The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation $J_z.$ Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase-space projection associated with the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase-space borderline produces a maximum rate of entanglement. The consequence of this fact for initial conditions centered at periodic orbits in regular regions is a clear periodic recoherence. For chaotic situations the same phenomenon (proximity of the atomic phase-space borderline) is, in general, responsible for oscillations in the entanglement properties.

The apparent superluminal propagation of electromagnetic signals seen in recent experiments is shown to be the result of simple and robust properties of relativistic field equations. Although the wave front of a signal passing through a classically forbidden region can never move faster than light, an attenuated replica of the signal is reproduced “instantaneously” on the other side of the barrier. The reconstructed signal, causally connected to the forerunner rather than the bulk of the input signal, appears to move through the barrier faster than light.

For the periodic orbit quantization of a system of particles confined in a two-dimensional disk billiard, the proliferation of multiparticle periodic orbits with length precludes standard length truncation of the trace formula and alternative truncation schemes are necessary. An amplitude ordering of the single-particle periodic orbits reveals a quantum-classical correspondence for the angular momentum of a particle in the disk which is useful for the quantization of all the low energy states of the multiparticle problem. We explicitly show that a simple amplitude truncation of the trace formula better approximates the semiclassical density of states and in particular resolves closely spaced levels that are otherwise unresolved using the standard approach.

In non-Hermitian quantum mechanics the density probability is a complex function $\rho .$ Here we show that when ${\Psi }_{\mathrm{left}}\ne {\Psi }_{\mathrm{right}}$ the spatial phase of $\sqrt{\rho }=({\Psi }_{\mathrm{left}}{\Psi }_{\mathrm{right}}{)}^{1/2}$ and not of ${\Psi }_{\mathrm{right}}$ or ${\Psi }_{\mathrm{left}}$ provides the phase of the measurable complex transition probability amplitude in scattering experiments, $\arg \{t\left(E\right)\mathrm{}\}.$ Using the non-Hermitian representation of quantum mechanics we derived a formula for the resonant tunneling probability amplitude of an electron which is scattered from a general potential. We illustrate the applicability of our formula to a one-dimensional double-barrier potential problem, although the derivation of this formula holds for many-body problems with multidimensional potentials.

Photoionization in the regime of the barrier suppression is investigated within a three-dimensional, fully quantum-mechanical, time-dependent model. It is shown how a structure is formed in the envelope of the above threshold ionization spectra, for energies smaller than the ponderomotive potential. A correspondence between this structure and the shape of the initial-state decay curve, as well as the radial distribution of the electron wave packet, is proven.

The influence of a second active electron is studied in the high-order regime of nonrelativistic harmonic generation in model helium. The major deviation of the harmonic yield due to the second active electron is small and associated mostly with the descreening of the helium nucleus while only an even smaller part remains as a consequence of the electron-electron repulsion.

We report experimental observations of second-harmonic generation (SHG) from single micrometer-size polystyrene, silica, and polymethylmethacrylate spheres on flat substrates by SHG microscopy. At low input light intensities the SH signals depend quadratically on the intensity of the excitation beam, but at larger input intensities some of the SH signals increase exponentially with increasing input intensity. This exponential enhancement depends on particle size and sphere composition. We describe the experiments, and parametrize the observations.

Near-threshold cross sections for elastic scattering and for excitation of the 100 symmetric stretch vibrational mode of ${\mathrm{CO}}_2$ have been calculated using the energy-modified adiabatic phase matrix method. These calculations are based on fixed-nuclei R matrices at several internuclear geometries that incorporate short-range exchange and correlation effects. The representation of the polarization response of the target inside the R-matrix box is improved using an alternative numerical technique, the $\Delta R$ procedure. These calculations over a range of internuclear distances reveal unanticipated behavior of the near-threshold scattering matrix. A fixed-nuclei virtual state occurs only in a limited range of internuclear separation, changing to a weakly bound state outside this range. Thus an energy pole of the scattering matrix remains near threshold and has a large effect on both elastic and vibrational cross sections, but cannot be simply described as a virtual state. Our quantitative results, in good agreement with experiment, indicate that the present modified adiabatic methodology is adequate to treat this complex behavior.

