arXiv:1401.0005 · Physical Review B

Impurity entanglement through electron scattering in a magnetic field

Alexandros Metavitsiadis, Raoul Dillenschneider, Sebastian Eggert

Published Apr 4, 2014• 6 citations

Abstract

We study the entanglement of magnetic impurities in an environment of electrons through successive scattering while an external magnetic field is applied. We show that the dynamics of the problem can be approximately described by a reduced model of three interacting spins, which reveals an intuitive view on how spins can be entangled by controlled electron scattering. The role of the magnetic field is rather crucial. Depending on the initial state configuration, the magnetic field can either increase or decrease the resulting entanglement but more importantly it can allow the impurities to be maximally entangled.

DOI: 10.1103/physrevb.89.155406

Related papers

Entanglement of Two Impurities through Electron Scattering

A. T. Costa, Sougato Bose, Yasser Omar

We study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electron's state. We start by investigating an ideal case where only the electronic spin interacts successively through the same unitary operation with the spins of the two impurities. We find conditions for the impurity spins to be maximally entangled with a significant success probability. We then consider a more realistic description which includes both the forward and backscattering amplitudes. In this scenario, we obtain the entanglement between the impurities as a function of the interaction strength of the electron-impurity coupling. We find that our scheme allows us to entangle the impurities maximally with a significant probability.

arXiv:quant-ph/0503183Physical Review LettersJun 15, 200659 citations

Impurity effect on entanglement in an XY two-dimensional spin lattice

Gehad Sadiek

We consider a finite two dimensional XY spin model. The model consists of a set of seven localized spin- 12 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction in presence of an external magnetic field. We study the effect of a single impurity spin coupled to its nearest neighbor through an exchange interaction J′ on the pairwise entanglement between the different spins in the lattice. We found that when the spin is located at a border site the entanglement between the impurity and its nearest neighbors increases monotonically with J′ reaching a saturation value that depends on the magnetic field strength h. On the other hand the entanglement with the next nearest spins shows a critical behavior where the entanglement increases and then decreases rapidly until it vanishes. The critical coupling value at which the entanglement vanishes increases as h increases. Studying the entanglement between two spins excluding the impurity show that while the entanglement between two spins coupled to the impurity reach a saturation value as J′ increases, it vanishes for spins not coupled to the impurity. Furthermore studying the effect of a central impurity show that the entanglement between nearest neighbor and next nearest neighbor spins reaches an asymptotic value as J′ increases. Interestingly it was demonstrated that the impurity can be used as a switch to control the entanglement between different spins in the lattice turning it on and off.

Journal of King Saud University - ScienceAug 23, 20112 citations

Two-spin entanglement induced by electron scattering in nanostructures

Gian Luca Giorgi, FERDINANDO DE PASQUALE

We present a model where two magnetic impurities in a discrete tight-binding ring become entangled because of scattering processes associated to the injection of a conduction electron. We introduce a weak-coupling approximation that allows us to solve the problem in an analytical way and compare the theory with the exact numerical results. We obtain the generation of entanglement both in a deterministic way and in a probabilistic one. The first case is intrinsically related to the structure of the two-impurity reduced density matrix, while the second one occurs when a projection on the electron state is performed.

arXiv:cond-mat/0607603Physical Review BOct 20, 200619 citations

Pairwise entanglement in the XX model with a magnetic impurity

Hong‐Chen Fu, A. I. Solomon, Xiaoguang Wang

For a three-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modelling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanced to the maximal value 1; while when the field acts on a site of the pair the corresponding concurrence can only be increased from 1/3 to 2/3.

arXiv:quant-ph/0201025Journal of Physics A Mathematical and GeneralMay 3, 200249 citations

Electron Fabry–Perot interferometer with two entangled magnetic impurities

Francesco Ciccarello, G. Massimo Palma, Michelangelo Zarcone +2 more

We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave vectors, the triplet and singlet maximally entangled spin states of the impurities can respectively largely inhibit the electron transport or make the wire completely transparent for any electron spin state. In the latter case, a resonance condition can always be found, representing an anomalous behaviour compared to typical decoherence induced by magnetic impurities. We provide an explanation for these phenomena in terms of the Hamiltonian symmetries. Finally, a scheme to generate maximally entangled spin states of the two impurities via electron scattering is proposed.

arXiv:quant-ph/0611025Journal of Physics A Mathematical and TheoreticalJun 27, 200733 citations

Modulating thermal robustness and entanglement distribution in a two-dimensional dissipative spin system using impurities

Gehad Sadiek, Maryam AlQasimi

We consider a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian environment at finite temperature in the presence of an external uniform magnetic field. We show how inserting a magnetic impurity in the spin system can be used to effectively control the dynamics and asymptotic state of the system. A strong impurity, at a border or central site, was found to enhance its entanglement with the other spins and their thermal robustness to the dissipative environment reaching an asymptotic state that is independent of the system initial state. However, it reduces the entanglement among the other spins in the lattice and their thermal robustness and may diminish them depending on its strength and the environment temperature. Moreover, the effect of the impurity increases significantly as the degree of anisotropy of the spin system increases. Therefore, the entanglement distribution over the different sites of the lattice can be modulated by tuning the impurity strength, system anisotropy and environment temperature. The impurity can be used as a switch that turns the entanglement on among specific spins and off among others simultaneously.

Results in PhysicsMar 11, 20222 citations