The entanglement content of superpositions of quantum states is investigated based on a measure called concurrence. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we find simple inequalities relating the concurrence of the state to that of its components. We derive an exact expression for the concurrence when the component states are biorthogonal and provide elegant upper and lower bounds in all other cases. For quantum bits, our upper bound is tighter than the previously derived bound [N. Linden et al., Phys. Rev. Lett. 97, 100502 (2006)].

The entanglement of superpositions [Linden et al., Phys. Rev. Lett. 97, 100502 (2006)]is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed states and the superposition coefficients. This bound is proven to be tight for a class of states composed of an arbitrary number of qubits. We also extend the result to a large family of quantifiers, which includes the negativity, the robustness of entanglement, and the best separable approximation measure.

Cross sections for dissociation of ${\mathrm{H}}_2$ due to collision with He are calculated for highly excited rovibrational states using the quantum-mechanical coupled-states approximation. An $L^2$ Sturmian basis set with multiple length scales is used to provide a discrete representation of the ${\mathrm{H}}_2$ continuum which includes orbiting resonances and a nonresonant background. Cross sections are given over a range of translational energies for both resonant and nonresonant dissociation together with the most important bound-state transitions for many different initial states. The results demonstrate that it is possible to compute converged quantum-mechanical cross sections using basis sets of modest size. It is found that collision-induced dissociation competes with inelastic scattering as a depopulation mechanism for the highly excited states. The relevance of the present calculations to astrophysical models is discussed.

We have studied the problem of light scattering by an ensemble of dipoles with both electric and magnetic polarizabilities. Using the coupled electric and magnetic dipole method as the formal base, we have generalized the eigenvector decomposition of the local dipole moments previously derived for purely electric particles to the case of both electric and magnetic dipoles. We have analyzed the properties of eigenvalues and eigenvectors in the most elementary case of two particles. In the purely electric case, the eigenvalues correspond to the resonance modes of the system due to the electromagnetic coupling of its components. For a two-dipole system with both electric and magnetic responses, purely electric, purely magnetic, and mixed states can be distinguished. The resonance spectrum is analyzed as a function of the magnetic permeability, and it is shown that the latter can be fitted quite accurately by the eigenmode decomposition.

The properties of atoms close to an absorptive dielectric are studied using the phenomenological Maxwell’s equations. Although radiative decay has been considered by many authors, the coupling of atoms with longitudinal modes does not seem to have been treated in detail. Here we show that there are two main effects. The first is a change in the atomic interaction potential from the Coulomb one to a static potential, i.e., one that satisfies a Poisson equation featuring the static dielectric function ${\epsilon }_{\mathrm{stat}}=\epsilon \left(\omega \right){\mid }_{\omega =0}$. The second is the decay of excited atomic states through longitudinal field interactions. We find that the corresponding decay constant is nonzero only for atom-dielectric distances in the order of an atomic diameter and that it decreases exponentially fast on an atomic scale with increasing distance. We also show that the Hamiltonian used by the Jena group [Dung et al., Phys. Rev. A 65, 043813 (2002)], featuring the Coulomb potential, is unitarily equivalent to one containing the static potential.

We present an exactly solvable model to study the role of the system-bath coupling for the generalized canonical thermalization, which reduces almost all the pure states of the “universe” (formed by a system $S$ plus its surrounding heat bath $B$) to a canonical equilibrium state of $S$. It is found that, for the overwhelming majority of the “universe” states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between $S$ and $B$. Particularly, a decoherence mechanism is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of $S$. The nonvanishing off-diagonal elements due to the finite size of the bath and the stronger system-bath interaction might offer more to quantum thermalization.

We have analyzed the transverse correlation in multiphoton entanglement. The generalization of quantum ghost imaging is extended to the $N$-photon state. The Klyshko’s two-photon advanced-wave picture is generalized to the $N$-photon case.

We complete the stability analysis for three-dimensional dissipative solitons with intrinsic vorticity $S$ in the complex Ginzburg-Landau equation with cubic and quintic terms in its dissipative and conservative parts. It is found and qualitatively explained that a necessary stability condition for all vortex solitons, but not for the fundamental ones $(S=0)$, is the presence of nonzero diffusivity in the transverse plane. The fundamental solitons are stable in all cases when they exist, while the vortex solitons are stable only in a part of their existence domain. However, the spectral filtering (i.e., the temporal-domain diffusivity) is not necessary for the stability of any species of dissipative solitons. In addition to the recently studied solitons with $S=0,1,2$, a stability region is also found for ones with $S=3$.

This paper discusses some tests of Bell-like inequalities not requiring entangled states. The proposed tests are based on consecutive measurements on a single qubit. Available hidden-variable models for a single qubit [see, e.g., J. S. Bell, Rev. Mod. Phys. 38, 447 (1966)] reproduce the predictions of quantum mechanics and hence violate the Bell-like inequalities addressed in this paper. It is shown how this fact is connected with the state “collapse” and with its random nature. Thus, it becomes possible to test truly realistic and deterministic hidden-variable models. In this way, it can be shown that a hidden-variable model should entail at least one of the following features: (i) nonlocality, (ii) contextuality, or (iii) discontinuous measurement-dependent probability functions. The last two features are put to the test with the experiments proposed in this paper. A hidden-variable model that is noncontextual and deterministic would be at variance with some predictions of quantum mechanics. Furthermore, the proposed tests are more likely to be loophole-free, as compared to former ones.

