It is demonstrated that exact diagonalization of the microscopic many-body Hamiltonian via systematic full configuration-interaction (FCI) calculations is able to predict the spectra as a function of detuning of three-electron hybrid qubits based on GaAs asymmetric double quantum dots (QDs). It is further shown that, as a result of strong inter-electron correlations, these spectroscopic patterns, including avoided crossings between states associated with different electron occupancies of the left and right wells, are inextricably related to the formation of Wigner molecules (WMs). These physical entities cannot be captured by the previously employed independent-particle or Hubbard-type theoretical modeling of the hybrid qubit. We report remarkable agreement with recent experimental results. Moreover, the present FCI methodology for multi-well QDs can be straightforwardly extended to treat Si/SiGe hybrid qubits, where the central role of WMs was recently experimentally confirmed as well.
It is demonstrated that exact diagonalization of the microscopic many-body Hamiltonian via systematic full configuration-interaction (FCI) calculations is able to predict the spectra as a function of detuning of three-electron hybrid qubits based on GaAs asymmetric double quantum dots (QDs). It is further shown that, as a result of strong inter-electron correlations, these spectroscopic patterns, including avoided crossings between states associated with different electron occupancies of the left and right wells, are inextricably related to the formation of Wigner molecules (WMs). These physical entities cannot be captured by the previously employed independent-particle or Hubbard-type theoretical modeling of the hybrid qubit. We report remarkable agreement with recent experimental results. Moreover, the present FCI methodology for multi-well QDs can be straightforwardly extended to treat Si/SiGe hybrid qubits, where the central role of WMs was recently experimentally confirmed as well.
Quantum Wigner molecules (WMs) in strongly interacting few-body fermionic moir\'e quantum dots in twisted bilayers of transition metal dichalcogenide (TMD) materials are uncovered via full configuration interaction calculations, going beyond the Aufbau principle of natural atoms and Hubbard modeling. Nested polygonal sliding rings of localized fermions, hidden in the exact particle densities, are revealed through wavefunction correlation analysis [see (3,9) and (1,6,10) electron WMs in 2D semiconductors], broadening the WM portfolio to include the TMD trilobal symmetry as an added resource in twistronics, and providing benchmarks for AI-based many-body computations.
Energy spectra, spin configurations, and entanglement characteristics of a system of four electrons in lateral double quantum dots are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field, and strength of interelectron repulsion. A distinctly different quantum behavior is found compared to that of circular single quantum dots. 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 of the four electrons and the ensuing spin degeneracies. These six states appear to cross at a single value of the magnetic field, with the crossing point becoming sharper for larger interdot distances. As the strength of the Coulomb repulsion increases, the six states tend to become degenerate and a well defined energy gap separates 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 rectangular parallelogram. Using the spin-resolved pair-correlation functions, one can map the EXD many-body wave functions onto the spin functions associated with the four localized electrons. Analogies with nanomagnets, such as finite Heisenberg clusters, are discussed. The ability to determine associated spin functions enables investigations concerning entanglement properties of the system of four electrons. In particular, the formation of Wigner supermolecules generates EXD solutions belonging to the class of strongly entangled states referred to as N-qubit Dicke states in the quantum-information literature.
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 spin-resolved 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 four-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.
The paper reviews the theoretical and experimental progress achieved in the last 25 years in understanding the novel physics of artificial atoms and molecules as arising from the formation of Wigner molecules (WMs) of localized (to a stronger or lesser extent) fermionic or bosonic particles, which are finite quantum analogs of the more familiar bulk Wigner crystal (WC). The term artificial atoms, as used here, encompasses a broad range of recently fabricated quantum nanodevices and experimental apparatuses consisting of a finite number of mutually repelling confined particles, including two-dimensional semiconductor and moiré transition metal dichalcogenide quantum dots, as well as trapped ultracold neutral atoms or ions. These nano-sized or micro-sized artificial devices and apparatuses (in single well or multi-well of variable-shape arrangements) hold a great promise for technological applications in the field of quantum information and quantum computers, as well as for advances in fundamental many-body physics. Prominent quantum effects of Wigner molecularization (WM) are the strong quenching of the spectral energy gaps, the appearance of rovibational spectra (in analogy with natural molecules), entanglement, and pinning due to an external perturbation. In high magnetic fields or at rapid rotation, Wigner molecules (WMs) provide an alternative theory to the fractional quantum Hall effect. The physics of WMs is shown to derive from the solutions of the many-body Schrödinger equation (MBSE) in the regime of strong interparticle correlations arising from the dominance of the potential over the kinetic energy, or from a high magnetic field, as well as from a rapid rotation. With the help of a hierarchical scheme of computational approaches involving group-theoretical projection techniques beyond the mean field and exact configuration interaction, in parallel to experimental investigations, WMs are shown to provide an ideal platform for investigating the interplay between symmetry-preserving (stationary, referred to as rotating or sliding WMs) and broken-symmetry (superposition-necessitating, referred to as pinned or static WMs) solutions of the MBSE. In the process, a germane view of the phenomenon of symmetry breaking, based exclusively on finite systems and referred to as emergent symmetry breaking, is developed as a replacement to the formalistic spontaneous symmetry breaking that requires invocation of a singular thermodynamic limit. Attention is drawn to the counterintuitive fact that the very MBSE, which was inspired by de Broglie's undulatory matter waves and successfully explained the shell structure of delocalized electrons in atomic physics, is nevertheless capable of yielding contrasting solutions, which relate to corpuscular geometries of localized particles. This unforeseen behavior classifies the recent developments concerning WM and WC as an example of weak emergence, and thus of an arrow of reductionist explanation according to Weinberg's reasoning. Finally, this review, demonstrating the unexpected mathematical effectiveness beyond original expectations of the Schrödinger equation, is dedicated as a tribute to its 100 year anniversary.
Exploring strongly correlated spinful states of few fermionic ultracold atoms in a rapidly rotating trap, an example of which was recently realized for two fermionic 6Li atoms in an optical tweezer, we derive analytical (algebraic) total-spin-eigenstate wavefunctions through the development and employment of a theoretical platform that integrates exact numerical diagonalization (full configuration interaction, FCI) with symbolic language processing. For such rapid rotations, where the atoms occupy the lowest Landau level (LLL), the obtained algebraic expressions can address the full LLL spectrum in all its complexity, demonstrating that their spatial, spectral, and spin characteristics manifest formation of collectively rotating and vibrating Wigner molecules. The explicitly exhibited analytic wavefunctions (for two and three spinful 6Li atoms) reproduce precisely the corresponding numerical FCI results, and they are shown to reach beyond the limited range of applicability of previous Jastrow-type treatments. These results, and their extension to bosonic systems, provide the impetus and analysis tools for future experimental and theoretical simulations of larger mesoscopic systems
A quantitative description of the exchange interaction in quantum dots is relevant for modeling gate operations of spin qubits. By measuring the amplitude and frequency of exchange-driven qubit state oscillations, we measure the detuning dependence of the exchange coupling in a GaAs double quantum dot over three orders of magnitude. Both 1D and 3D full configuration interaction simulations can replicate the observed behavior. Extending a Hubbard model by including excited states increases the range of detuning where it provides a good fit, thus elucidating the underlying physics.