We show that phase-coherent states of a single-mode quantized electromagnetic field are well approximated by certain superpositions of the squeezed vacuum and one-photon states. We further show that the squeezed vacuum and one-photon states can be understood, approximately, as superpositions of phase-coherent states. Our approximate phase-coherent states may be generated by a degenerate parametric down-converter acting on a prepared input state of the form $|0⟩+\alpha |1⟩$. The input superposition state itself can be prepared from a coherent state $|\alpha ⟩$ by a quantum scissors device.

We demonstrate the existence of three-dimensional localized structures, known as cavity light bullets, that circulate in a driven cavity filled with a self-focusing dispersive medium. Though unstable, we show through a linear stability analysis how a multiphoton absorption can stabilize these structures. Bullets may be written and erased from the cavity at controlled positions, allowing them to act as elements in three-dimensional pixel arrays. We illustrate the process of writing and erasing bullets in the cavity through dynamic numerical simulations.

Spin chains have been proposed as quantum wires for information transfer in solid-state quantum architectures. We show that huge gains in both transfer speed and fidelity are possible using a minimalist control approach that relies only on a single local on-off switch actuator. Effective switching time sequences can be determined using optimization techniques for both ideal and disordered chains. Simulations suggest that effective optimization is possible even in the absence of knowledge of the Hamiltonian or accurate models.

Absolute cross sections for the formation of ${\text{Pt}}^{+}$, ${\text{Pt}}^{2+}$, and ${\text{Pt}}^{3+}$ following $4f$ and $5p$ inner-shell photoexcitation and detachment of ${\text{Pt}}^{-}4f^{14}5d^{9}6s^2{}^{2}D$ are measured. Signal in the ${\text{Pt}}^{3+}$ production channel is dominated by $4f$ detachment and allows for the observation of a $d$-wave Wigner threshold law following single-photon absorption. Promoting a $5p$ electron into the $5d$ orbital produces a shape resonance while promoting a $4f$ electron produces Feshbach resonances, demonstrating the importance of core-valence interactions.

Simultaneous two-electron emission upon $2p$ core-electron excitation in Ar has been studied using a state-of-the-art multielectron coincidence method. Simultaneous two-electron emission effectively populates Rydberg-excited ${\text{Ar}}^{2+}$ states, in which the excited electron behaves as a spectator of the direct double Auger decay of the core hole. This observation constitutes experimental evidence that the shake-off mechanism is not sufficient to model direct double Auger decay of a $2p$ hole in Ar and suggests an important contribution from the knock-out mechanism.

The best clocks to date control the atomic motion by trapping the sample in an optical lattice and then interrogate the atomic transition by shining on these atoms a distinct laser of controlled frequency. In order to perform both tasks simultaneously and with the same laser field, we propose to use instead the levitation of a Bose-Einstein condensate through multiple-wave atomic interferences. The levitating condensate experiences a coherent localization in momentum and a controlled diffusion in altitude. The sample levitation is bound to resonance conditions used either for frequency or for acceleration measurements. The chosen vertical geometry solves the limitations imposed by the sample free fall in previous optical clocks using also atomic interferences. This configuration yields multiple-wave interferences enabling levitation and enhancing the measurement sensitivity. This setup, analogous to an atomic resonator in momentum space, constitutes an attractive alternative to existing atomic clocks and gravimeters.

We present theory for the critical temperature of a Bose gas in a combined harmonic lattice potential based on a mean-field description of the system. We develop practical expressions for the ideal-gas critical temperature and corrections due to interactions, the finite-size effect, and the occupation of excited bands. We compare our expressions to numerical calculations and find excellent agreement over a wide parameter regime.

The radial part of the Schrödinger equation for atomic hydrogen in a spherical box of radius $\delta$ is numerically solved. Two sets of energy levels are obtained, the first one reproduces the unperturbed (bound) levels up to a given principal quantum number while the other one (unbound) describes levels with energy greater than the unperturbed ionization energy of atomic hydrogen $E_{\text{H}}$. These last levels asymptotically converge to the corresponding set which can be obtained by the particle in the box model, i.e., levels which increase their energy as $n^2$ thus ensuring the convergence of the electronic partition function.

We present a way of experimentally determining the concurrence in terms of the expectation values of local observables for arbitrary multipartite pure states. Instead of the joint measurements on two copies of a state in the experiment for two-qubit systems [S. P. Walborn et al., Nature (London) 440, 20 (2006)], we only need one copy of the state in every measurement for any arbitrary dimensional multipartite systems, avoiding the preparation of twin states or the imperfect copy of the state.

Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a need for better approximations to the exchange-correlation energy functional. Furthermore, the need for properly describing current-carrying states represents an additional challenge for the development of approximate functionals. In order to make progress along these directions, we show that simple and efficient expressions for the exchange energy can be obtained by considering the short-range behavior of the one-body spin-density matrix. Applications to several two-dimensional systems confirm the excellent performance of the derived approximations, and verify the gauge-invariance requirement to be of great importance for dealing with current-carrying states.

