We calculate the corrections to the Casimir force between two metals due to the spatial dispersion of their response functions. We employ model-independent expressions for the force in terms of the optical coefficients. We express the nonlocal corrections to the Fresnel coefficients employing the surface $d_{\perp }$ parameter, which accounts for the distribution of the surface screening charge. Within a self-consistent jellium calculation, spatial dispersion increases the Casimir force significatively for small separations. The nonlocal correction has the opposite sign than previously predicted employing hydrodynamic models and assuming abruptly terminated surfaces.

A semiclassical approximation to the time evolution of coherent states may be derived from a saddle point approximation to the exact quantum propagator, and in general it involves complex classical dynamics. We generalize previous one-dimensional results to $d$ dimensions, and for the case $d=2$ we present several applications. We also consider other simple approximations that depend only on real classical trajectories, but are not initial value representations. These approximations are able to reproduce interference and tunneling effects and involve propagating a few classical initial conditions compatible with the quantum uncertainties.

We address the generation, propagation, and application of multipartite continuous variable entanglement in a noisy environment. In particular, we focus our attention on the multimode entangled states achievable by second-order nonlinear crystals—i.e., coherent states of the $\mathrm{SU}(m,1)$ group—which provide a generalization of the twin-beam state of a bipartite system. The full inseparability in the ideal case is shown, whereas thresholds for separability are given for the tripartite case in the presence of noise. We find that entanglement of tripartite states is robust against thermal noise, both in the generation process and during propagation. We then consider coherent states of $\mathrm{SU}(m,1)$ as a resource for multipartite distribution of quantum information and analyze a specific protocol for telecloning, proving its optimality in the case of symmetric cloning of pure Gaussian states. We show that the proposed protocol also provides the first example of a completely asymmetric $1\to m$ telecloning and derive explicitly the optimal relation among the different fidelities of the $m$ clones. The effect of noise in the various stages of the protocol is taken into account, and the fidelities of the clones are analytically obtained as a function of the noise parameters. In turn, this permits the optimization of the telecloning protocol, including its adaptive modifications to the noisy environment. In the optimized scheme the clones’ fidelity remains maximal even in the presence of losses (in the absence of thermal noise), for propagation times that diverge as the number of modes increases. In the optimization procedure the prominent role played by the location of the entanglement source is analyzed in details. Our results indicate that, when only losses are present, telecloning is a more effective way to distribute quantum information than direct transmission followed by local cloning.

The matrix element for the decay of orthopositronium to three photons can be expressed in terms of three independent amplitudes. We describe the analytic evaluation of these amplitudes, both to lowest order and with the inclusion of all one-loop corrections. We use these amplitudes to find precise values for the one-loop correction to the orthopositronium decay rate ${\Gamma }_1=-10.286606\left(10\right)(\alpha ∕\pi ){\Gamma }_{\mathrm{LO}}$, and for the order-${\alpha }^2$ “square” correction to the decay rate ${\Gamma }_2\left(\text{square}\right)=28.860\left(2\right){(\alpha ∕\pi )}^2{\Gamma }_{\mathrm{LO}}$, where ${\Gamma }_{\mathrm{LO}}$ is the lowest order rate. We give in explicit form the function describing the one-loop correction to the distribution in phase space of the final state photons.

We present numerical solutions of the Schrödinger equation for three identical bosons from very large to essentially infinite two-body $s$-wave scattering lengths $a$. We have considered scattering lengths up to $2\times {10}^5\mathrm{a.u.}$ and solved the hyperangular part of the Schrödinger equation for distances up to ${10}^6\mathrm{a.u.}$ From these, we obtained the three-body effective potentials, hyperspherical channel functions and the asymptotic behavior of the nonadiabatic couplings in order to characterize the main aspects of the Efimov states. These results allow us to test and quantify the assumptions related to the Efimov effect.

Recently, Tyliszczak et al. [J. Electron Spectrosc. Rel. Phenom. 114, 93 (2001)] have observed oscillations in the generalized oscillator strength (GOS) profile of molecular inner-shell excitations by electron impact. In order to check the mechanism that gives rise to these oscillations, we have calculated GOS profiles for different $\text{inner}\text{−}\text{shell}\to \text{Rydberg}$ excitation processes in $\mathrm{C}{\mathrm{O}}_2$ and butadiene. The comparison of the oscillations appearing in these ab initio results with a simple analytical model in which the interference term is explicit brings out very strong evidence favorable to the hypothesis that the observed oscillations in the GOS are due to Young-type quantum interference related to symmetry-equivalent atoms.

A classical, three-dimensional analysis of excitation and control of vibrational-rotational degrees of freedom of a polar diatomic molecule by chirped laser field is presented. The control strategy is based on autoresonance (adiabatic nonlinear synchronization) phenomenon, in which the molecule automatically adjusts its state for staying in a persistent resonance with the laser field despite variation of the laser frequency. Thresholds on driving field amplitudes for entering the autoresonant excitation regime by passage through different resonances are calculated. In autoresonance, the molecule can be excited to large energies and approach the dissociation limit by substantially weaker laser fields than with constant-frequency drives.

