In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, ${[u,v]}_n=uv-e^{i2\pi ∕(n+1)}vu$, which corresponds to intermediate statistics in which the maximum occupation number of one quantum state is an arbitrary integer, $n$. A further study of the operator realization of intermediate statistics is given. We construct the intermediate-statistics coherent state. An intermediate-statistics oscillator is constructed, which returns to bosonic and fermionic oscillators respectively when $n\to \infty$ and $n=1$. The energy spectrum of such an intermediate-statistics oscillator is calculated. Finally, we discuss the intermediate-statistics representation of angular momentum [su(2)] algebra. Moreover, a further study of the operator realization of intermediate statistics is given in the Appendix.

We introduce and describe in detail a different quantum-information protocol: quantum telecloning of optical images or spatially multimode states of light. This protocol is a natural generalization of a continuous-variable quantum telecloning of single-mode states, investigated earlier theoretically and recently realized experimentally. Our protocol is an example of a multiuser parallel quantum channel. In order to realize this scheme one needs a multimode multipartite entanglement between the original and the target systems. We calculate the fidelity of quantum parallel telecloning in dependence on the spatiotemporal scales of our scheme and on the number of pixels. The fidelity is superior to the best classical fidelity that can be achieved without this kind of entanglement.

We propose schemes for entanglement concentration and purification for qubit systems encoded in flying atomic pairs. We use cavity-quantum electrodynamics as an illustrative setting within which our proposals can be implemented. Maximally entangled pure states of qubits can be produced as a result of our protocols. In particular, the concentration protocol yields Bell states with the largest achievable theoretical probability while the purification scheme produces arbitrarily pure Bell states. The requirements for the implementation of these protocols are modest, within the state of the art, and we address all necessary steps in two specific setups based on experimentally mature microwave technology.

We present a theoretical study of dissociative and nondissociative photoionization of ${\mathrm{H}}_2$ from the $E,F{}^1\Sigma _g^{+}(\upsilon ,J=0)$ excited state for $\upsilon =0–9$ in the photon energy range $3\text{to}14\mathrm{eV}$. We have found that, for most initial $\upsilon$’s, dissociative ionization is the dominant process for photon energies well above the dissociative ionization threshold. In this photon energy range, resonance structures arising from autoionization of the $Q_1$ doubly excited states of ${\mathrm{H}}_2$ are observed. Cross sections differential in the energy of the remaining ${\mathrm{H}}_2^{+}$ ion or in the proton kinetic energy are analyzed in detail for a photon energy of $6.4\mathrm{eV}$ corresponding to the wavelength of an ArF excimer laser. Comparison of our results with the available experimental measurements is good. We show, however, that contribution of the $Q_1$ doubly excited states to the measured dissociative ionization cross section is more important than originally believed.

The diagonalization approximation is applied to the photoionization process of ${\mathrm{Ne}}^{8+}$ to determine the energies of autoionizing states converging to the $n=3,4,5$ thresholds of the residual ion. The calculations are carried out for ${}^{1,3}P^o$ states. The results are compared with available results obtained by other theoretical approaches.

The angular distribution of photoelectrons for single photon detachment from ${\mathrm{As}}^{-}$ was measured at six discrete wavelengths in the range $715–532\mathrm{nm}$ using crossed laser–ion-beam interaction and a linear time of flight photoelectron spectrometer. Asymmetry parameters were determined from the measured angular distributions at these wavelengths. These parameters were fit to the known simplified form of the independent particle model for photodetachment. This fit is compared with available data on $P^{-}$, which has similar electronic configuration [core, $(\mathrm{n}{s}^2,\mathrm{n}{p}^4)$] to that of ${\mathrm{As}}^{-}$, and anions of group IV elements.

