Estimating ground-state properties of quantum dot arrays using a local Thomas-Fermi-Dirac approximation

An exactly solvable local Thomas-Fermi-Dirac approximation is applied to the calculation of the ground-state density of three-dimensional quantum dot arrays, where we give estimates to properties like total energy, chemical potential, and differential capacitance. Numeric examples are calculated for pairs of quantum dots using a Gaussian confining potential. The computational complexity of the present method is linear in the number of electrons and centers of the system.     

Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring. Received 18 January 2002 Published online 13 August 2002     

Electronic structure of three-dimensional quantum dots

We study the electronic structure of three-dimensional quantum dots using the Hartree-Fock approximation. The confining potential of the electrons in the quantum dot is assumed to be spatially isotropic and harmonic. For up to 40 interacting electrons the ground-state energies and ground-state wavefunctions are calculated at various interaction strengths. The quadrupole moments and electron densities in the quantum dot are computed. Hund's rule is confirmed and a shell structure is identified via the addition energies and the quadrupole moments. While most of the shell structure can be understood on the basis of the unperturbed non-interacting problem, the interplay of an avoided crossing and the Coulomb interaction results in an unexpected closed shell for 19 electrons. Received 5 November 2001 / Received in final form 12 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: vorrath@physnet.uni-hamburg.de     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Characteristics of transmission of electrons in a quantum wire tangentially attached to a superconductor ring threaded by magnetic flux

We present numerical investigations of the transmission properties of electrons in a normal quantum wire tangentially attached to a superconductor ring threaded by magnetic flux. A point scatterer with a δ -function potential is placed at node to model scattering effect. We find that the transmission characteristics of electrons in this structure strongly depend on the normal or superconducting state of the ring. The transmission probability as a function of the energy of incident electrons, in the case of a superconductor ring threaded by one quantum magnetic flux, emerges one deep dip, imposed upon the first broad bump in spectrum. This intrinsic conductance dip originates from the superconductor state of the ring. When increasing the magnetic flux from one quantum magnetic flux to two, the spectrum shifts toward higher energy region in the whole. This conductance dip accordingly shifts and appears in the second bump. In the presence of a point-scatterer at the node, the spectrum is substantially modified. Based on the condition of the formation of the standing wave functions in the ring and the broken of the time-reserve symmetry of Schr?dinger equation after switching magnetic flux, the characteristics of transmission of electrons in this structure can be well understood. Received 6 November 2001     

Emergence of Fermi-Dirac thermalization in the quantum computer core

We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. In the limit when fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure and we study the quantum computer core (central band) with the highest density of states. Above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of eigenstates in an isolated quantum computer. The onset of chaos results in the interaction induced dynamical thermalization and the occupation numbers well described by the Fermi-Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability. Received 3 July 2001 and Received in final form 9 September 2001     

Quantum key distribution using quantum-correlated photon sources

Quantum key exchanges using weak coherent (Poissonian) single-photon sources are open to attack by a variety of eavesdropping techniques. Quantum-correlated photon sources provide a means of flagging potentially insecure multiple-photon emissions and thus extending the secure quantum key channel capacity and the secure key distribution range. We present indicative photon-counting statistics for a fully correlated Poissonian multibeam photon source in which the transmitted beam is conditioned by photon number measurements on the remaining beams with non-ideal multiphoton counters. We show that significant rejection of insecure photon pulses from a twin-beam source cannot be obtained with a detector having a realistic quantum efficiency. However quantum-correlated (quadruplet or octuplet) multiplet photon sources conditioned by high efficiency multiphoton counters could provide large improvements in the secure channel capacity and the secure distribution range of high loss systems such as those using the low earth orbit satellite links proposed for global quantum key distribution. Received 14 July and Received in final form 20 November 2001     

Quantum computational gates with radiation free couplings

We examine a generic three level mechanism of quantum computation in which all fundamental single and double qubit quantum logic gates are operating under the effect of adiabatically controllable static (radiation free) bias couplings between the states. Under the time evolution imposed by these bias couplings the quantum state cycles between the two degenerate levels in the ground state and the quantum gates are realized by changing Hamiltonian at certain time intervals when the system collapses to a two state subspace. We propose a physical implementation of the mechanism using Aharonov-Bohm persistent-current loops in crossed electric and magnetic fields, with the output of the loop read out by using a quantum Hall effect aided mechanism. Received 26 March 2002 / Received in final form 8 July 2002 Published online 19 November 2002     

