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arXiv:0905.3445

Entanglement generation through an open quantum dot: an exact approach

Imamura, Takashi, Akinori Nishino, Naomichi Hatano

Published May 21, 2009• 0 citations
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Abstract

We analytically study entanglement generation through an open quantum dot system described by the two-lead Anderson model. We exactly obtain the transition rate between the non-entangled incident state in one lead and the outgoing spin-singlet state in the other lead. In the cotunneling process, only the spin-singlet state can transmit. To discuss such an entanglement property in the open quantum system, we construct the exact two-electron scattering state of the Anderson model. It is striking that the scattering state contains spin-singlet bound states induced by the Coulomb interaction. The bound state describes the scattering process in which the set of momenta is not conserved and hence it is not in the form of a Bethe eigenstate.

DOI
10.48550/arxiv.0905.3445

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We analytically study entanglement generation through an open quantum dot system described by the two-lead Anderson model. We exactly obtain the transition rate between the non-entangled incident state in one lead and the outgoing spin-singlet state in the other lead. In the cotunneling process, only the spin-singlet state can transmit. To discuss such an entanglement property in the open quantum system, we construct the exact two-electron scattering state of the Anderson model. It is striking that the scattering state contains spin-singlet bound states induced by the Coulomb interaction. The bound state describes the scattering process in which the set of momenta is not conserved and hence it is not in the form of a Bethe eigenstate.
We analytically study entanglement generation through an open quantum-dot system described by the two-lead Anderson model. We exactly obtain the transition rate between the nonentangled incident state in one lead and the outgoing spin-singlet state in the other lead. We find that only the spin-singlet state can transmit in the cotunneling process. To discuss such an entanglement property in the open quantum system, we construct the exact two-electron scattering state of the Anderson model. It is striking that the scattering state contains spin-singlet bound states induced by the Coulomb interaction. The bound state describes a scattering process in which the set of momenta is not conserved and hence, it is not in the form of a Bethe eigenstate.
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.
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 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.
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 show how two qubits encoded in the orbital states of two quantum dots can be entangled or disentangled in a controlled way through their interaction with a weak electron current. The transmission/reflection spectrum of each scattered electron, acting as an entanglement mediator between the dots, shows a signature of the dot–dot entangled state. Strikingly, while a few scattered carriers produce decoherence of the whole two-dot system, a larger number of electrons injected from one lead with proper energy are able to recover its quantum coherence. Our numerical simulations are based on a real-space solution of the three-particle Schrödinger equation with open boundaries. The computed transmission amplitudes are inserted in the analytical expression for the system density matrix to evaluate the entanglement.