The $ϵ$ expansion (expansion around four spatial dimensions) developed by Nishida and Son for a cold Fermi gas with infinite scattering length is extended to finite scattering length to study the Bose-Einstein condensate (BEC) to BCS crossover. A resummation of higher-order logarithms and a suitable extension of fermion coupling in $d$ dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, $\mu ∕{\epsilon }_F$, is computed to next-to-leading order in the $ϵ$ expansion as a function of $\eta =1∕\left(a{k}_F\right)$, where $a$ is the scattering length and $k_F$ is the Fermi momentum in a noninteracting system. Near the unitarity limit $\mid \eta \mid \to 0$, we found $\mu ∕{\epsilon }_F=0.475-0.707\eta -0.5{\eta }^2$. Near the BEC limit $\eta \to \infty$, $\mu ∕{\epsilon }_F=0.062∕\eta -{\eta }^2$, while near the BCS limit $\eta \to -\infty$, $\mu ∕{\epsilon }_F=1+0.707∕\eta$. Overall good agreement with quantum Monte Carlo results is found.

We describe a number-conserving approach to the dynamics of Bose-Einstein condensed dilute atomic gases. This builds upon the works of Gardiner [Phys. Rev. A 56, 1414 (1997)] and Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We consider what is effectively an expansion in powers of the ratio of noncondensate to condensate particle numbers, rather than inverse powers of the total number of particles. This requires the number of condensate particles to be a majority, but not necessarily almost equal to the total number of particles in the system. We argue that a second-order treatment of the relevant dynamical equations of motion is the minimum order necessary to provide consistent coupled condensate and noncondensate number dynamics for a finite total number of particles, and show that such a second-order treatment is provided by a suitably generalized Gross-Pitaevskii equation, coupled to the Castin-Dum number-conserving formulation of the Bogoliubov–de Gennes equations. The necessary equations of motion can be generated from an approximate third-order Hamiltonian, which effectively reduces to second order in the steady state. Such a treatment as described here is suitable for dynamics occurring at finite temperature, where there is a significant noncondensate fraction from the outset, or dynamics leading to dynamical instabilities, where depletion of the condensate can also lead to a significant noncondensate fraction, even if the noncondensate fraction is initially negligible.

We present the observation of optical fields carrying squeezed vacuum states at sideband frequencies from $10\mathrm{Hz}$ to above $35\mathrm{MHz}$. The field was generated with type-I optical parametric oscillation below threshold at $1064\mathrm{nm}$. A coherent, unbalanced classical modulation field at $40\mathrm{MHz}$ enabled the generation of error signals for stable phase control of the squeezed vacuum field with respect to a strong local oscillator. Broadband squeezing of approximately $-4\mathrm{dB}$ was measured with balanced homodyne detection. The spectrum of the squeezed field allows a quantum noise reduction of ground-based gravitational wave detectors over their full detection band, regardless of whether homodyne readout or radio-frequency heterodyne readout is used.

We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to the environment. Two kinds of coupling are taken into account. With the first kind of coupling dominating, decoherence can enhance self-trapping by increasing the damping of the oscillations in the dynamics, while decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.

A uniform dilute Bose system with repulsive interactions is studied in the grand canonical ensemble formalism. We present a parametric equation of state that holds true from high temperatures down to below the transition temperature, thus providing a scheme for exploring the quantum-statistical nature of the Bose-Einstein condensation transition in interacting gases. As an application, the interaction-induced shift of the transition temperature is derived to be $\mathrm{\Delta }{T}_c∕T_c^0=2.83n^{1∕3}a$, where $n$ is the density and $a$ is the $S$-wave scattering length.

Based on macroscopic quantum electrodynamics in linearly and causally responding media, we study the local-field corrected van der Waals potentials and forces for unpolarized ground-state atoms placed within a magnetoelectric medium of arbitrary size and shape. We start from general expressions for the van der Waals potentials in terms of the (classical) Green tensor of the electromagnetic field and the atomic polarizability and incorporate the local-field correction by means of the real-cavity model. In this context, special emphasis is given to the decomposition of the Green tensor into a medium part multiplied by a global local-field correction factor and, in the single-atom case, a part that only depends on the cavity characteristics. The result is used to derive general formulas for the local-field corrected van der Waals potentials and forces. As an application, we calculate the van der Waals potential between two ground-state atoms placed within magnetoelectric bulk material.

The time-of-flight distribution for a cloud of cold atoms falling freely under gravity is considered. We generalize the probability current density approach to calculate the quantum arrival time distribution for the mixed state describing the Maxwell-Boltzmann distribution of velocities for the falling atoms. We find an empirically testable difference between the time-of-flight distribution calculated using the quantum probability current and that obtained from a purely classical treatment which is usually employed in analyzing time-of-flight measurements. The classical time-of-flight distribution matches with the quantum distribution in the large mass and high temperature limits.

