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Energy spectra, spin configurations, and entanglement characteristics of asystem of four electrons in lateral double quantum dots are investigated usingexact diagonalization (EXD), as a function of interdot separation, appliedmagnetic field, and strength of interelectron repulsion. A distinctly differentquantum behavior is found compared to that of circular single quantum dots. Asa function of the magnetic field, the energy spectra exhibit a low-energy bandconsisting of a group of six states, with the number six being a consequence ofthe conservation of the total spin of the four electrons and the ensuing spindegeneracies. These six states appear to cross at a single value of themagnetic field, with the crossing point becoming sharper for larger interdotdistances. As the strength of the Coulomb repulsion increases, the six statestend to become degenerate and a well defined energy gap separates them from thehigher-in-energy excited states.  The appearance of the low-energy band is a consequence of the formation of aWigner supermolecule, with the four electrons (two in each dot) being localizedat the vertices of a rectangular parallelogram. Using the spin-resolvedpair-correlation functions, one can map the EXD many-body wave functions ontothe spin functions associated with the four localized electrons. Analogies withnanomagnets, such as finite Heisenberg clusters, are discussed. The ability todetermine associated spin functions enables investigations concerningentanglement properties of the system of four electrons. In particular, theformation of Wigner supermolecules generates EXD solutions belonging to theclass of strongly entangled states referred to as N-qubit Dicke states in thequantum-information literature.

Excitation spectra, spin structures, and entanglement characteristics of four-electron double-quantum-dot artificial molecules