The entanglement of collaboration (EOC) quantifies the maximum amount of entanglement that can be generated between two parties, $A$ and $B$, given collaboration with $N-2$ other parties, when the $N$ parties share a multipartite (possibly mixed) state and where the collaboration consists of local operations and classical communication by all parties. The localizable entanglement (LE) is defined similarly except that $A$ and $B$ do not participate in the effort to generate bipartite entanglement. We compare between these two operational definitions and find sufficient conditions for which the EOC is equal to the LE. In particular, we find that the two are equal whenever they are measured by the concurrence or by one of its generalizations called the G-concurrence. We also find a simple expression for the LE in terms of the Jamiolkowski isomorphism and prove that it is convex.

The lifetimes of singly charged protonated oligonucleotide cations, $d{\left(A\right)}_2$, $d{\left(A\right)}_3$, $d{\left(A\right)}_4$, and $d{\left(A\right)}_5$, were measured after UV photoabsorption in a storage ring. Two lifetime components were observed for $d{\left(A\right)}_3$, $d{\left(A\right)}_4$, and $d{\left(A\right)}_5$ but only one for $d{\left(A\right)}_2$. Assuming that the major fragmentation channel is the same for all oligonucleotide cations, namely loss of a protonated adenine base, with similar Arrhenius parameters, then the lifetimes are a result of different final temperatures after photon absorption. Such an analysis provides an activation energy $E_a$ of $0.88\mathrm{eV}$ and preexponential factor $A$ of ${10}^{10.2}{\mathrm{s}}^{-1}$. Nonstatistical fragmentation was an important channel for all of the oligonucleotide cations, but most so for $d{\left(A\right)}_2$, the one with the lowest number of neutral adenines.

We present new measurements of photoionization cross sections from the $4s{}^{2}S$, $4p{}^{2}P$, and $4d{}^{2}D$ excited states of lithium, above the first ionization threshold. The experiments have been conducted using two dye lasers pumped by a Nd:yttrium aluminum garnet (YAG) laser in conjunction with a thermionic diode ion detector and pump-probe saturation technique. The behavior of the photoionization cross sections from $n=4$ and $l=0,1,2$ excited states have been investigated. A smooth wavelength dependence of photoionization cross sections has been observed for the $4p$ and $4d$ excited states, which decrease monotonically with the decrease in the ionizing laser wavelength; however, the falloff for the $4d$ excited state is purely hydrogenic. The cross section for the $4s$ excited state first increases, attains a maximum value, and then decreases monotonically with a decrease in the ionizing wavelength—strictly nonhydrogenic. The measured values of the cross section are compared with the earlier theoretical work.

Two-dimensional (2D) electron momentum distributions and energy spectra for multiphoton ionization of atoms by intense laser pulses, calculated by solving the time-dependent Schrödinger equation (TDSE) for different wavelengths and intensities, are compared to those predicted by the strong-field approximation (SFA). It is shown that the momentum spectra at low energies between the TDSE and SFA are quite different and the differences arise largely from the absence of a long-range Coulomb interaction in the SFA. We further found that the low-energy 2D momentum spectra from the TDSE exhibit ubiquitous fanlike features where the number of stripes is due to a single dominant angular momentum of the low-energy electron. The specific dominant angular momentum in turn has been found to be decided by the minimum number of photons needed to ionize the atom only. The electron momentum spectra predicted by models modified from the SFA are also examined and found to lack the fanlike features as in the SFA.

We consider $N$ atoms trapped in an isotropic harmonic potential, with $s$-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, existence of a decoupled bosonic degree of freedom, and relations between the moments of the trapping potential energy and the moments of the total energy.

We perform fully three-dimensional simulations, using the truncated Wigner method, to investigate the reflection of Bose-Einstein condensates from abrupt potential barriers. We show that the interatomic interactions can disrupt the internal structure of a cigar-shaped cloud with a high atom density at low approach velocities, damping the center-of-mass motion and generating vortices. Furthermore, by incorporating quantum noise we show that scattering halos form at high approach velocities, causing an associated condensate depletion. We compare our results to recent experimental observations.

By numerical solution of the time-dependent Schrödinger equation, highly accurate electron spectra are calculated for strong-field ionization of a one-dimensional $\mathrm{H}_2{}^{+}$ molecular ion at large internuclear distances. Compared to the atomic spectra, we find additional cutoffs at high electron energies. The classical model for ionization (simple-man’s model) adapted to the molecular geometry predicts cutoffs up to $50U_{\mathrm{p}}$, where $U_{\mathrm{p}}$ is the ponderomotive potential. The cutoffs correspond to various scattering scenarios of the tunneled electron from the molecular sites. For certain internuclear distances the agreement between the classical predictions and the numerical spectra is unsatisfactory. We propose a modified simple-man’s model based on complex electron trajectories, allowing for electrons appearing in the continuum with nonzero initial velocity from the tunneling ionization process. Agreement of the resulting cutoffs with the numerical results is recovered.

We present a generic method to construct a product basis exhibiting nonlocality without entanglement with $n$ parties each holding a system of dimension at least $n-1$. This basis is generated via a quantum circuit made of controlled discrete Fourier transform gates acting on the computational basis. The simplicity of our quantum circuit allows for an intuitive understanding of this new type of nonlocality. We also show how this circuit can be used to construct unextendible product bases and their associated bound entangled states. To our knowledge, this is the first method which, given a general Hilbert space $\mathcal{H}={\otimes }_{i=1}^n{\mathcal{H}}_{d_i}$ with $d_i⩽n-1$, makes it possible to construct (i) a basis exhibiting nonlocality without entanglement, (ii) an unextendible product basis, and (iii) a bound entangled state.

