanglement results to be controllable by a proper tuning of the carrier energy and of the QD potential. Such a system consists of a quasi-1D double-barrier resonant tunneling device, where an electron incoming from one lead is scattered by the potential structure and, via the Coulomb interaction, by another electron bound in the QD.…”

“…What we found here is in agreement with previous analyses on the two-electron entanglement production in two-electron systems for a two-channel scattering model, where both particles are injected in only one of two leads. 8,33 In fact, also in those cases, the entanglement shows a maximum when the transmission probabilities for the two channels are identical, while it vanishes in correspondence to the single-particle resonances, where there is no uncertainty about the energy of the particle. Figure 3 shows that the TC of channel 0 presents a BreitWigner resonance for E IN Ӎ 17.5 meV.…”

On demand entanglement in double quantum dots via coherent carrier scattering

“…On the other hand, the QTBM takes explicitely into account the spatial structure and therefore the size and the shape of the dots, thus permitting to overcome the approximations implied in the description of a dot in terms of a two-level point-like system. We single-out the peculiar mechanisms of electron transport through DQDs resulting in resonances in the transmission and reflection spectra and thus leading to entanglement and decoherence [24,25,23,26,27]. In the evaluation of such effects, both the transmitted and reflected components of the scattered wavefunction are taken into account.…”

Two-electron-entanglement enhancement by an inelastic scattering process

“…Entanglement is indeed a very subtle global feature in which perturbation theory has to be considered carefully. 5,14 The main goal of our work is to determine how the inelastic nature of the scattering process modifies the wave function of the fermion system changing the mutual information encoded in the entanglement among the particles. In order to quantify entanglement we use the concurrence 15 and take advantage of Beenakker's second quantized scheme 8 which takes full account of the scattering ingredients for two noninteracting fermions in a second quantized description.…”