Artificial quantum-dot helium molecules: Electronic spectra, spin structures, and Heisenberg clusters

Abstract

Energy spectra and spin configurations of a system of N = 4 electrons in lateral double quantum dots (quantum dot Helium molecules) are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field (B), and strength of interelectron repulsion. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin and the ensuing spin degeneracies for four electrons. The energies of the six states appear to cross at a single value of the magnetic field, and with increasing Coulomb repulsion they tend to become degenerate, with a well defined energy gap separating them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangle. Using spinresolved pair-correlation distributions, a method for mapping the complicated EXD many-body wave functions onto simpler spin functions associated with a system of four localized spins is introduced. Detailed interpretation of the EXD spin functions and EXD spectra associated with the low-energy band via a 4-site Heisenberg cluster (with B-dependent exchange integrals) is demonstrated. Aspects of spin entanglement, referring to the well known N -qubit Dicke states, are also discussed. PACS numbers: 73.21.La, 31.15.V-, 03.67.Mn, 03.65.Ud

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg andt–Jmodels

“…In this paper, using large-scale configuration-interaction (CI) calculations as means for exact diagonalization of the microscopic Hamiltonian, we report that for N=4 (even number) strongly interacting ultracold fermions in a DW trap with parallel arrangement (DWPA [26]; see figures 1(II), (III)) the many-body problem can be reduced to that of a 2D rectangular AFM Heisenberg ring. The associated mapping between the many-body wave function and the spin eigenfunctions [31] for N=3 and N=4 electrons confined in single and double semiconductor quantum dots has been predicted in previous studies [11,12] to occur through the formation of quantum molecular structures in the regime of strong long-range Coulombic repulsion. Such molecular structures are usually referred to as Wigner molecules (WMs) [32].…”

“…The external confining potential (in H(i)) that models a DW is based on a two-center-oscillator (TCO) model [12,26] exhibiting a variable smooth neck along the x-direction. Along the x direction, this TCO model allows for an independent variation of both the separation d and of the barrier height V b between the two wells; see figure 3.…”

“…Thus a detailed description of the CI method will not be repeated here (see additional details in [26]). Specific adaptations by us of this method to a few electrons in 2D semiconductor quantum dots and rotating bosons in the lowest Landau level have been reported in [12,32,50], respectively. An earlier application by us of this method to the case of N=2 trapped ultracold fermions was reported in [26].…”

“…For lack of space, we will not consider here many-body wave functions with ¹ S 0 z for four fermions or with ¹ S 1 2 z for three fermions. For an earlier study of such wave functions in the case of four electrons in a double quantum dot, see [12].…”

“…The unparalleled experimental advances and control achieved in the field of ultracold atoms have rekindled an intense interest in emulating magnetic behavior using ultracold atoms in optical traps [1,2]. Quantum magnetism and spintronics in both extended [3][4][5][6][7] and finite-size [8][9][10][11][12] systems have a long history. Recently antiferromagnetism (AFM) without the assistance of an external periodic ordering potential has been demonstrated experimentally for N=3 and N=4 ultracold 6 Li atoms confined in a single-well (SW) onedimensional optical trap [13].…”