We propose a scheme for parallel spatially multimode quantum memory for light. The scheme is based on a counterpropagating quantum signal wave and a strong classical reference wave as in a classical volume hologram and therefore can be called a quantum volume hologram. The medium for the hologram consists of a spatially extended ensemble of atoms placed in a magnetic field. The write-in and readout of this quantum hologram is as simple as that of its classical counterpart and consists of a single-pass illumination. In addition, we show that the present scheme for a quantum hologram is less sensitive to diffraction and therefore is capable of achieving a higher density of storage of spatial modes as compared to previous proposals. We present a feasibility study and show that experimental implementation is possible with available cold atomic samples. A quantum hologram capable of storing entangled images can become an important ingredient in quantum information processing and quantum imaging.

We investigate high-precision measurements beyond the standard quantum limit, utilizing nonclassical states. Although entanglement was considered a resource for achieving the Heisenberg limit in measurements, we show that any advantage expected from using entanglement is dependent on the measurement in question. We investigate several measurement scenarios and illustrate the role of entanglement as a resource for quantum high-precision measurement. In particular, we demonstrate that there is a regime wherein entanglement not only does not help, but prevents the achievement of the fundamental limit.

Complex numbers are an intrinsic part of the mathematical formalism of quantum theory and are perhaps its most characteristic feature. In this article, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued function of this number pair. By making use of elementary symmetry conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman’s sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes.

The aim of this paper is to perform a numerical and analytical study of a rotating Bose-Einstein condensate placed in a harmonic plus Gaussian trap, following the experiments of Bretin et al. [Phys. Rev. Lett. 92, 5 (2004)]. The rotational frequency $\Omega$ has to stay below the trapping frequency $\omega$ of the harmonic potential and we find that the condensate has an annular shape containing a triangular vortex lattice. As $\Omega$ approaches $\omega$, the width of the condensate and the circulation inside the central hole get large. We are able to provide analytical estimates of the size of the condensate and the circulation both in the lowest Landau level limit and in the Thomas-Fermi limit, providing an analysis that is consistent with experiment.

We introduce the concept of energy density flux as a characterization tool for the propagation of ultrashort laser pulses with spatiotemporal coupling. In contrast with calculations for the Poynting vector, those for energy density flux are derived in the local frame moving at the velocity of the envelope of the wave packet under examination and do not need knowledge of the magnetic field. We show that the energy flux defined from a paraxial propagation equation follows specific geometrical connections with the phase front of the optical wave packet, which demonstrates that the knowledge of the phase fronts amounts to the measurement of the energy flux. We perform a detailed numerical study of the energy density flux in the particular case of conical waves, with special attention paid to stationary-envelope conical waves ($\text{X}$ or $\text{O}$ waves). A full characterization of linear conical waves is given in terms of their energy flux. We extend the definition of this concept to the case of nonlinear propagation in Kerr media with nonlinear losses.

We address theoretically and numerically the possibility of observing ellipticity in high-order harmonic generation (HHG) from aligned molecules driven by linearly polarized fields—a subject of controversy in the recent literature with significant implications. To that end we develop a numerical method for solution of the electronic dynamics and extend a recently developed theory of HHG from aligned molecules. Our numerical results are in good agreement with recent experimental data. The theory explains analytically several observations of polarization experiments. We note the conditions under which ellipticity can be observed and the information content of elliptically polarized harmonics regarding the molecular system.

We investigate the particle trapping and scattering properties in a tight-binding network, which consists of several subgraphs. The particle trapping condition is proved under which particles can be trapped in a subgraph without leaking. Based on exact solutions for the configuration of a $\pi$-shaped lattice, it is argued that the bound states in a specified subgraph are of two types, resonant and evanescent. We also link the result to the scattering problem. The scattering features of the $\pi$-shaped lattice is investigated in the framework of the Bethe ansatz.

