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arXiv:cond-mat/0402603 · Europhysics Letters (EPL)

Entangled electronic state via an interacting quantum dot

Gabriela Arias León, Otto Rendón, Horacio M. Pastawski, Vladimiro Mújica, Ernesto A. Medina

Published May 27, 2004• 4 citations

Abstract

We study a device for entangling electrons as co-tunneling occurs through a quantum dot where on-site electron-electron interactions U are in place. The main advantage of this device is that single-particle processes are forbidden by energy conservation as proposed by Oliver et al. ( Phys. Rev. Lett. 88 (2002) 7901). Within this model we calculated the two-electron transition amplitude, in terms of the T-matrix, to all orders in the coupling to the dot, and consider a finite lead bandwidth. The model filters singlet entangled pairs with the sole requirement of Pauli principle. Feynman paths involving consecutive and doubly occupied dot interfere destructively and produce a transition amplitude minimum at a critical value of the onsite repulsion U . Singlet filtering is demonstrated as a function of a gate voltage applied to the dot with a special resonance condition when the dot levels are symmetrically placed about the input lead energy.

DOI: 10.1209/epl/i2003-10257-1

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We study a device for entangling electrons as co-tunneling occurs through a quantum dot where on-site electron-electron interactions U are in place. The main advantage of this device is that single-particle processes are forbidden by energy conservation as proposed by Oliver et al. ( Phys. Rev. Lett. 88 (2002) 7901). Within this model we calculated the two-electron transition amplitude, in terms of the T-matrix, to all orders in the coupling to the dot, and consider a finite lead bandwidth. The model filters singlet entangled pairs with the sole requirement of Pauli principle. Feynman paths involving consecutive and doubly occupied dot interfere destructively and produce a transition amplitude minimum at a critical value of the onsite repulsion U . Singlet filtering is demonstrated as a function of a gate voltage applied to the dot with a special resonance condition when the dot levels are symmetrically placed about the input lead energy.

We study the two-qubit controlled-NOT gate operating on qubits encoded in the spin state of a pair of electrons in a double quantum dot. We assume that the electrons can tunnel between the two quantum dots encoding a single qubit, while tunneling between the quantum dots that belong to different qubits is forbidden. Therefore, the two qubits interact exclusively through the direct Coulomb repulsion of the electrons. We find that entangling two-qubit gates can be performed by the electrical biasing of quantum dots and/or tuning of the tunneling matrix elements between the quantum dots within the qubits. The entangling interaction can be controlled by tuning the bias through the resonance between the singly occupied and doubly occupied singlet ground states of a double quantum dot.

It has been suggested (Giavaras et al 2007 Phys. Rev. B 75 085302) that a quantum dot structure, which consists of a small open dot formed within a larger dot, can generate spin entanglement between two electrons and filter singlet–triplet states as a consequence of Coulomb interaction and the Pauli exclusion principle. In this work, we show via numerical modelling how to form the dot structure in an AlGaAs/GaAs/AlGaAs quasi-one-dimensional channel using top and back gates. We calculate the confining potential of the dot and the corresponding low-lying two-electron states and demonstrate a way of controlling the degree of entanglement and filtering by tuning the dot potential with the voltage applied to a back gate.

We consider a three-port single-level quantum dot system with one input and two output leads. Instead of considering an empty dot, we study the situations that two input electrons co-tunnel through the quantum dot occupied by one or two dot electrons. We show that electron entanglement can be generated via the co-tunneling processes when the dot is occupied by two electrons, yielding non-local spin-singlet states at the output leads. When the dot is occupied by a single electron, we show that by carefully selecting model parameters non-local spin-triplet electrons can also be obtained at the output leads if the final dot electron has the same spin as that of the initial dot electron.

This Letter presents a method of electron entanglement generation. The system under consideration is a single-level quantum dot with one input and two output leads. The leads are arranged such that the dot is empty, single-electron tunneling is suppressed by energy conservation, and two-electron virtual cotunneling is allowed. Such a configuration effectively filters the singlet-state portion of a two-electron input, yielding a nonlocal spin-singlet state at the output leads. Coulomb interaction mediates the entanglement generation, and, in its absence, the singlet state vanishes. This approach is a four-wave mixing process analogous to the photon entanglement generated by a chi((3)) parametric amplifier.

We study two simple mesoscopic models of interacting two electrons; first one consists of two quantum coherent parallel conductors with long-range Coulomb interaction in some localized region and the other is of an interacting quantum dot (QD) side-coupled to a noninteracting quantum wire. We evaluate exact two-particle scattering matrix as well as two-particle current which are relevant in a two-particle scattering experiment in these models. Finally we show that the on-site repulsive interaction in the QD filters out the spin-singlet two-electron state from the mixed two-electron input states in the side-coupled QD model.