Abstract
We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process. Employing the complex-coordinate rotation method, we determine the resonance widths and energies and discuss their dependence on the longitudinal confinement potential and the lateral radius of the quantum dot. The stability properties of the system are discussed.
Highlights
It has become possible to fabricate few-particle systems that realize simple models of quantum theory and enable quantitative comparison with the accurate solutions of the Schrodinger equation
The calculations were performed with the number of basis functions M = 342 in the singlet case and M = 324 in the triplet case, which proved sufficient to obtain convergent results
The depth of the trap has an important effect on the critical value of the interaction strength gth at which the bound state is transformed into a resonance, namely the larger is the value of V0, the larger is gth
Summary
It has become possible to fabricate few-particle systems that realize simple models of quantum theory and enable quantitative comparison with the accurate solutions of the Schrodinger equation. The number of constituents, and the interactions between them and the geometry of the system can be modelled at will by applying appropriately designed electromagnetic fields. Those systems create a versatile platform for testing the effectiveness of approximation methods used in solving quantum many-body problems. The new experimental possibilities gave an impetus for accurate theoretical studies of simple two-body systems subjected to external potentials.
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