Balance network of asymmetric simple exclusion process

We investigate a balance network of the asymmetric simple exclusion process (ASEP). Subsystems consisting of ASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network includes some specific important cases discussed in earlier works such as the ASEP with the Langmuir kinetics, multiple lanes and finite reservoirs. Probability distributions of particles in the steady state are exactly given in factorized forms according to their balance properties. Although the system has nonequilibrium parts, the expressions are well described in a framework of statistical mechanics based on equilibrium states. Moreover, the overall argument does not depend on the network structures, and the knowledge obtained in this work is applicable to a broad range of problems

On-chip quantum interference between silicon photon-pair sources

Large-scale integrated quantum photonic technologies1, 2 will require on-chip integration of identical photon sources with reconfigurable waveguide circuits. Relatively complex quantum circuits have been demonstrated already1, 2, 3, 4, 5, 6, 7, but few studies acknowledge the pressing need to integrate photon sources and waveguide circuits together on-chip8, 9. A key step towards such large-scale quantum technologies is the integration of just two individual photon sources within a waveguide circuit, and the demonstration of high-visibility quantum interference between them. Here, we report a silicon-on-insulator device that combines two four-wave mixing sources in an interferometer with a reconfigurable phase shifter. We configured the device to create and manipulate two-colour (non-degenerate) or same-colour (degenerate) path-entangled or path-unentangled photon pairs. We observed up to 100.0 ± 0.4% visibility quantum interference on-chip, and up to 95 ± 4% off-chip. Our device removes the need for external photon sources, provides a path to increasing the complexity of quantum photonic circuits and is a first step towards fully integrated quantum technologies

Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs

We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite, and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and the Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations of the SU(2) is briefly developed. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.Comment: Final version as published, 19 pages, 4 figures, 40 references given in full forma

Probing the Shape of Quantum Dots with Magnetic Fields

A tool for the identification of the shape of quantum dots is developed. By preparing a two-electron quantum dot, the response of the low-lying excited states to a homogeneous magnetic field, i.e. their spin and parity oscillations, is studied for a large variety of dot shapes. For any geometric configuration of the confinement we encounter characteristic spin singlet - triplet crossovers. The magnetization is shown to be a complementary tool for probing the shape of the dot.Comment: 11 pages, 4 figure

Rotational and vibrational spectra of quantum rings

One can confine the two-dimensional electron gas in semiconductor heterostructures electrostatically or by etching techniques such that a small electron island is formed. These man-made ``artificial atoms'' provide the experimental realization of a text-book example of many-particle physics: a finite number of quantum particles in a trap. Much effort was spent on making such "quantum dots" smaller and going from the mesoscopic to the quantum regime. Far-reaching analogies to the physics of atoms, nuclei or metal clusters were obvious from the very beginning: The concepts of shell structure and Hund's rules were found to apply -- just as in real atoms! In this Letter, we report the discovery that electrons confined in ring-shaped quantum dots form rather rigid molecules with antiferromagnetic order in the ground state. This can be seen best from an analysis of the rotational and vibrational excitations

Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality

We study the energy spectra of small three-dimensional (3D) and two-dimensional (2D) semiconductor quantum dots through different theoretical approaches (single-site Hubbard and Hartree-Fock hamiltonians); in the smallest dots we also compare with exact results. We find that purely 2D models often lead to an inadequate description of the Coulomb interaction existing in realistic structures, as a consequence of the overestimated carrier localization. We show that the dimensionality of the dots has a crucial impact on (i) the accuracy of the predicted addition spectra; (ii) the range of validity of approximate theoretical schemes. When applied to realistic 3D geometries, the latter are found to be much more accurate than in the corresponding 2D cases for a large class of quantum dots; the single-site Hubbard hamiltonian is shown to provide a very effective and accurate scheme to describe quantum dot spectra, leading to good agreement with experiments.Comment: LaTeX 2.09, RevTeX, 25 pages, 9 Encapsulated Postscript figures. To be published in Physical Review

Full Quantum Analysis of Two-Photon Absorption Using Two-Photon Wavefunction: Comparison with One-Photon Absorption

For dissipation-free photon-photon interaction at the single photon level, we analyze one-photon transition and two-photon transition induced by photon pairs in three-level atoms using two-photon wavefunctions. We show that the two-photon absorption can be substantially enhanced by adjusting the time correlation of photon pairs. We study two typical cases: Gaussian wavefunction and rectangular wavefunction. In the latter, we find that under special conditions one-photon transition is completely suppressed while the high probability of two-photon transition is maintained.Comment: 6 pages, 4 figure

On the formation of Wigner molecules in small quantum dots

It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of Wigner molecules occurs at a density parameter $r_s\approx 4 a_B^*$ to the results of a straight-forward diagonalization of the Hamiltonian matrix