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arXiv:cond-mat/0612452 · Physical Review B

Generation of spin entanglement in nonequilibrium quantum dots

Stefan Legel, Jürgen König, Guido Burkard, Gerd Schön

Published Aug 22, 2007• 19 citations
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Abstract

We propose schemes for generating spatially separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin entanglement is found in nonequilibrium situations with one extra electron on each dot, either in the transient state after rapid changes of the gate voltage or in the steady state with applied bias voltage. In both cases, so-called Werner states with spin-singlet fidelity exceeding $1∕2$ are generated, which indicates entanglement.

DOI
10.1103/physrevb.76.085335

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We propose schemes for generating spatially separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin entanglement is found in nonequilibrium situations with one extra electron on each dot, either in the transient state after rapid changes of the gate voltage or in the steady state with applied bias voltage. In both cases, so-called Werner states with spin-singlet fidelity exceeding 1∕21∕21∕2 are generated, which indicates entanglement.
Spin entanglement between two spatially separated electrons can be generated in nonequilibrium interacting quantum dots, coherently coupled to a common lead. In this system entangled two-electron states develop which are Werner states with an imbalance between singlet and triplet probabilities. We propose a multi-terminal, multiply connected set-up for the generation and detection of this imbalance. In particular, we identify a regime in which the formation of spin entanglement leads to a cancellation of Aharonov–Bohm oscillations.
Spin entanglement between two spatially separated electrons can be generated in nonequilibrium interacting quantum dots, coherently coupled to a common lead. In this system entangled two-electron states develop which are Werner states with an imbalance between singlet and triplet probabilities. We propose a multi-terminal, multiply connected set-up for the generation and detection of this imbalance. In particular, we identify a regime in which the formation of spin entanglement leads to a cancellation of Aharonov–Bohm oscillations.
We propose a simple setup of three coupled quantum dots in the Coulomb blockade regime as a source for spatially separated currents of spin-entangled electrons. The entanglement originates from the singlet ground state of a quantum dot with an even number of electrons. To preserve the entanglement of the electron pair during its extraction to the drain leads, the electrons are transported through secondary dots. This prevents one-electron transport by energy mismatch, while joint transport is resonantly enhanced by conservation of the total two-electron energy.
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.
A theoretical scheme is presented for the entanglement of two-electron spin qubits bound in series within a quasi-one-dimensional mesoscopic structure at a distance beyond their normal range of interaction. A third electron is scattered from them, and full entanglement is achieved upon measurement of a transmitted electron in the correct spin state. Critically, each bound electron is trapped within an individual structure that has at least two spatial states. Two simple examples of such structures are discussed here. One is a 'stub', in which a quantum dot (for example) is coupled to one side of the quasi-one-dimensional structure. The other is a pair of degenerate, coupled quantum dots, with strong interdot Coulomb repulsion, placed within the one-dimensional superstructure. Both of these are shown to allow generation of entanglement with a significant probability of success. In contrast to the results of the authors' previous works, this allows for the generation of entanglement in a series, rather than in a parallel, configuration of the bound electrons with respect to the propagating electron.