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Modern Physics Letters B

QUANTUM ENTANGLEMENT OF DOUBLE ELECTRONS IN TWO COUPLED QUANTUM DOTS

Haiyu Li

Published Jul 20, 2007• 2 citations
Publisher

Abstract

We study the system of vertically coupled two quantum dots in confined single electron. Coulomb interaction between two electrons and Rashba type spin-orbit coupling are taken into account. It is a two-Fermion system, hence the antisymmetric requirement of electronic states must be considered. Four lower antisymmetric eigenfunctions are found out. Based on the rotation wave approximation, the coherent manipulation of quantum state in an external electric pulse with some resonance harmonic frequencies are investigated. The instantaneous degree of quantum entanglement of the state in time-dependent external electronic field is calculated.

DOI
10.1142/s0217984907013419

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We study the system of vertically coupled two quantum dots in confined single electron. Coulomb interaction between two electrons and Rashba type spin-orbit coupling are taken into account. It is a two-Fermion system, hence the antisymmetric requirement of electronic states must be considered. Four lower antisymmetric eigenfunctions are found out. Based on the rotation wave approximation, the coherent manipulation of quantum state in an external electric pulse with some resonance harmonic frequencies are investigated. The instantaneous degree of quantum entanglement of the state in time-dependent external electronic field is calculated.
We theoretically explore the possibility of creating spin quantum entanglement in a system of two electrons confined respectively in two vertically coupled quantum dots in the presence of Rashba-type spin-orbit coupling. We find that the system can be described by a generalized Jaynes-Cummings model of two-mode bosons interacting with two spins. The lower excited states of this model are calculated to reveal the underlying physics of the far-infrared absorption spectra. The analytic perturbation approach shows that an effective transverse coupling of spins can be obtained by eliminating the orbital degrees of freedom in the large-detuning limit. Here, the orbital degrees of freedom of the two electrons, which are described by two-mode bosons, serve as a quantized data bus to exchange the quantum information between the two electron spins. Then a nontrivial two-qubit logic gate is realized and spin entanglement between the two electrons is created by virtue of spin-orbit interactions.
Recently, an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using spin states of coupled single-electron quantum dots was proposed. It was demonstrated that it is possible to execute a coherent control of a quantum system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. This possibility is based on rapid electrical control of the spin exchange interaction. These results motivated us to develop a formal theoretical study of the corresponding model of two coupled spins placed in a magnetic field and subjected to a time-dependent mutual Heisenberg interaction. Using possible exact solutions of the corresponding quantum problem, we study entangling of different separable initial states in this model. It is demonstrated that the entanglement due to a time-dependent Heisenberg interaction is dominating in comparison with the entanglement due to the action of an external magnetic field.
Recently a pair of vertically aligned quantum dots has been suggested as optically driven quantum gate. The later is built when two different particles, an electron and a hole, are created optically. The two particles form entangled states. We study theoretically the dynamics of a single heavy hole exciton confined in a small vertically coupled quantum dot. We use harmonic potentials to model the confining of electrons and holes and calculate the exciton's energy spectrum using the Hund-Mulliken approach, and including the Coulomb interaction. The entanglement may be controlled by the application of external electric field. At certain times of dynamical evolution one can generate a maximally entangled coherent exciton state by initially preparing the quantum dots in a superposition of coherent state. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, a real quantum system is inevitably influenced by its environment. Since, we study the decoherence effect caused by the interaction of the confined carriers with the acoustic phonon effects. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
In this work, we study the thermal quantum coherence and fidelity in a two-level system with spin-orbit coupling. The proposed model involves a single electron in a double quantum dot with Rashba spin-orbit coupling in the presence of an external magnetic field. In our scenario, the thermal entanglement of the single electron is driven by the charge and spin qubits, the latter controlled by Rashba coupling. Analytical expressions are obtained for thermal concurrence and correlated coherence using the density matrix formalism. The main goal of this work is to provide a good understanding of the effects of temperature and several parameters in quantum coherence. In addition, our findings show that we can use the Rashba coupling to tune the thermal entanglement, quantum coherence, and the thermal fidelity behavior of the system. Moreover, we focus on the role played by thermal entanglement and correlated coherence responsible for quantum correlations. We observe that the correlated coherence is more robust than the thermal entanglement in all cases, so quantum algorithms based only on correlated coherence may be stronger than those based on entanglement.
A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.
Finding efficient methods for controlling entanglement is an important issue in quantum information processing. Here, we inspect theoretically possible ways for tuning orbital and spin entanglement of two interacting particles confined to a double quantum dot with spin-orbit coupling (SOC) which renders possible the coupling of spin to an external electric field. The entanglement in the spin part is sensitive to a transverse electric field. We show that through the field-induced SOC the entanglement of the spin subsystem can be slightly increased; the effect of a longitudinal electric field is more subtle: For a small interdot distance, a longitudinal electric field enhances substantially the entanglement of spins, while for a large interdot distance it has no impact. An external longitudinal electric field has a minor effect on the entanglement in the orbital part irrespective of the interdot distance. We trace back this observed phenomenon to a combined effect of the applied external electric field and the overlap of wave functions which is enhanced for decreasing interdot distances. As a result, at large interdot separation, the concurrence of the two-electron states turns insensitive to the applied electric field.