Towards an Explanation of the Mesoscopic Double-Slit Experiment: a new model for charging of a Quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.Comment: 4 pages, 2 figures, Journal versio

Scattering phases in quantum dots: an analysis based on lattice models

The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum rule and discuss the deviation of the phase of the transmission amplitude from the Friedel phase at the zeroes of the transmission. The occurrence of such zeroes is related to the parity of the isolated dot levels. A statistical analysis of the isolated dot wave-functions reveals the absence of significant correlations in the parity for large disorder and the appearance, for weak disorder, of certain dot states which are strongly coupled to the leads. It is shown that large differences in the coupling to the leads give rise to an anomalous charging of the dot levels. A mechanism for the phase lapse observed experimentally based on this property is discussed and illustrated with model calculations.Comment: 18 pages, 9 figures. to appear in Physical Review

Spin Effects and Transport in Quantum Dots with overlapping Resonances

The role of spin is investigated in the transport through a quantum dot with two overlapping resonances (one having a width larger than the level separation and the other very narrow, cf. Silvestrov and Imry, Phys. Rev. Lett. {\bf 85}, 2565 (2000)). For a series of consecutive charging resonances, one electron from the leads populates one and the same broad level in the dot. Moreover, there is the tendency to occupy the same level also by the second electron within the same resonance. This second electron is taken from the narrow levels in the dot. The narrow levels are populated (and broad level is depopulated) via sharp rearrangements of the electronic configuration in the Coulomb blockade valleys. Possible experimental manifestations of this scenario are considered. Among these there are sharp features in the valleys and in the Mixed Valence regime and an unusual Kondo effect.Comment: 7 pages, 3 figures, just a published versio

Quantum characterization of superconducting photon counters

We address the quantum characterization of photon counters based on transition-edge sensors (TESs) and present the first experimental tomography of the positive operator-valued measure (POVM) of a TES. We provide the reliable tomographic reconstruction of the POVM elements up to 11 detected photons and M=100 incoming photons, demonstrating that it is a linear detector.Comment: 3 figures, NJP (to appear

Phases of the one-dimensional Bose-Hubbard model

The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.Comment: Revised version, 4 pages, 5 figure

Correlations in the cotunneling regime of a quantum dot

Off-resonance conductance through weakly coupled quantum dots ("valley conductance") is governed by cotunneling processes in which a large number of dot states participate. Virtually the same states participate in the transport at consecutive valleys, which leads to significant valley-valley conductance correlations. These correlations are calculated within the constant interaction model. Comparison with experiment shows that these correlations are less robust in reality. Among the possible reasons for this is the breakdown of the constant interaction model, accompanied by "scrambling" of the dot as the particle number is varied.Comment: 10 pages, 4 eps-figures; reference adde

Transmission phase lapses in quantum dots: the role of dot-lead coupling asymmetry

Lapses of transmission phase in transport through quantum dots are ubiquitous already in the absence of interaction, in which case their precise location is determined by the signs and magnitudes of the tunnelling matrix elements. However, actual measurements for a quantum dot embedded in an Aharonov-Bohm interferometer show systematic sequences of phase lapses separated by Coulomb peaks -- an issue that attracted much attention and generated controversy. Using a two-level quantum dot as an example we show that this phenomenon can be accounted for by the combined effect of asymmetric dot-lead couplings (left lead/right lead asymmetry as well as different level broadening for different levels) and interaction-induced "population switching" of the levels, rendering this behaviour generic. We construct and analyse a mean field scheme for an interacting quantum dot, and investigate the properties of the mean field solution, paying special attention to the character of its dependence (continuous vs. discontinuous) on the chemical potential or gate voltage.Comment: 34 LaTeX pages in IOP format, 9 figures; misprints correcte

The low-energy theory for the Bose-Hubbard model and the normal ground state of bosons

A bosonic realization of the SU(2) Lie algebra and of its vector representation is constructed, and an effective low-energy description of the Bose-Hubbard model in the form of anisotropic theory of quantum rotors is proposed and discussed. A possibility of a normal zero-temperature bosonic phase with neither crystalline nor superfluid order around the tip of the checkerboard-solid lobe at half-integer fillings is examined.Comment: 8 pages, LaTex, one postscript figur

Informationally complete measurements and groups representation

Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM's) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.Comment: 9 pages, no figures, IOP style. Some new references adde