Entanglement generation through an open quantum dot: an exact approach

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.

💡 Research Summary

This paper presents an exact analytical study of entanglement generation in an open quantum‑dot system modeled by the two‑lead Anderson Hamiltonian. The authors consider two electrons initially injected from one lead in a non‑entangled product state with opposite spins, |k₁,↑;k₂,↓⟩, and examine their scattering into the opposite lead. By solving the Lippmann‑Schwinger equation for the full two‑electron problem, they construct the exact scattering state |Ψ⟩ of the Anderson model. A striking feature of this state is the emergence of a spin‑singlet bound component that is induced solely by the on‑site Coulomb repulsion U on the dot. This bound component describes processes in which the set of individual momenta is not conserved; only the total energy remains fixed. Consequently the scattering state does not belong to the family of Bethe‑Ansatz eigenstates, which always preserve the full set of momenta.

From the exact scattering solution the transition amplitude T(k₁,k₂→q₁,q₂) between the incident product state and an outgoing state is derived. The corresponding transition rate Γ∝|T|² is evaluated analytically as a function of the tunnelling amplitude t, the dot‑lead hybridisation, the dot level ε_d, and the Coulomb interaction U. The central result is that in the cotunnelling regime—where electrons virtually occupy the dot before emerging in the other lead—only the spin‑singlet channel contributes to Γ; the spin‑triplet (parallel‑spin) channel is completely suppressed when U≠0. In the non‑interacting limit (U=0) both channels are allowed, reproducing the familiar result for a resonant level.

Physically, the Coulomb interaction creates a virtual two‑electron bound state on the dot. While the electrons reside on the dot, they experience an effective attraction in the spin‑singlet sector, lowering the intermediate energy and enhancing the cotunnelling amplitude for this channel. The bound state’s lifetime is set by the tunnelling rate, and its existence leads to a non‑conservation of individual momenta—a hallmark of a process that cannot be captured by a simple Bethe‑Ansatz description.

The authors discuss experimental implications. By fabricating a quantum dot coupled to two leads and employing spin‑resolved detection (e.g., spin filters or quantum point contacts with spin sensitivity), one can measure the spin‑resolved current or current‑current correlations in the output lead. The theory predicts a pronounced increase in the singlet‑pair transmission probability and a complete absence of triplet transmission when the dot is in the Coulomb‑blockade regime. Noise spectroscopy or time‑resolved charge detection could further reveal the bound‑state dynamics.

Finally, the work highlights the potential of quantum dots as deterministic sources of electron‑spin entanglement. Unlike photonic schemes, the electron‑based approach is naturally compatible with solid‑state quantum‑information architectures, allowing direct integration with spin qubits, spin‑filter devices, and entanglement‑distribution networks. The exact solution presented here provides a benchmark for future studies of interacting open quantum systems and opens avenues for engineering interaction‑driven entanglement in nanoscale electronic devices.