Abstract:
A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the limits of measurement possible with Planck wavelength radiation. The indeterminacy predicts fluctuations from a classically defined geometry in the form of ``holographic noise'' whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature, and a flat power spectral density given by the Planck time. An interferometer signal displays noise due to the uncertainty of relative positions of reflection events. The noise corresponds to an accumulation of phase offset with time that mimics a random walk of those optical elements that change the orientation of a wavefront. It only appears in measurements that compare transverse positions, and does not appear at all in purely radial position measurements. A lower bound on holographic noise follows from a covariant upper bound on gravitational entropy. The predicted holographic noise spectrum is estimated to be comparable to measured noise in the currently operating interferometer GEO600. Because of its transverse character, holographic noise is reduced relative to gravitational wave effects in other interferometer designs, such as LIGO, where beam power is much less in the beamsplitter than in the arms.

Abstract:
We study the combined effect of thermal and quantum fluctuations in a zero dimensional superconductor. By using path integral techniques, we obtain novel expressions for the partition function and the superconducting order parameter which include both types of fluctuations. Our results are valid for any temperature and to leading order in \delta/\Delta_{0} where \delta is the mean level spacing and \Delta_{0} is the bulk energy gap. We avoid divergences at low temperatures, previously reported in the literature, by identifying and treating non-perturbatively a low-energy collective mode. In the low and high temperature limit our results agrees with those from the random phase (RPA) and the static path approximation (SPA) respectively.

Abstract:
I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

Abstract:
We investigate the effect of different edge types on the statistical properties of both the energy spectrum of closed graphene billiards and the conductance of open graphene cavities in the semiclassical limit. To this end, we use the semiclassical Green's function for ballistic graphene flakes that we have derived in Reference 1. First we study the spectral two point correlation function, or more precisely its Fourier transform the spectral form factor, starting from the graphene version of Gutzwiller's trace formula for the oscillating part of the density of states. We calculate the two leading order contributions to the spectral form factor, paying particular attention to the influence of the edge characteristics of the system. Then we consider transport properties of open graphene cavities. We derive generic analytical expressions for the classical conductance, the weak localization correction, the size of the universal conductance fluctuations and the shot noise power of a ballistic graphene cavity. Again we focus on the effects of the edge structure. For both, the conductance and the spectral form factor, we find that edge induced pseudospin interference affects the results significantly. In particular intervalley coupling mediated through scattering from armchair edges is the key mechanism that governs the coherent quantum interference effects in ballistic graphene cavities.

Abstract:
The subtle interplay between quantum statistics and interactions is at the origin of many intriguing quantum phenomena connected to superfluidity and quantum magnetism. The controlled setting of ultracold quantum gases is well suited to study such quantum correlated systems. Current efforts are directed towards the identification of their magnetic properties, as well as the creation and detection of exotic quantum phases. In this context, it has been proposed to map the spin-polarization of the atoms to the state of a single-mode light beam. Here we introduce a quantum-limited interferometer realizing such an atom-light interface with high spatial resolution. We measure the probability distribution of the local spin-polarization in a trapped Fermi gas showing a reduction of spin-fluctuations by up to 4.6(3) dB below shot-noise in weakly interacting Fermi gases and by 9.4(8) dB for strong interactions. We deduce the magnetic susceptibility as a function of temperature and discuss our measurements in terms of an entanglement witness.

Abstract:
In a recent letter [Auzinsh {\it{et. al.}} (physics/0403097)] we have analyzed the noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned probe light. Here we consider maximally squeezed probe light, and carry out a detailed derivation of the contribution to the noise in a magnetometric measurement due to the differential AC Stark shift between Zeeman sublevels arising from quantum fluctuations of the probe polarization.

Abstract:
Decoherence caused by nuclear field fluctuations is a fundamental obstacle to the realization of quantum information processing using single electron spins. Alternative proposals have been made to use spin qubits based on valence band holes having weaker hyperfine coupling. However, it was demonstrated recently both theoretically and experimentally that the hole hyperfine interaction is not negligible, although a consistent picture of the mechanism controlling the magnitude of the hole-nuclear coupling is still lacking. Here we address this problem by performing isotope selective measurement of the valence band hyperfine coupling in InGaAs/GaAs, InP/GaInP and GaAs/AlGaAs quantum dots. Contrary to existing models we find that the hole hyperfine constant along the growth direction of the structure (normalized by the electron hyperfine constant) has opposite signs for different isotopes and ranges from -15% to +15%. We attribute such changes in hole hyperfine constants to the competing positive contributions of p-symmetry atomic orbitals and the negative contributions of d-orbitals. Furthermore, we find that the d-symmetry contribution leads to a new mechanism for hole-nuclear spin flips which may play an important role in hole spin decoherence. In addition the measured hyperfine constants enable a fundamentally new approach for verification of the computed Bloch wavefunctions in the vicinity of nuclei in semiconductor nanostructures.

Abstract:
Droplet epitaxy is an alternative growth technique for several quantum nanostructures. Indium droplets are distributed randomly on GaAs substrates at low temperatures (120-350'C). Under background pressure of group V elements, Arsenic and Phosphorous, InAs and InP nanostructures are created. Quantum rings with isotropic shape are obtained at low temperature range. When the growth thickness is increased, quantum rings are transformed to quantum dot rings. At high temperature range, anisotropic strain gives rise to quantum rings with square holes and non-uniform ring stripe. Regrowth of quantum dots on these anisotropic quantum rings, Quadra-Quantum Dots (QQDs) could be realized. Potential applications of these quantum nanostructures are also discussed.

Abstract:
We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasi-condensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three body correlations in the system.

Abstract:
Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral nanostructures possessing matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these "quantum drums" [degenerate two-dimensional electron states on the Cu(111) surface confined by individually positioned CO molecules] reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and phase extraction.