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The result of the modified approach is shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. The effective thermodynamic limit is defined for any confining dimension. The behavior of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.

We derive and study a model describing passive mode locking—a set of differential equations with time delay. Unlike classical mode locking models based on the Haus master equation, this model does not assume small gain and loss per cavity round trip. Therefore, it is valid in a parameter range typical of semiconductor lasers. The limit of a slow saturable absorber is analyzed analytically. Bifurcations responsible for the appearance and breakup of the mode locking regime are studied numerically.

Entanglement of an open bipartite system is investigated. In particular, we calculate the entanglement of a subsystem $A$ with $k$ particles in an $N$ atoms of two-level system $(k⩽N∕2)$ initially prepared in a mesoscopic superposition $\mid \psi ⟩=[{\mid {\varphi }_1\left({\theta }_0\right)⟩}^{\otimes N}+{\mid 0⟩}^{\otimes N}]$, with $\mid {\varphi }_1\left({\theta }_0\right)⟩=\cos {\theta }_0\mid 0⟩+\sin {\theta }_0\mid 1⟩$, subject to the time evolution described by a dephasing channel. For an arbitrary number of particles $N$, numerical results are given for the full time evolution up to ten particles and $1⩽k⩽5$. Analytical results are obtained for short times and asymptotic time regimes. Entanglement is maximum when ${\theta }_0=\pi ∕2$ [Greenberger-Horne-Zeilinger (GHZ) state], independently of the number of particles in each partition. As $N$ gets larger, entanglement tends to $1∕2$, and becomes independent of ${\theta }_0$. The “thermodynamic” regime ($N\to \infty$ with $fN$ finite, where $f=k∕N$) is reached already for $N=1000$ particles. In the regime of $k⪡N$ and $N\to \infty$, the entanglement has its maximum value at ${\theta }_0=\pi ∕2$ and for ${\theta }_0=0,\pi$ its minimum value. The time evolution reduces the maximum value of entanglement, showing that the subsystem $A$ loses coherence to the environment. Finally, we point out the differences between the entanglement rate obtained here from that one in Phys. Rev. Lett. 89, 210402 (2002), where only one $N$-particle subsystem is used.

We present a way to realize an $n$-qubit controlled phase gate with superconducting quantum-interference devices (SQUIDs) by coupling them to a superconducting resonator. In this proposal, the two logical states of a qubit are represented by the two lowest levels of a SQUID. An intermediate level of each SQUID is utilized to facilitate coherent control and manipulation of quantum states of the qubits. It is interesting to note that an $n$-qubit controlled phase gate can be achieved with $n$ SQUIDs by successively applying a $\pi ∕2$ Jaynes-Cummings pulse to each of the $n-1$ control SQUIDs before and after a $\pi$ Jaynes-Cummings pulse on the target SQUID.

A density matrix approach is developed for the control of a mixed-state quantum system using a time-dependent external field such as a train of pulses. This leads to the definition of a target density matrix constructed in a reduced Hilbert space as a specific combination of the eigenvectors of a given observable through weighting factors related to the initial statistics of the system. A train of pulses is considered as a possible strategy to reach this target. An illustration is given by considering the laser control of molecular alignment and orientation in thermal equilibrium.

The double processes of He in electron-impact ionization, single ionization with simultaneous excitation and double ionization, have been studied at large momentum transfer using an energy- and momentum-dispersive binary $(e,2e)$ spectrometer. The experiment has been performed at an impact energy of $2080\mathrm{eV}$ in the symmetric noncoplanar geometry. In this way we have achieved a large momentum transfer of $9\mathrm{a.u.}$, a value that has never been realized so far for the study on double ionization. The measured $(e,2e)$ and $(e,3-1e)$ cross sections for transitions to the $n=2$ excited state of ${\mathrm{He}}^{+}$ and to doubly ionized ${\mathrm{He}}^{2+}$ are presented as normalized intensities relative to that to the $n=1$ ground state of ${\mathrm{He}}^{+}$. The results are compared with first-order plane-wave impulse approximation (PWIA) calculations using various He ground-state wave functions. It is shown that shapes of the momentum-dependent $(e,2e)$ and $(e,3-1e)$ cross sections are well reproduced by the PWIA calculations only when highly correlated wave functions are employed. However, noticeable discrepancies between experiment and theory remain in magnitude for both the double processes, suggesting the importance of higher-order effects under the experimental conditions examined as well as of acquiring more complete knowledge of electron correlation in the target.

State-specific dissociation dynamics for excited fragments of gaseous ${\mathrm{SiCl}}_4$ following Cl $2p$ and Si $2p$ core-level excitations were characterized by the dispersed UV/optical fluorescence spectroscopy. The core-to-Rydberg excitations at both Si $2p$ and Cl $2p$ edges lead to a noteworthy production of excited atomic fragments, neutral and ionic $({\mathrm{Si}}^{*},{\mathrm{Si}}^{+*})$. In particular, the excited neutral atomic fragments ${\mathrm{Si}}^{*}$ are significantly reinforced. The core-to-valence excitation at the Si $2p$ edge generates an enhancement of excited molecular-ion ${\mathrm{SiCl}}_4^{+}$. The experimental results provide deeper insight into the dissociation dynamics for excited neutral fragments of molecules via core-level excitation.

