Speaker
Description
We present an analytical study of the quantum dynamics of a bipartite spin-½ system modeling a two-electron quantum dot, extending our recently developed framework for the bipartite Pauli equation in a constant magnetic field to include the spin–spin (Heisenberg exchange) interaction between the two components. Retaining the closed-form Hermite–Gaussian solutions for the spatial part under quadratic confinement and an approximated Coulomb potential, we augment the spin Hamiltonian with an isotropic exchange coupling and recompute the eigenvalues and eigenbispinors. The exchange interaction lifts the degeneracy between the singlet and the zero-projection triplet found in the non-interacting, charge-symmetric case, opening a tunable singlet–triplet gap while preserving the Zeeman splitting within the triplet manifold. The competition between the exchange and magnetic contributions produces a singlet–triplet level crossing at a critical field, modifying the selective Zeeman response reported previously. These results provide an analytically tractable description of exchange-driven spin dynamics and coherent entanglement generation in confined two-electron quantum dots, directly relevant to singlet–triplet qubit operation.