The optimal dynamical decoupling sequence for a qubit coupled to an Ohmic environment is investigated. By analytically computing the derivatives of the decoherence function, the optimal pulse locations are found to satisfy a set of nonlinear equations which can be easily solved. These equations incorporate the environment information such as the high-energy (UV) cutoff frequency ${\omega }_c$, giving a complete description of the decoupling process. The solutions explain previous experimental and theoretical results of locally optimized dynamical decoupling sequence in high-frequency-dominated environment, which were obtained by purely numerical computation and experimental feedback. As shown in numerical comparison, these solutions outperform the Uhrig dynamical decoupling sequence by one or more orders of magnitude in the Ohmic case.

Decoy states have been proven to be a very useful method for significantly enhancing the performance of quantum key distribution systems with practical light sources. Although active modulation of the intensity of the laser pulses is an effective way of preparing decoy states in principle, in practice passive preparation might be desirable in some scenarios. Typical passive schemes involve parametric down-conversion. More recently, it has been shown that phase-randomized weak coherent pulses (WCP) can also be used for the same purpose [M. Curty et al., Opt. Lett. 34, 3238 (2009).] This proposal requires only linear optics together with a simple threshold photon detector, which shows the practical feasibility of the method. Most importantly, the resulting secret key rate is comparable to the one delivered by an active decoy-state setup with an infinite number of decoy settings. In this article we extend these results, now showing specifically the analysis for other practical scenarios with different light sources and photodetectors. In particular, we consider sources emitting thermal states, phase-randomized WCP, and strong coherent light in combination with several types of photodetectors, like, for instance, threshold photon detectors, photon number resolving detectors, and classical photodetectors. Our analysis includes as well the effect that detection inefficiencies and noise in the form of dark counts shown by current threshold detectors might have on the final secret key rate. Moreover, we provide estimations on the effects that statistical fluctuations due to a finite data size can have in practical implementations.

The PH radical is an interesting case to study because of its ${\pi }^2$ electronic configuration, which leads to the three low-lying electronic states, $X$ ${}^3{\Sigma }^{-}$, $a$ ${}^1\Delta$, and $b$ ${}^1{\Sigma }^{+}$. The singlet states possess long lifetimes, because direct combination with the ground state is not allowed. This is similar to the ${\mathrm{O}}_2$ case. The $\mathit{R}$-matrix method is employed to calculate elastic differential and integral cross sections, momentum-transfer cross sections, and inelastic cross sections. The energy range is 0–10 eV. The Hartree-Fock ground-state configuration of PH is $1{\sigma }^{2}2{\sigma }^{2}3{\sigma }^{2}1{\pi }^{4}4{\sigma }^{2}5{\sigma }^{2}2{\pi }^2$. We have included thirty-seven target states in the trial wave function of the scattering system in our best model. Each target state is represented by a configuration interaction (CI) wave function. In our CI model, we freeze ten electrons in orbitals $1\sigma$, $2\sigma$, $3\sigma ,$ and $1\pi$; the remaining six electrons are free to move among the seven orbitals $4\sigma$, $5\sigma$, $6\sigma$, $7\sigma$, $8\sigma$, $2\pi ,$ and $3\pi$. Our CI model yields a dipole moment of 0.67 D at the equilibrium PH bond length, $R_e$, of 2.687 $a_0$; this dipole moment compares favorably with the experimental value 0.70 D. We have carried our scattering calculations in one state with the CI wave function and thirty-seven-state model. We have detected a stable anionic bound state ${}^2{B}_1$ of PH at various bond lengths of PH molecule. The vertical electron affinity value is 0.97 eV, which is in excellent agreement with experimental value of 1.00 eV. We have included up to $g$ partial waves in the scattering calculations. The contribution of higher partial waves is accounted for by using a Born-closure procedure.

Single-electron capture from heliumlike atomic systems by bare projectiles is investigated by means of the four-body boundary-corrected first Born approximation (CB1-4B). The effect of the dynamic electron correlation is explicitly taken into account through the complete perturbation potential. The quantum-mechanical post and prior transition amplitudes for single charge exchange encompassing symmetric and/or asymmetric collisions are derived in terms of two-dimensional real integrals in the case of the prior form and five-dimensional quadratures for the post form. An illustrative computation is performed for single-electron capture from helium by protons and $\alpha$ particles at intermediate and high impact energies. The role of dynamic correlations is examined as a function of increased projectile energy. The validity and utility of the proposed CB1-4B method is critically assessed in comparison with the existing experimental data for total cross sections, and excellent agreement is obtained.

