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arXiv:cond-mat/9504033 · Physical review. B, Condensed matter

Entangled electronic states in multiple-quantum-dot systems

Simon C. Benjamin, Neil F. Johnson

Published May 15, 1995• 30 citations
arXivHTMLPDF

Abstract

We present an analytically solvable model of P colinear, two-dimensional quantum dots, each containing two electrons. Interdot coupling via the electron-electron interaction gives rise to sets of entangled ground states. These ground states have crystal-like interplane correlations and arise discontinuously with increasing magnetic field. Their ranges and stabilities are found to depend on dot size ratios and to increase with P.

DOI
10.1103/physrevb.51.14733

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Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individual-particle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, which results in the states with symmetries related to the latter representation only being entangled even at the vanishing interaction, is discussed. The analytical expression for the entanglement measure based on the linear entropy is derived in the limit of noninteracting electrons. It reproduces remarkably well the numerical results for the lowest states with the magnetic quantum number $M\ensuremath{\ge}2$ in the interacting regime. It is found that the entanglement of the ground state is a discontinuous function of the field strength. A method to estimate the entanglement of the ground state, characterized by the quantum number MMM, with the aid of the magnetic-field dependence of the addition energy is proposed.
Incompressible (magic) states that result from many-body effects in vertically coupled quantum dots submitted to strong magnetic fields such that only the lowest Landau level is relevant are studied within an exact diagonalization calculation for N=3,N=3,N=3, 5, and 6, electrons. We find that the sequences of total angular momentum M for which these incompressible states exist depend on the interplay between the interdot hopping parameter ${\ensuremath{\Delta}}_{t}$ and the interdot distance d. For d of the order of the magnetic length and for all values of ${\ensuremath{\Delta}}_{t},$ we conclude that, in contrast to previous claims, these incompressible states appear at magic values of M which do not differ from those obtained for a single dot: namely, $M=N(N\ensuremath{-}1)/2+jN,$ where j is a positive integer number. For large interdot distance and simultaneously small interdot hopping parameter, new sequences of magic values of M are observed. These new sequences can be easily understood in terms of a transition regime towards a system of two decoupled single dots. However, important differences in the nature of the incompressible ground states are found with respect to those of a single dot.