We propose a scalable approach to building cluster states of matter qubits using coherent states of light. Recent work on the subject relies on the use of single-photonic qubits in the measurement process. These schemes have a low initial success probability and low detector efficiencies cause a serious blowup in resources. In contrast, our approach uses continuous variables and highly efficient measurements. We present a two-qubit scheme, with a simple homodyne measurement system yielding an entangling operation with success probability 1/2. Then we extend this to a three-qubit interaction, increasing this probability to 3/4. We discuss the important issues of the overhead cost and the time scaling, showing how these can be vastly improved with access to this new probability range.

We reformulate the strong-interaction limit of electronic density functional theory in terms of a classical problem with a degenerate minimum. This allows us to clarify many aspects of this limit, and to write a general solution, which is explicitly calculated for spherical densities. We then compare our results with previous approximate solutions and discuss the implications for density-functional theory.

Time-dependent density-functional theory is used to calculate the energy loss of antiprotons and protons traversing metal clusters of variable size. We find that the effective energy loss per unit path length inside the cluster shows no significant cluster size effects over the wide range of projectile velocities studied. This allows us to compare the calculated stopping power with the experimental values for a solid metal target. Excellent agreement between the theoretical results and recent experimental data is found for velocities below the inner-shell excitation threshold. We thus present a nonperturbative quantum-mechanical approach to obtain the energy loss of charges in solids.

We investigate the linewidth of a quasicontinuous atom laser within a semiclassical framework. In the high flux regime, the lasing mode can exhibit a number of undesirable features such as density fluctuations. We show that the output therefore has a complicated structure that can be somewhat simplified using Raman outcoupling methods and energy-momentum selection rules. In the weak outcoupling limit, we find that the linewidth of an atom laser is instantaneously Fourier limited, but, due to the energy “chirp” associated with depletion of the condensate, the long-term linewidth of an atom laser is equivalent to the chemical potential of the condensate source. We show that correctly sweeping the outcoupling frequency can recover the Fourier-limited linewidth.

The linewidth of an atom laser can be limited by excitation of higher energy modes in the source Bose-Einstein condensate, energy shifts in that condensate due to the atomic interactions, or phase diffusion of the lasing mode due to those interactions. The first two are effects that can be described with a semiclassical model, and have been studied in detail for both pumped and unpumped atom lasers. The third is a purely quantum statistical effect and has been studied only in zero-dimensional models. We examine an unpumped atom laser in one dimension using a quantum field theory using stochastic methods based on the truncated Wigner approach. This allows spatial and statistical effects to be examined simultaneously, and the linewidth limit for unpumped atom lasers is quantified in various limits.

We address binary and quaternary communication channels based on correlated multiphoton two-mode states of radiation in the presence of losses. The protocol are based on photon number correlations and realized upon choosing a shared set of thresholds to convert the outcome of a joint photon number measurement into a symbol from a discrete alphabet. In particular, we focus on channels built using feasible photon-number entangled states (PNES) as two-mode coherently-correlated (TMC) or twin-beam (TWB) states and compare their performances with that of channels built using feasible classically correlated (separable) states. We found that PNES provide larger channel capacity in the presence of loss, and that TWB-based channels may transmit a larger amount of information than TMC-based ones at fixed energy and overall loss. Optimized bit discrimination thresholds, as well as the corresponding maximized mutual information, are explicitly evaluated as a function of the beam intensity and the loss parameter. The propagation of TMC and TWB in lossy channels is analyzed and the joint photon number distribution is evaluated, showing that the beam statistics, either sub-Poissonian for TMC or super-Poissonian for TWB, is not altered by losses. Although entanglement is not strictly needed to establish the channels, which are based on photon-number correlations owned also by separable mixed states, purity of the support state is relevant to increase security. The joint requirement of correlation and purity individuates PNES as a suitable choice to build effective channels. The effects of losses on channel security are briefly discussed.

The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.’s heuristic claim, the multiphoton absorption rate of a $(\mid N,0⟩+\mid 0,N⟩)$ quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D’Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.