Single, double, triple, and quadruple ionization cross sections of small cationic carbon clusters $\mathrm{C}_n{}^{+}$ colliding with helium atoms at a fixed velocity (2.6 atomic units) have been measured. The size ranges from $n=1$ to $n=10$ for single to triple ionization, from $n=5$ to $n=10$ for the quadruple ionization. The dependence of the cross sections with the cluster size is found to be well reproduced by predictions of the independent atom and electron (IAE) collision model. This extends the applicability of this simple model to higher $n$ values and to a higher ionization degree than previously done [M. Chabot et al., Eur. Phys. J. D 14, 5 (2001)]. The branching ratios of multiply charged $\mathrm{C}_n{}^{q+}$ clusters remaining intact over a $100\mathrm{ns}$ time window have been measured ($n=3–10$, $q=2–3$). Branching ratios of nonfragmented doubly charged clusters have been interpreted on the basis of calculated internal energies of $\mathrm{C}_n{}^{2+}$ due to single ionization of $\mathrm{C}_n{}^{+}$ clusters using the IAE model. This allowed estimates of the minimum energies required to fragment these $\mathrm{C}_n{}^{2+}$ species to be derived.

Cross sections for single ionization and dissociative ionization of molecular targets under the impact of atomic anions were measured. Three systems were investigated, a ${\mathrm{H}}_2$ target with ${\mathrm{C}}^{-}$ and ${\mathrm{O}}^{-}$ projectiles, and a ${\mathrm{N}}_2$ target with ${\mathrm{O}}^{-}$ projectiles. The velocity range was 1.07–2.14 a.u. Recoil ions originated from the target (${\mathrm{H}}_2^{+},{\mathrm{H}}^{+},{\mathrm{N}}_2^{+},{\mathrm{N}}^{+}$, and ${\mathrm{N}}^{2+}$) were measured in coincidence with projectiles in several final charge states ($q=-1$, 0, $+1$, and $+2$). These states, negative, neutral, and positive, respectively, correspond to direct, single, and multiple electron loss channels. Target ionization is mostly due to the projectile single electron loss and direct processes, while target fragmentation is dominated by the projectile double electron loss. These results point to both target ionization and projectile direct or single electron loss processes being dominated by large impact parameters, while fragmentation and multiple electron loss are associated to small impact parameters.

We derive an exact analytic expression for the boson-diboson elastic scattering phase shift in the shape-independent model for positive two-body scattering lengths when the total energy vanishes. A three-body hard-core potential depending upon a hyperradial cutoff parameter $R_0$ is introduced to obtain a finite result. The exact result is compared with adiabatic hyperspherical calculations of the phase shift, and a similar functional dependence on the cutoff parameter is found. The cutoff parameter plays the role of a renormalization constant in that it renormalizes the wave function at vanishing hyperradius.

Rigorous and complete definitions of two partitions and one expansion for the kinetic energy of a general $N$-particle classical system are given. Our recent work, which also provides examples of applications to the molecular dynamics of nanoaggregates, based on computer programs formulated on the basis of the theory presented here, is extended to cover arbitrary physical space dimensions. The partitions and the expansion are in terms of quantities conceived to be instantaneous phase-space invariants—a far-reaching generalization of integrals of the motion. These quantities are introduced setting out as starting points the position matrix $Z$ of the system and the time derivative of $Z$. In the simplest case, the matrix $Z$ contains the mass-scaled Cartesian coordinates of the $N$ particles. From the position matrix, the kinematic rotations naturally arise through orthogonal transformations, as a concept “dual” to the ordinary physical rotations. The physical meaning of each partition (expansion) term is clearly described and emphasized, and formulas for the various quantities are provided as well as inequalities among them. Proofs are presented making extensive use of the singular value decomposition (SVD) of matrices and of the signed SVD, an extended version overcoming possible singularities for particular values of $N$.

A technique for creation of well-defined preselected coherent superpositions of multiple quantum states is proposed. It is based on an extension of the technique of stimulated Raman adiabatic passage (STIRAP) to degenerate levels. As an example, the nine-state system composed of the magnetic sublevels of three levels with angular momenta $J_g=0$, $J_e=1$, and $J_f=2$ is studied in detail. Starting from the $\mid J_g=0,M_g=0⟩$ state, STIRAP can create an arbitrary preselected coherent superposition between the five $M_f$ sublevels $(M_f=-2,-1,0,+1,+2)$ of the $J_f=2$ level with 100% efficiency in the adiabatic limit. The populations and the phases of the $M_f$ states in this superposition are determined entirely by the polarizations of the two laser fields. It is shown that this technique allows one to create any superposition of the five $M_f$ states, that is, to reach any point in the Hilbert space of the $J_f=2$ manifold, and the corresponding recipes for choosing the laser polarizations are presented.