Uncertainty Principle and Off-Diagonal Long Range Order in the Fractional Quantum Hall Effect

A natural generalization of the Heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long range order in the ground state of several 1D systems with continuous group symmetries. In this letter we use it to rule out the occurrence of Bose-Einstein condensation in the bosonic representation of the FQHE wave function proposed by Girvin and MacDonald. We show that the absence of off-diagonal long range order in this 2D problem is directly connected with the $q^2$ behavior of the static structure function $S(q)$ at small momenta.Comment: 10 pages, plain TeX, UTF-09-9

Quantum Hall Ferrimagnetism in lateral quantum dot molecules

We demonstrate the existance of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from Hartree-Fock Configuration Interaction method as a function of electron numbers N, magnetic field B, Zeeman energy, and tunneling barrier height. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong inter-dot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between $\nu=2$ and $\nu=1$.Comment: 4 pages, 4 figure

Incidence of the boundary shape in the effective theory of fractional quantum Hall edges

Starting from a microscopic description of a system of strongly interacting electrons in a strong magnetic field in a finite geometry, we construct the boundary low energy effective theory for a fractional quantum Hall droplet taking into account the effects of a smooth edge. The effective theory obtained is the standard chiral boson theory (chiral Luttinger theory) with an additional self-interacting term which is induced by the boundary. As an example of the consequences of this model, we show that such modification leads to a non-universal reduction in the tunnelling exponent which is independent of the filling fraction. This is in qualitative agreement with experiments, that systematically found exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory.Comment: 12 pages, minor changes, replaced by published versio

Noise spectroscopy and interlayer phase-coherence in bilayer quantum Hall systems

Bilayer quantum Hall systems develop strong interlayer phase-coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current-noise is that of the zero wavevector collective mode, which is sensitive to the degree of order in the system. Local electric potential noise measured in a plane above the bilayer system on the other hand is sensitive to finite-wavevector collective modes and hence to the soft-magnetoroton picture of the order-disorder phase transition.Comment: 5 pages, 2 figure

Observability of radiation pressure shot noise in optomechanical systems

We present a theoretical study of an experiment designed to detect radiation pressure shot noise in an optomechanical system. Our model consists of a coherently driven optical cavity mode that is coupled to a mechanical oscillator. We examine the cross-correlation between two quadratures of the output field from the cavity. We determine under which circumstances radiation pressure shot noise can be detected by a measurement of this cross-correlation. This is done in the general case of nonzero detuning between the frequency of the drive and the cavity resonance frequency. We study the qualitative features of the different contributions to the cross-correlator and provide quantitative figures of merit for the relative importance of the radiation pressure shot noise contribution to other contributions. We also propose a modified setup of this experiment relevant to the "membrane-in-the-middle" geometry, which potentially can avoid the problems of static bistability and classical noise in the drive.Comment: 12 pages + 4 page appendix, 10 figure

Possible Quantum Spin Liquid States on the Triangular and Kagome Lattices

The frustrated spin-one-half Heisenberg model on triangualr and Kagome Lattices is mapped onto a single specis of fermion carrying statistical flux. The corresponding Chern-Simons gauge theory is analyzed at the Gaussian level and found to be massive. This provides a new motivation for the spin-liquid Kalmeyer-Laughlin wave function. Good overlap of this wave function with the numerical ground state is found for small clusters.Comment: 13 pages, revtex. IUCM-920

Numerical evidences of spin-1/2 chain approaching spin-1 chain

In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.Comment: 9pages,8page

State-dependent impedance of a strongly coupled oscillator-qubit system

We investigate the measurements of two-state quantum systems (qubits) at finite temperatures using a resonant harmonic oscillator as a quantum probe. The reduced density matrix and oscillator correlators are calculated by a scheme combining numerical methods with an analytical perturbation theory. Correlators provide us information about the system impedance, which depends on the qubit state. We show in detail how this property can be exploited in the qubit measurement.Comment: 8 pages, 16 image