Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results

We present a comprehensive list of ground state energies and spin gaps of finite kagome clusters with up to 42 spins obtained using large-scale exact diagonalization techniques. This represents the current limit of this exact approach. For a fixed number of spins N we study several cluster shapes under periodic boundary conditions in both directions resulting in a toroidal geometry. The clusters are characterized by their side length and diagonal as well as the shortest "Manhattan" diameter of the torii. A finite-size scaling analysis of the ground state energy as well as the spin gap is then performed in terms of the shortest toroidal diameter as well as the shortest "Manhattan" diameter. The structure of the spin-spin correlations further supports the importance of short loops wrapping around the torii.Comment: 4 pages, 4 figures, added one referenc

Bogoliubov theory of entanglement in a Bose-Einstein condensate

We consider a Bose-Einstein condensate which is illuminated by a short resonant light pulse that coherently couples two internal states of the atoms. We show that the subsequent time evolution prepares the atoms in an interesting entangled state called a spin squeezed state. This evolution is analysed in detail by developing a Bogoliubov theory which describes the entanglement of the atoms. Our calculation is a consistent expansion in $1/\sqrt{N}$, where $N$ is the number of particles in the condensate, and our theory predict that it is possible to produce spin squeezing by at least a factor of $1/\sqrt{N}$. Within the Bogoliubov approximation this result is independent of temperature.Comment: 14 pages, including 5 figures, minor changes in the presentatio

Electro-optomechanical equivalent circuits for quantum transduction

Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input-output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.Comment: 30 pages, 9 figure

Analyticity of the density of electronic wavefunctions

We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.Comment: 19 page

Probing spatial spin correlations of ultracold gases by quantum noise spectroscopy

Spin noise spectroscopy with a single laser beam is demonstrated theoretically to provide a direct probe of the spatial correlations of cold fermionic gases. We show how the generic many-body phenomena of anti-bunching, pairing, antiferromagnetic, and algebraic spin liquid correlations can be revealed by measuring the spin noise as a function of laser width, temperature, and frequency.Comment: Revised version. 4 pages, 3 figures. Accepted for PR

Opto-mechanical transducers for long-distance quantum communication

We describe a new scheme to interconvert stationary and photonic qubits which is based on indirect qubit-light interactions mediated by a mechanical resonator. This approach does not rely on the specific optical response of the qubit and thereby enables optical quantum interfaces for a wide range of solid state spin and charge based systems. We discuss the implementation of quantum state transfer protocols between distant nodes of a large scale network and evaluate the effect of the main noise sources on the resulting state transfer fidelities. For the specific examples of electronic spin qubits and superconducting charge qubits we show that high fidelity quantum communication protocols can be implemented under realistic experimental conditions.Comment: Version as accepted by PR

Entanglement in Anderson Nanoclusters

We investigate the two-particle spin entanglement in magnetic nanoclusters described by the periodic Anderson model. An entanglement phase diagram is obtained, providing a novel perspective on a central property of magnetic nanoclusters, namely the temperature dependent competition between local Kondo screening and nonlocal Ruderman-Kittel-Kasuya-Yoshida spin ordering. We find that multiparticle entangled states are present for finite magnetic field as well as in the mixed valence regime and away from half filling. Our results emphasize the role of charge fluctuations.Comment: 5 pages, 3 figure