A Wentzel-Kramers-Brillouin (WKB) approach for calculating the lifetime of the ground state of two coupled oscillators with the most probable escape path along one of the coordinate axes is suggested. The WKB approximation of the wave function in the neighborhood of this path is obtained by scaling the corresponding variable. An analytic formula for the lifetime is derived and numerically verified. The method is applied to the Henon-Heiles potentials. It is shown that the WKB method can be, in contrast to the numerical ones, easily extended to the problems of an arbitrary number of spatial dimensions.

We examine the Casimir effect between two dispersive dissipative slabs in three dimensions. The dielectric function of the slabs is assumed to be an arbitrary complex function of frequency satisfying Kramers-Kronig relations. The Maxwell stress tensor is used to evaluate the vacuum radiation pressure of the electromagnetic field on each slab in terms of the field correlation functions. These correlations are simply related to the imaginary part of the vector potential Green function by using the fluctuation dissipation theorem and Kubo’s formula. The response function is obtained by employing the standard method for the present configuration. The formalism enables us to calculate the attractive Casimir force between a pair of dielectric slabs without resorting to the electromagnetic field quantization. Special attention is paid to the various limits of the general expression and the results are compared with previous work whenever possible. The Lorentz model of the dielectric function is also used to show the typical behavior of this force in terms of the slab thickness. We also consider the effect of finite temperature on the Casimir force between two dielectric slabs.

The general conditions for the orthogonal product states of the multistate systems to be used in quantum key distribution (QKD) are proposed, and a novel QKD scheme with orthogonal product states in the $3\times 3$ Hilbert space is presented. We show that this protocol has many distinct features such as great capacity and high efficiency. The generalization to $n\times n$ systems is also discussed and an asymptotic limit of 1/2 for the eavesdropper’s success probability is obtained.

We investigate the entanglement arising naturally in a one-dimensional Ising chain in a magnetic field in an arbitrary direction. We find that for different temperatures, different orientations of the magnetic field give maximum entanglement. In the high-temperature limit, this optimal orientation corresponds to the magnetic field being perpendicular to the Ising orientation $(z$ direction). In the low-temperature limit, we find that varying the angle of the magnetic field very slightly from the z direction leads to a rapid rise in entanglement. We also find that the orientation of the magnetic field for maximum entanglement varies with the field amplitude. Furthermore, we have derived a simple rule for the mixing of concurrences (a measure of entanglement) due to the mixing of pure states satisfying certain conditions.

The formation mechanism and structural and electronic properties of the metal-substituted fullerenes ${\mathrm{C}}_{69}M$ $(M=\mathrm{Co},$ Rh, and Ir) have been studied using the frontier orbitals and density functional theories. According to the symmetry of the ${\mathrm{C}}_{70}$ $D_{5h}$ structure, we have studied five kinds of possible substitution site for the M atom and found that it has a tendency to substitute in the site where the substituted carbon atom has the maximum contribution to the lowest unoccupied molecular orbital of ${\mathrm{C}}_{70}.$ The clusters are found to be stable in the cage structure, while the deformation of the fullerene network due to the substituted metal atom is larger than that due to a substituted boron or nitrogen atom. The electronic structure of ${\mathrm{C}}_{69}M$ can be described in terms of defect levels in the host fullerene. Deep defect states due to the metal atom appear in the carbon-derived energy gap, and high chemical reactivity is predicted for the clusters. The magnetic moment of the M atom in ${\mathrm{C}}_{69}M$ is found to be almost completely quenched due to the strong hybridization between the orbitals of the M atom and those of its neighboring carbons.

We consider electron scattering by hydrogen atoms in a linearly polarized laser field. The electrons may have sufficiently high energy in order that the scattering process can be treated in the first-order Born approximation. The scattered electrons, embedded in the laser field, are described by Gordon-Volkov waves. We assume that during the scattering, the hydrogen atoms are in an excited state (in particular, in the $2s,$ $2p,$ or $3s$ state) and that for moderate laser field intensities, it is sufficient to describe the interaction of the target atoms with the radiation field by first-order time-dependent perturbation theory. We discuss the angular dependence of the nonlinear differential scattering cross sections for low values N of emitted or absorbed laser photons, inspecting the contributions of the various electronic and atomic terms of the matrix elements. Detailed numerical results are presented for one-photon absorption at low-field intensities. We also compare our results with those obtained from the assumption of a static atomic polarizability, describing the laser dressing of the excited atomic states.