The double valence photoionization spectra of methanol, ethanol, and $n$-propyl alcohol have been recorded using a time-of-flight photoelectron-photoelectron coincidence technique. The spectra show a well-defined onset followed by broad rounded bands. The lowest vertical double ionization energies have been determined for all molecules and are found to be 32.1, 29.6, and 28.2 eV, respectively. These energies have been applied along with single ionization energies from conventional photoelectron spectra to investigate a recently derived rule of thumb for determination of the lowest double ionization energy in molecules. Many-electron ab initio calculations have been performed on the dicationic ground states in good agreement with the experimental values. For methanol, also excited dicationic states have been calculated up to about 40 eV and used for a detailed interpretation of the experimental spectrum.

The contribution of the axial triangle anomalous graph to the parity-nonconservation effect in atoms is evaluated. The final answer looks like the emission of the electric photon by the magnetic dipole. The relative contribution to the parity-nonconservation effect in neutral atoms appears to be negligible but is essentially larger in case of multicharged ions.

Previous experimental and theoretical studies on HCN and HNC have indicated the presence of both $\sigma$ and $\pi$ low-lying shape resonances. The energy and autoionization width of these resonant states depend on the stretching and bending of the molecule and lead primarily to a $\left({\text{CN}}^{-}+\text{H}\right)$ product. In this work, we present a comparative study of the dissociation mechanism of these isomers. We carried out electron scattering calculations using the complex-Kohn variational method as a function of the three internal degrees of freedom to obtain the resonance energy surfaces and autoionization widths. We then use these data as input to form the Hamiltonian relevant to the nuclear dynamics. The multidimensional wave equation is solved using the multiconfiguration time-dependent Hartree approach. We compute the relative dissociative electron attachment cross sections and examine the isotope effect relative to each isomer.

Illumination of an adsorbate-covered metal surface with an xuv and a delayed ir laser pulse can result in sidebands in the photoelectron (PE) spectra. We present a theoretical model for the delay-dependent PE spectra and show how the relaxation dynamics of xuv-induced core-level holes in adsorbate atoms can be deduced from the temporal shift between sideband peaks in the spectra of secondary adsorbate (Auger) electrons and conduction-band PEs from the substrate. Furthermore, in comparison with gaseous targets, we find a characteristic sideband-intensity enhancement in the laser-assisted photoemission from the substrate core-level bands. This sideband enhancement effect can be tested in experiments with tunable xuv wavelength. Our calculated PE spectra support time-resolved experiments for Xe-covered Pt(111) surfaces, promoting the direct analysis in the time domain of surface dynamical processes.

A practical finite-temperature theory is developed for the superfluid regime of a weakly interacting Bose gas in an optical lattice with additional harmonic confinement. We derive an extended Bose-Hubbard model that is valid for shallow lattices and when excited bands are occupied. Using the Hartree-Fock-Bogoliubov-Popov mean-field approach, and applying local-density and coarse-grained envelope approximations, we arrive at a theory that can be numerically implemented accurately and efficiently. We present results for a three-dimensional system, characterizing the importance of the features of the extended Bose-Hubbard model and compare against other theoretical results and show an improved agreement with experimental data.

We formally link the concept of steering (a concept created by Schrödinger but only recently formalized by Wiseman, Jones, and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]) and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variable observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell nonlocality and entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.

We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state and we discuss how they are related to the quantum mutual information of the state. We show with several examples how complementarity gives rise to a gap between the quantum and the classical correlations and we relate our quantitative finding to the so-called classical correlation locked in a quantum state. We derive upper bounds for the sum of classical correlation obtained by measurements in different mutually unbiased bases and we show that the complementarity gap is also present in the deterministic quantum computation with one quantum bit.

We study the ground-state properties of a spin-3 Cr condensate subject to an external magnetic field by numerically solving the Gross-Piteavskii equations. We show that the widely adopted single-mode approximation is invalid under a finite magnetic field. In particular, a phase separationlike behavior may be induced by the magnetic field. We also point out the possible origin of the phase separation phenomenon.

The dynamical properties of partially coherent Bose-Einstein condensates in double wells are investigated in three typical regimes. In the extreme Fock regime, the time evolution of the degree of coherence is shown to decay rapidly. In the Rabi regime, a relation between the amplitude of Rabi oscillation and the degree of coherence is obtained, which is expected to determine the degree of coherence by measuring the amplitude of Rabi oscillation. The study on the self-trapping phenomena in the Josephson regime exhibits that both the degree of coherence and the initial relative phase can affect the final particle distribution.

The propagation of several spatial modes has a significant impact on the structure of the emission from parametric down-conversion in a nonlinear waveguide. This manifests itself not only in the spatial correlations of the photon pairs but also, due to new phase-matching conditions, in the output spectrum, radically altering the degree of entanglement within each pair. Here we investigate both theoretically and experimentally the results of higher-order spatial-mode propagation in nonlinear waveguides. We derive conditions for the creation of pairs in these modes and present observations of higher-order mode propagation in both the spatial and spectral domains. Furthermore, we observe correlations between the different degrees of freedom and finally we discuss strategies for mitigating any detrimental effects and optimizing pair production in the fundamental mode.