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arXiv:cond-mat/0205553 · Physical Review Letters

Spin-Entangled Currents Created by a Triple Quantum Dot

Daniel S. Saraga, Daniel Loss

Published Apr 24, 2003• 190 citations
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Abstract

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.

DOI
10.1103/physrevlett.90.166803

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We present electron spin entanglers-devices creating mobile spin-entangled electrons that are spatially separated-where the spin-entanglement in a superconductor present in form of Cooper pairs and in a single quantum dot with a spin singlet groundstate is transported to two spatially separated leads by means of a correlated two-particle tunneling event. The unwanted process of both electrons tunneling into the same lead is suppressed by strong Coulomb blockade effects caused by quantum dots, Luttinger liquid effects or by resistive outgoing leads. In this review we give a transparent description of the different setups, including discussions of the feasibility of the subsequent detection of spin-entanglement via charge noise measurements. Finally, we show that quantum dots in the spin filter regime can be used to perform Bell-type measurements that only require the measurement of zero frequency charge noise correlators.
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.
We propose and analyze a spin-entangler for electrons based on an s-wave superconductor coupled to two quantum dots, each of which is coupled to normal Fermi leads. We show that in the presence of a voltage bias and in the Coulomb blockade regime two correlated electrons provided by the Andreev process can coherently tunnel from the superconductor via different dots into different leads. The spin singlet coming from the Cooper pair remains preserved in this process, and the setup provides a source of mobile and nonlocal spin-entangled electrons. The transport current is calculated and shown to be dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at exactly the same orbital energy, which is a crucial requirement for the detection of spin entanglement via noise measurements. The coherent tunneling of both electrons into the same lead is suppressed by the on-site Coulomb repulsion and/or the superconducting gap, while the tunneling into different leads is suppressed through the initial separation of the tunneling electrons. In the regime of interest the particle-hole excitations of the leads are shown to be negligible. The Aharonov-Bohm oscillations in the current are shown to contain single- and two-electron periods with amplitudes that both vanish with increasing Coulomb repulsion albeit differently fast.
A Pauli spin blockade in quantum dot systems occurs when the charge transport is allowed only for some spin states, and it has been an efficient tool in spin-based qubit devices in semiconductors. We theoretically investigate a Pauli spin blockade in a triple quantum dot molecule consisting of three identical quantum dots in a semiconductor in the presence of an external magnetic field through the molecule. When the three-electron state is on resonance with two- or four-electron states, the Aharonov–Bohm oscillation and the Zeeman splitting lead to a periodic spin blockade effect. We focus on the spin blockade at a two- and three-electron resonance and show that we can tune the magnetic field to selectively allow only either a spin-singlet or spin-triplet state to add an additional electron from tunnel-coupled leads. This spin blockade maintains the three quantum dots at the optimal sweet spot against the charge noise, demonstrating its potential as an efficient readout scheme for the qubits in quantum dot systems.