Two-electron quantum dot molecule: composite particles and the spin phase diagram

A path integral study of the role of correlation in exchange coupling of spins in double quantum dots and optical lattices

We explore exchange coupling of a pair of spins in a double dot and in an optical lattice, using the frequency of exchanges in a bosonic path integral, evaluated using Monte Carlo simulation. The algorithm gives insights into the role of correlation through visualization of two-particle probability densities, instantons, and the correlation hole. We map the problem to the Hubbard model and see that exchange and correlation renormalize the model parameters, dramatically reducing the effective on-site repulsion at larger separations.

Tuning the exchange interaction by an electric field in laterally coupled quantum dots

The effect of an external electric field on the exchange interaction has been studied by an exact diagonalization method for two electrons in laterally coupled quantum dots (QDs). We have performed a systematic study of several nanodevices that contain two gate-defined QDs with different shapes and sizes located between source and drain contacts. The confinement potential is modeled by two potential wells with a variable range and softness. In all the considered nanodevices, the overall dependence of exchange energy J on electric field F is similar, i.e. for low fields J increases with increasing F, while for intermediate fields J reaches a maximum and then abruptly falls to zero if F exceeds a certain critical value. However, the J(F) dependence also shows certain characteristic properties that depend on the nanodevice geometry. We have found that the low- and intermediate-field behavior can be accurately parameterized by a linear function J(F) = αF+β, where α is independent of the nanodevice geometry and softness of the confinement potential. We have shown that the linear J(F) relation appears only if the tunnel coupling between the QDs is weak, i.e. the interdot separation is sufficiently large. This relation becomes nonlinear for the strong interdot coupling. For specific nanodevices we have found that the J(F) dependence exhibits a plateau in a broad electric-field regime. The properties of the exchange energy found in the present paper can be applied to all electrical manipulation of electron spin qubits.

Non-monotonic variation of the exchange energy in double elliptic quantum dots

We study the properties of a few-electron system confined in coupled elongated quantum dots (QDs) using a model Gaussian potential and the numerical exact diagonalization technique. In the absence of magnetic fields, as the aspect ratio r between the QD extensions in the directions perpendicular and parallel to the coupling directions increases, the exchange energy exhibits a sharp variation at the specific value r = 3.9, before (after) which the exchange energy increases (declines). The sharp variation occurs because of a sudden change in the single-particle configuration of the triplet state. The stability region with one electron in each of the QDs is found to shrink, and finally vanishes as it becomes progressively easier to localize both electrons into the QD with the lower electron potential energy. For r>3.9, the first singlet-triplet transition shifts to a small magnetic field.

Optical control in coupled two-electron quantum dots

The dynamics of two electrons in a 2-dimensional quantum dot molecule in the presence of a time-dependent electromagnetic field is calculated from first principles. We show that carefully selected microwave pulses can exclusively populate a single state of the first excitation band and that the transition time can be further decreased by optimal pulse control. Finally we demonstrate that an oscillating charge localized state may be created by multiple transitions using a sequence of pulses.

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations.Strongly-correlated phenomena emerging from symmetry breaking include the following.Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices.Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules.At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit).Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross-Pitaevskii solutions describing vortex formation.We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.

Full configuration interaction approach to the few-electron problem in artificial atoms

We present a new high performance configuration interaction code optimally designed for the calculation of the lowest-energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a single-particle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted up to the Wigner regime, where correlations become dominant. Comparison with previous quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.

Role of interactions in the far-infrared spectrum of a lateral quantum-dot molecule

We study the effects of electron-electron correlations and confinement potential on the far-infrared spectrum of a lateral two-electron quantum-dot molecule by exact diagonalization. The calculated spectra directly reflect the lowered symmetry of the external confinement potential. Surprisingly, we find interactions to drive the spectrum towards that of a high-symmetry parabolic quantum-dot. We conclude that far-infrared spectroscopy is suitable for probing effective confinement of the electrons in a quantum-dot system, even if interaction effects cannot be resolved in a direct fashion.