We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias toward a given state, the problem may be faced by minimizing the quantum relative entropy (Kullback entropy) with the constraint of reproducing the data. We exploit the resulting minimum Kullback entropy principle for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit and harmonic oscillator systems are analyzed in some detail.

Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space—either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase factor that reflects the topology of the SO(3) group: since rotations by $\pi$ around antiparallel axes are identical, this space is doubly connected. Using a pair of nuclear spins in a maximally entangled state, we subject one of the spins to a cyclic evolution. If the corresponding trajectory in SO(3) can be smoothly deformed to a point, the quantum state at the end of the trajectory is identical to the initial state. For all other trajectories the quantum state changes sign.

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular, it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.

The possibility of detecting correlations between two quantum-mechanical systems from only the information of a subsystem is investigated. For generic cases, we prove that there exist correlations between two quantum systems if the time derivative of the reduced purity is not zero. Therefore, an experimentalist can conclude that correlations between the system and some environment are nonzero if the time derivative of the reduced purity is found not to be zero. A quantitative estimation of the time derivative of the reduced purity with respect to correlations is also given. This clarifies the role of correlations in the mechanism of decoherence in open quantum systems.

We study analytically the structure of an arbitrary-order correlation function for a pair of Fock states and prove without any approximations that, in a single measurement of particle positions, interference effects must occur as experimentally observed with Bose-Einstein condensates. We also show that the noise level present in the statistics is slightly lower than for a corresponding measurement of phase states.

We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in detail the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single-mode and multimode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows one to define a corresponding measure for the non-Gaussian character of a quantum operation.

Hylleraas-type calculations of the hyperfine constants for the four lowest excited $3{}^{2}S$, $4{}^{2}S$, $5{}^{2}S$, and $6{}^{2}S$ states of the lithium atom are reported. Hyperfine constants are determined for the stable isotopes ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ and for the unstable isotopes ${}^8\mathrm{Li}$, ${}^9\mathrm{Li}$, and ${}^{11}\mathrm{Li}$ for each state. Finite-nuclear-mass, lowest-order relativistic, quantum electrodynamic, Bohr-Weisskopf, Breit-Rosenthal, and Sushkov corrections are incorporated.

We have created a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate in a magnetic trapping potential produced by a hard disk platter written with a periodic pattern. Cold atoms were loaded from an optical dipole trap and then cooled to Bose-Einstein condensation on the surface with radio-frequency evaporation. Fragmentation of the atomic cloud due to imperfections in the magnetic structure was observed at distances closer than $40\mathrm{\mu }\mathrm{m}$ from the surface. Attempts to use the disk as an atom mirror showed dispersive effects after reflection.

We theoretically show that selection of a single quantum path in high-order harmonics generation can be realized in a few-optical-cycle regime with two-color schemes. We also demonstrate, in theory as well, the generation of spectrally smooth and ultrabroad extreme ultraviolet supercontinuum in argon gas which can produce single $\sim 79$ as pulses with currently available ultrafast laser sources. Our finding can be beneficial for generating isolated sub-100 as extreme ultraviolet pulses.

Circularly polarized short laser pulse induces nonequilibrium population of spin levels in the excited state of ${\mathrm{Ce}}^{3+}$-ion embedded in yttrium aluminium garnet crystal and, consequently, the magnetization of the crystal associated with spin polarization. Dynamic behavior of laser-induced magnetization is studied as a function of the external magnetic field. It reveals spin oscillations attributed to the effect of hyperfine magnetic field produced by ${}^{27}\mathrm{Al}$ nuclei on the ${\mathrm{Ce}}^{3+}$ spin. A simple theoretical model explaining spin oscillations is presented. It shows that circularly polarized light induces spin coherence at the transition between Zeeman sublevels of ${\mathrm{Ce}}^{3+}$ ion in the lowest $5d$ state. Temporal shape of laser-induced magnetization signal reveals the following parameters of this state: (1) the spin-lattice relaxation constant is $\approx 2\times {10}^7{\mathrm{s}}^{-1}$, (2) inhomogeneous spin dephasing time is $\approx 4\mathrm{ns}$, and (3) the $g$ tensor of the state seems to be isotropic with the $g$ factor being in the range 0.7–0.9. In addition, the width of the local hyperfine field distribution is $\approx 40\mathrm{G}$.

We present a detailed analytical and numerical analysis of the inelastic coherent backscattering spectrum of laser light incident on cold atoms. We identify frequency domains where the interference contribution can be positive as well as negative—or exhibits dispersive character. These distinctive features are explained by reciprocity arguments and dressed-state two-photon scattering amplitudes.