An experimental and theoretical study of electron-impact ionization of the $3p$ orbital in argon is presented. The $\mathrm{}(e,2e)\mathrm{}$ technique was used to measure the relative triple-differential cross section for this process in the coplanar asymmetric geometry. The experimental results were obtained at an incident electron energy of 113.5 eV, a scattering angle of 15°, and ejected electron energies of 10, 7.5, 5, and 2 eV. The experimental data are compared with a distorted-wave Born approximation (DWBA) calculation, and also with previous results for argon $3s$ ionization obtained under identical kinematic conditions. Discrepancies between the experimental and theoretical data are attributed to the effects of charge-cloud polarization and higher-order scattering processes, which are not incorporated in the DWBA calculation.

We have realized a scheme for continuous loading of a magnetic trap (MT). ${}^{52}\mathrm{Cr}$ atoms are continuously captured and cooled in a magneto-optical trap (MOT). Optical pumping to a metastable state decouples atoms from the cooling light. Due to their high magnetic moment $\left(6\mathrm{}\hspace{0.5em}{\mu }_B\right),$ low-field seeking metastable atoms are trapped in the magnetic quadrupole field provided by the MOT. Limited by inelastic collisions between atoms in the MOT and in the MT, we load ${10}^8$ metastable atoms at a rate of ${10}^8$ atoms/s below $100\hspace{0.5em}\mu \mathrm{K}$ into the MT. Optical repumping after the loading allows us to realize a MT of ground-state chromium atoms.

From a three-dimensional time-dependent Schrödinger equation simulation for alignment of ${\mathrm{Cl}}_2$ by short laser pulses, we show that alignment of the ground state $\left(X{}^1{\Sigma }_g^{+}\right)$ can be increased by photodissociation via a repulsive dissociative state ${(}^1{\Pi }_u).\mathrm{}$ Initially, an intense nonresonant laser pulse ($2\times {10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ 1064 nm) with linear polarization aligns the molecule in the direction of the polarization as measured by $〈{\cos }^2\theta 〉,$ which depends on the $J,$ $M_J$ initial conditions. Then, a second pulse with the same polarization is added in order to make perpendicular resonant transitions to the repulsive state $(1\mathrm{}\times {10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ 375 nm). We show as an example for $J=4\mathrm{}$ that the second pulse increases the alignment for each initial $M_J$ condition as measured by $〈{\cos }^2\theta {〉}_{{J=4,M}_J}$ and the average alignment $〈〈{\cos }^2\theta 〉{〉}_{J=4\mathrm{}}$ by reducing the proportion of the $M_J\ne 0$ states. This improvement in the alignment of the molecule increases the amplitudes of the average rotational recurrences after the laser pulse and reduces the randomness in these recurrences by removing nonaligned $M_J\ne 0$ states.

We demonstrate spatially nonuniform polarization of the fundamental transverse mode in a vertical-cavity surface-emitting laser. Using a vectorial electromagnetic model, we find orthogonal linearly polarized components in the field of a solitary mode. We give experimental evidence for our predictions by polarization-resolved near-field measurements: the fundamental transverse mode contains a four-lobed intensity distribution in one linear polarization direction that is weaker than the dominant orthogonally polarized Gaussian-shaped distribution by 35 dB in excellent agreement between experiment and model.

We present a method to protect the entanglement in a maximally entangled n-qubit state of the Greenberger-Horne-Zeilinger or “Schrödinger cat” form against decoherence, by pairing up each qubit with another one in such a way that each pair of qubits undergoes collective decoherence. Under these conditions, if t pairs experience an error, we show how one can still, in general, extract a maximally entangled state of the remaining $n-t$ pairs. Two versions of the method are considered: one of them applies when the locations of the decohered qubits are known, and it might be useful, for instance, in secret-sharing protocols. Another version, which is free from this restriction, provides only partial protection (the resulting state is, generally, not a maximally entangled state), but could nonetheless be useful for the important special case in which the source of error is spontaneous emission.