Quantum limits of cold damping with optomechanical coupling

Thermal noise of a mirror can be reduced by cold damping. The displacement is measured with a high-finesse cavity and controlled with the radiation pressure of a modulated light beam. We establish the general quantum limits of noise in cold damping mechanisms and we show that the optomechanical system allows to reach these limits. Displacement noise can be arbitrarily reduced in a narrow frequency band. In a wide-band analysis we show that thermal fluctuations are reduced as with classical damping whereas quantum zero-point fluctuations are left unchanged. The only limit of cold damping is then due to zero-point energy of the mirror. Received 1st August 2001 and Received in final form 12 October 2001     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Charge carrier dynamics in CdSe nanocrystals: implications for the use of quantum dots in novel photovoltaics

The dynamics of photo-generated electrons and holes in CdSe quantum dots have been studied using the femtosecond fluorescence upconversion technique, permitting an unambiguous examination of the excited state. The band edge emission shows an expected size dependence on the decay rate. We find that the deep trap emission is coupled to the band edge fluorescence, implicating surface states as important factors in the excited state lifetime of the hole. As a factor of the overall efficiency of solar cells, the rate of charge separation and the fate of the exciton are important considerations in the design of nanocrystal-based photovoltaic devices. Received 30 November 2000     

Investigation of excitation energies and Hund's rule in open shell quantum dots by diffusion Monte Carlo

We use diffusion Monte Carlo to study the ground state, the low-lying excitation spectrum and the spin densities of circular quantum dots with parabolic radial potentials containing N = 16 and N = 24 electrons, each having four open-shell electrons and compare the results to those obtained from Hartree-Fock (HF) and density functional local spin density approximation (LSDA) calculations. We find that Hund's first rule is obeyed in both cases and that neither HF nor LSDA correctly predict the ordering of the energy levels. Received 20 November 2001 and Received in final form 20 February 2002 Published online 6 June 2002     

Infinite chain of different deltas: A simple model for a quantum wire

We present the exact diagonalization of the Schr?dinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced. Received 24 June 2002 Published online 29 November 2002     

Computational leakage: Grover's algorithm with imperfections

We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that ideal Grover's algorithm operates in a 2-dimensional Hilbert space. The simulation results of this model and Grover's algorithm with imperfections are compared, and it is found that they are in good agreement for appropriately tuned parameters. It turns out that the main features of Grover's algorithm with imperfections can be understood in terms of two basic mechanisms, namely, a diffusion of probability density into the full Hilbert space and a stochastic rotation within the original 2-dimensional Hilbert space. Received 12 August 2002 / Received in final form 14 October 2002 Published online 4 February 2003     

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions. Received 19 September 2002 Published online 4 February 2003     

Energy gaps for fractional quantum Hall states described by a Chern-Simons composite fermion wavefunction

The Jain's composite fermion wavefunction has proven quite succesful to describe most of the fractional quantum Hall states. Its mathematical foundation lies in the Chern-Simons field theory for the electrons in the lowest Landau level, despite the fact that such wavefunction is different from a typical mean-field level Chern-Simons wavefunction. It is known that the energy excitation gaps for fractional Hall states described by Jain's composite fermion wavefunction cannot be calculated analytically. We note that analytic results for the energy excitation gaps of fractional Hall states described by a fermion Chern-Simons wavefunction are readily obtained by using a technique originating from nuclear matter studies. By adopting this technique to the fractional quantum Hall effect we obtained analytical results for the excitation energy gaps of all fractional Hall states described by a Chern-Simons wavefunction. Received 9 March 2001     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II

In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio r _s = UL/(2t ). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L = 6, the ground state exhibits four regimes as r_s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime. Received 22 October 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

Localization of a macroscopic object induced by the factorization of internal adiabatic motion

To account for the phenomenon of quantum decoherence of a macroscopic object, such as the localization and disappearance of interference, we invoke the adiabatic quantum entanglement between its collective states (such as that of the center-of-mass (CM)) and its inner states based on our recent investigation. Under the adiabatic limit where motion of the CM does not excite the transition of inner states, it is shown that the wave function of the macroscopic object can be written as an entangled state with correlation between adiabatic inner states and quasi-classical motion configurations of the CM. Since the adiabatic inner states are factorized with respect to each component of the macroscopic object, this adiabatic separation can induce the quantum decoherence. This observation thus provides us with a possible solution to the Schr?dinger cat paradox. Received 24 October 2000 and Received in final form 8 March 2001     

Entangled Bell states of two electrons in coupled quantum dots—phonon decoherence

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned self assembled quantum dots by studying the dynamics of two interacting electrons driven by external electric field. The present entanglement involves the spatial degree of freedom for the two electrons system. We show that system of two interacting electrons initially delocalized (localized each in one dot) oscillate slowly in response to electric field, since the strong Coulomb repulsion makes them behaving so. We use an explicit formula for the entanglement of formation of two qubit in terms of the concurrence of the density operator. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, real quantum systems will inevitably be influenced by surrounding environments. We discuss the degree of entanglement of this system in which we introduce the decoherence effect caused by the acoustic phonon. In this entangled states proposal, the decohering time depends on the external parameters.