Free nanoscale tin clusters in the average size range of a few tens up to $~$500 atoms are studied by means of valence and core-level photoelectron spectroscopy. A self-consistent picture arises from comparison of the work functions derived from the $4\mathit{d}$ core-level spectra, the experimental ionization energies extracted from the $5\mathit{p}$ valence spectra, and the expectations from the metallic sphere model for the clusters. The present studies demonstrate that the 4d core-level energy changes are a sensitive probe of the metal-to-semiconductor transition in the size range under investigation.

The nonsequential double ionization (NSDI) yield and final electron-electon correlation are examined for a laser wavelength of $800$ nm over a wide range of laser intensities, using three-dimensional fully classical models. It is shown that in the transition region between NSDI and sequential ionization, turn-on stage recollisions can lead to having a majority of anticorrelated (back-to-back) electron pairs.

We describe how the nuclear recoil cross sections produced by two-photon double ionization of helium can reveal aspects of the underlying triple-differential cross sections (TDCSs) used in their computation—even though the recoil of the He${}^{2+}$ nucleus reflects an integration over all electron ejection directions and energy sharings. Accurate TDCSs, extracted from nonperturbative solutions of the time-dependent Schrödinger equation, are used here in computations of the nuclear recoil cross section at energies a few electron volts below the threshold for sequential double ionization. In this range of photon energies, the nuclear recoil patterns prefigure some important aspects of the sequential mechanism that dominates at higher energies.

We study a gas of repulsively interacting bosons in the first excited band of an optical lattice. We explore this $p$-band physics both within the framework of a standard mean-field theory as well as with the more accurate generalized Gutzwiller ansatz. We find the phase diagrams for two- and three-dimensional systems and characterize the first Mott-states which typically possess an integer or half-integer vortex structure. Furthermore, we find that even though the $p$-band model has strongly anisotropic kinetic energies and interflavor interaction terms are missing in the lowest band theory, the mean-field theory becomes useful quite rapidly once the transition from the Mott insulator to the superfluid is crossed.

We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum $\mathit{XY}$ chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We discuss trap-size scaling at the Mott insulator to superfluid transition in the Bose-Hubbard model. We present exact and accurate numerical results for the $\mathit{XY}$ chain and for the low-density Mott transition in the hard-core limit of the one-dimensional Bose-Hubbard model. Our results are relevant for systems of cold atomic gases in optical lattices.

We discuss electromagnetic modes in cavities formed by metamaterials with negative refraction and demonstrate that the straightforward approach to substitute negative values of the electric permittivity and the magnetic permeability leads to quasibound states with a negative quality factor. To ensure positive quality factors and a consistent physical interpretation of the quasibound states it is essential to include the frequency dispersion of the permittivity and the permeability, as required by positive field energy and causality. The basic mode equation and the boundary conditions including linear frequency dispersion are derived. As an example we consider a disklike cavity with deformed cross-sectional shape. The transition from the unphysical nondispersive case with negative quality factors to the dispersive case with positive quality factors is demonstrated numerically and in an analytical perturbative treatment.

We propose a general method to realize frustrated tunneling of ultracold atoms in a state-dependent optical lattice. Two typical lattice configurations are considered, the square lattice with competing interaction and the kagomé lattice with geometrical frustration. The ideal can be extended to implement frustrated tunneling of ultracold atoms in various geometries, which enable us to investigate the physics of frustration in both bosonic and spin systems. We study the mean-field phase diagrams of the considered models and the experimental situations are also discussed.

We report on a two-photon interference experiment in a quantum relay configuration using two picosecond regime periodically poled lithium niobate (PPLN) waveguide based sources emitting paired photons at 1550 nm. The results show that the picosecond regime associated with a guided-wave scheme should have important repercussions for quantum relay implementations in real conditions, essential for improving both the working distance and the efficiency of quantum cryptography and networking systems. In contrast to already reported regimes, namely, femtosecond and CW, it allows achieving a $99\%$ net visibility two-photon interference while maintaining a high effective photon pair rate using only standard telecom components and detectors.