Augusto Gonzalez

Electronic Raman scattering in quantum dots revisited

We present theoretical results concerning inelastic light (Raman) scattering from semiconductor quantum dots. The characteristics of each dot state (whether it is a collective or single-particle excitation, its multipolarity, and its spin) are determined independently of the Raman spectrum, in such a way that common beliefs used for level assignments in experimental spectra can be tested. We explore the usefulness of below band gap excitation and an external magnetic field to identify charge and spin excited states of a collective or single-particle nature.

GROUND-STATE ENERGY OF CONFINED CHARGED BOSONS IN TWO DIMENSIONS

The Pade approximant technique and the variational Monte Carlo method are applied to determine the ground-state energy of a finite number of charged bosons in two dimensions confined by a parabolic trap. The particles interact repulsively through a Coulombic, 1/r, potential. Analytic expressions for the ground-state energy are obtained. The convergence of the Pade sequence and comparison with the Monte Carlo results show that the error of the Pade estimate is less than 4 % at any boson density and is exact in the extreme situations of very dilute and high density.

Renormalised Perturbative Series for the Impurity Levels in a Quantum Well

The energy levels of an impurity center in a deep quantum well of width L and depth g are studied analytically . Renormalised perturbative series are constructed in the regions g L^ > 1. Maximal binding energy and wave function deformation to a quasi-twodimensional function are found to occur at a certain L_c satisfying sqrt{g} L_c ~ 1. Similar results may be obtained for the impurity in a quantum wire, in a dot or in a multiwell structure.

Photon emission as a source of coherent behavior of polaritons.

We show that the combined effect of photon emission and Coulomb interactions may drive an exciton-polariton system towards a dynamical coherent state, even without phonon thermalization or any other relaxation mechanism. Exact diagonalization results for a finite system (a multilevel quantum dot interacting with the lowest-energy photon mode of a microcavity) are presented in support of this statement.

Scaling in the correlation energies of two-dimensional artificial atoms

We find an unexpected scaling in the correlation energy of artificial atoms, i.e., harmonically confined two-dimensional quantum dots. The scaling relation is found through extensive numerical examinations including Hartree-Fock, variational quantum Monte Carlo, density functional, and full configuration interaction calculations. We show that the correlation energy, i.e., the true ground-state total energy minus the Hartree-Fock total energy, follows a simple function of the Coulomb energy, confinement strength and number of electrons. We find an analytic expression for this function, as well as for the correlation energy per particle and for the ratio between the correlation and total energies. Our tests for independent diffusion Monte Carlo and coupled-cluster results for quantum dots-including open-shell data-confirm the generality of the scaling obtained. As the scaling also applies well to ≳100 electrons, our results give interesting prospects for the development of correlation functionals within density functional theory.

Polariton lasing in a multilevel quantum dot strongly coupled to a single photon mode

We present an approximate analytic expression for the photoluminescence spectral function of a model polariton system, which describes a quantum dot, with a finite number of fermionic levels, strongly interacting with the lowest photon mode of a pillar microcavity. Energy eigenvalues and wave functions of the electron-hole-photon system are obtained by numerically diagonalizing the Hamiltonian. Pumping and photon losses through the cavity mirrors are described with a master equation, which is solved in order to determine the stationary density matrix. The photon first-order correlation function, from which the spectral function is found, is computed with the help of the quantum regression theorem. The spectral function qualitatively describes the polariton lasing regime in the model, corresponding to pumping rates two orders of magnitude lower than those needed for ordinary (photon) lasing. The second-order coherence functions for the photon and the electron-hole subsystems are computed as functions of the pumping rate.

A multiexcitonic quantum dot in an optical microcavity

We theoretically study the coupled modes of a medium-size quantum dot, which may confine a maximum of 10 electron–hole pairs, and a single photonic mode of an optical microcavity. Ground-state and excitation energies, exciton–photon mixing in the wave functions and the emission of light from the microcavity are computed as functions of the pair–photon coupling strength, photon detuning, and polariton number.

Resonant Raman scattering off neutral quantum dots

Resonant inelastic (Raman) light scattering off neutral GaAs quantum dots which contain a mean number, N = 42, of electron-hole pairs is computed. We find Raman amplitudes corresponding to strongly collective final states (charge-density excitations) of similar magnitude as the amplitudes related to weakly collective or single-particle excitations. As a function of the incident laser frequency or the magnetic field, they are rapidly varying amplitudes. It is argued that strong Raman peaks should come out in the spin-density channels, not related to valence-band mixing effects in the intermediate states.

Stochastic number projection method in the pairing-force problem

A new stochastic number projection method is proposed. The component of the BCS wave function corresponding to the right number of particles is obtained by means of a Metropolis algorithm in which the weight functions are constructed from the single-particle occupation probability. Either standard BCS or Lipkin-Nogami probability distributions can be used, thus the method is applicable for any pairing strength. The accuracy of the method is tested in the computation of pairing energies of model and real systems.

ATOMS IN THE ANIONIC DOMAIN, Z< N

We study atoms with N electrons, and nuclear charge Z. It is well known that the cationic regime, Z > N, is qualitatively described by Thomas–Fermi theory. The anionic regime, Z < N, on the other hand, is characterized by an instability threshold at Zc ≲ N-1, below which the atom spontaneously emits an electron. We compute the slope of the energy curve at Z = N - 1 by means of a simple model that depends on the electron affinity and the covalent radius of the neutral atom with N - 1 electrons. This slope is used in order to estimate Zc, which is compared with previous numerical results. Extrapolation of the linear behavior in the opposite direction, up to Z = N, allows us to estimate the ionization potential of the atom with N electrons. The fact that the obtained ionization potentials are qualitatively correct is an indication that, with regard to certain properties, neutral atoms are closer to the anionic instability threshold than they are to the Thomas–Fermi, large Z, region. A regularized series is w...