The semiclassical limit of the quantum few-body problem has not been studied in general terms from the point of view of periodic orbit theory. In a previous paper, we studied noninteracting two-body systems [Phys. Rev. A 62, 042109 (2000)] and discussed the fact that the periodic orbits occur in continuous families. Interactions destroy the periodic orbit families leaving a discrete set of isolated periodic orbits. In this paper, we consider the effect of weak two-body interactions, which can be thought of as symmetry-breaking perturbations and can thus be analyzed using a theory developed by Creagh [Ann. Phys. (N.Y.) 248, 1 (1996)]. The Pöschl-Teller two-body system confined in a square well is analyzed to illustrate the use of the formalism. It is shown that the effect of the interaction can be evaluated for all two-particle periodic orbits, and that the coarse-grained quantum density of states can be fully reproduced from simply summing the perturbed contributions of each periodic orbit family. Good numerical estimates of the quantum singlet energies can actually be obtained, but it is found that that perturbed trace formulas cannot reproduce the multiplet splittings predicted from quantum mechanics. Several interesting properties are observed depending on the range of the interaction and on whether the interaction is attractive or repulsive.

We discuss the monotonicity of systematically constructed quantities aiming at the quantification of the entanglement properties of multipartite quantum systems, under local operations and classical communication. We provide a necessary and sufficient condition for the monotonicity of generalized multipartite concurrences which qualifies them as legitimate entanglement measures.

We show that quantum mechanical entanglement can prevail in noisy open quantum systems at high temperature and far from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number $N$ of interacting quantum particles, and can interact and exchange particles with some environments. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g., by replacing them with particles from the environment. We present a master equation that describes this process, which we can solve analytically for small $N$. If we vary the interaction strength and the reset against decoherence rate, we find a threshold below which the equilibrium state is classically correlated and above which there is a parameter region with genuine entanglement.

We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given $m\text{th}$ partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.

We describe situations in which chains of $N$ degenerate quantum energy levels, coupled by time-dependent external fields, can be replaced by independent sets of chains of length $N$, $N-1,\dots ,2$ and sets of uncoupled single states. The transformation is a generalization of the two-level Morris-Shore transformation [J.R. Morris and B.W. Shore, Phys. Rev. A 27, 906 (1983)]. We illustrate the procedure with examples of three-level chains.

A model of two-level weakly interacting quantum systems is used to demonstrate that the phase of molecular vibrations excited through stimulated Raman scattering can be controlled by the relative phase of time-separated laser pulses, allowing synchronization and amplitude control of coherence excitation in a medium. For transients with a phase relaxation time less than the field cycle, the field half-cycle can serve as a subfemtosecond probe of coherent vibrations. In this regime, the high-frequency field-induced modulation of molecular dipole moments gives rise to a detectable modulation of the optical response of a medium at the frequency $2\omega$, $\omega$ being the frequency of the laser field.

The spectroscopic properties of a single tightly trapped atom are studied, when the electronic levels are coupled by three laser fields in an $N$-shaped configuration of levels, whereby a $\Lambda$-type level system is weakly coupled to a metastable state. We show that depending on the laser frequencies the response can be tuned from coherent population trapping at two-photon resonance to a behavior at three photon resonance, where the metastable state can get almost unit occupation in a wide range of parameters. For certain parameter regimes the system switches spontaneously between dissipative and coherent dynamics over long time scales.

We present an optical frequency-down-conversion process of the image of an object illuminated with chaotic light in which also the low-frequency field entering the second-order nonlinear crystal is chaotic. We show that the fulfillment of the phase-matching conditions by the chaotic interacting fields provides the rules to retrieve the object image by calculating suitable correlations of the local intensity fluctuations even if a single record of down-converted chaotic image is available.

A general scheme is presented for controlling quantum systems using evolution driven by nonselective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a two-level quantum system controlled by nonselective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive nonselective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.

We present converged, completely ab initio calculations of the triple differential cross sections for double photoionization of aligned ${\mathrm{H}}_2$ molecules for a photon energy of $75.0\mathrm{eV}$. The method of exterior complex scaling, implemented with both the discrete variable representation and $B$-splines, is used to solve the Schrödinger equation for a correlated continuum wave function corresponding to a single photon having been absorbed by a correlated initial state. Results for a fixed internuclear distance are compared to recent experiments and show that integration over experimental angular and energy resolutions is necessary to produce good qualitative agreement, but does not eliminate some discrepancies. Limitations of current experimental resolution are shown to sometimes obscure interesting details of the cross section.

We study the temporal and spatial dynamics of the large amplitude and frequency modulation that can be induced in an intense, few cycle laser pulse as it propagates through a rapidly ionizing gas. Our calculations include both single atom and macroscopic interactions between the nonlinear medium and the laser field. We analyze the harmonic generation by such pulses and show that it is spatially separated from the ionization dynamics which produce a large dynamical blueshift of the laser pulse. This means that small changes in the initial laser focusing conditions can lead to large differences in the laser frequency modulation, even though the generated harmonic spectrum remains essentially unchanged. We also show that the ionization dynamics strongly influences the possibility of synthesizing isolated attosecond pulses.