For a system of N bosons in a two-dimensional harmonic trap with frequency $\omega ,$ interacting via forces $V\ll ħ\omega ,$ we develop a method to find the ground states of rotating Bose condensate as a function of two quantum numbers, the total angular momentum and the angular momentum of internal excitations (generalized yrast states). The energies of these condensed vortex states are expressed through the single two-body matrix element of interaction, $V.\mathrm{}$ A broad universality class of predominantly repulsive interactions for which these results hold is described by a simple integral condition on $V.\mathrm{}$ It includes Gaussian, $\delta$ function, and log-Coulomb forces.

A femtosecond double-pulse experiment shows that molecular reorientation during multiple ionization is a very fast process for light molecules such as ${\mathrm{O}}_2$ or ${\mathrm{N}}_2\mathrm{O}$ using 60-fs laser pulses and variable time delays between ±1 ps in the ${10}^{15}$ $\mathrm{W}/{\mathrm{cm}}^2$ intensity range. A unified two-dimensional model of molecular multiple ionization allows one to get the multicharged fragment trajectories and consequently discuss the speed of alignment of a molecule. The numerical results confirm that the molecular reorientation process is faster when the laser intensity increases, in good agreement with the experimental data.

We consider a scattering process inside a dispersive and absorptive medium, and derive an analytical expression for the scattering-time parameter that characterizes the duration of this process. We consider a microwave wave packet that scatters from a dielectric inhomogeneity inside an otherwise homogeneous waveguide. The waveguide is filled with a dielectric medium with a finite inhomogeneity region in the direction of the wave-packet propagation. The permittivity of the entire medium is described by a complex function of the frequency. Hence both absorption and dispersion affect the propagation of the wave packet. We define the scattering-time parameter to be the difference in the “average arrival time” between the free and actual propagation. We show that this time difference (in the limit of a narrow-band wave packet) is given by a linear combination of the real and imaginary parts of the “complex tunneling time.” In the special case where there is no dissipation or attenuation outside the scatterer, we recover the well-known result that the scattering-time parameter is identical to the real part of the complex tunneling time. The contribution of the imaginary part of the complex tunneling time to the scattering-time parameter can, therefore, be attributed to absorption and attenuation outside the scatterer. We further show that the real and imaginary-time parameters satisfy dispersion relations. Causality in this process is briefly discussed.

We introduce a general wave-packet isotope-separation scheme exploiting the optical Ramsey method. Optically excited molecular wave packets in different isotopes develop a well-defined phase difference after just a few vibrational periods. Phase-locked pairs of optical pulses are able to selectively pump one isotope back down to the ground state and enhance the excited-state population of the other isotope. The method is illustrated by simulating wave-packet isotope separation of a mixture of ${}^{79}{\mathrm{Br}}_2,$ ${}^{81}{\mathrm{Br}}_2,$ and ${}^{79}{\mathrm{Br}}^{81}\mathrm{Br}.$ We also exploit phase-locked pairs of optical pulses to reduce the time required for the spatial separation of wave packets.

The photoionization cross section (PICS) of Be from the ground state is studied with the saddle-point complex-rotation method for photon energies from 25 to 122 eV. A full-core plus correlation wave function is used for the ground state. For the resonances in the continuum, the energy and width for the singly core-excited Be-like ${1s2s}^{2}2p{}^1{P}^o,$ ${1s2p}^3{}^1{P}^o,$ and ${1s2s}^{2}3p{}^1{P}^o$ are calculated to high precision. The PICS are studied with a single open-channel approximation as well as fully coupled open channels. The Auger decay branching ratios of these states are studied to check the spin-alignment theory recently proposed by Chung. These results are compared with the existing theoretical and experimental data in the literature. For beryllium, our energy and width of ${1s2s}^{2}2p$ are 115.513 eV and 36.6 meV and those of ${1s2s}^{2}3p$ are 121.420 eV and 50.4 meV, which agree with the experiment of Caldwell et al., [Phys. Rev. A 51, 542 (1990)].

The different aspects of single ionization of helium in relativistic collisions with highly charged ions are studied within the framework of first-order perturbation theory in the projectile-target interaction. Results of our calculations are compared with experimental data for $1\mathrm{GeV}/n$ ${\mathrm{U}}^{92+}$ projectiles. The signatures of relativistic effects in ionization of light targets in collisions at moderate values of the Lorentz factor, $\gamma \sim 2,$ are discussed.

In this paper, we give a theoretical description of resonant coupling between two collective excitations of a Bose-condensed gas on, or close to, a second-harmonic resonance. Using analytic expressions for the quasiparticle wave functions, we show that the coupling between quadrupole modes is strong, leading to a coupling time of a few milliseconds (for a TOP trap with radial frequency $\sim 100\hspace{0.5em}\mathrm{Hz}$ and $\sim {10}^4$ atoms). Using the hydrodynamic approximation, we derive an analytic expression for the coupling matrix element. These can be used with an effective Hamiltonian (that we also derive) to describe the dynamics of the coupling process and the associated squeezing effects.

We have analyzed the experimental method used by Şimşek [Phys. Rev. A 62, 052517 (2000)] for determination of the L-shell Coster-Kronig yield $f_{23}$ in Dy, W, and Bi. The $f_{23}$ yield for the target element was deduced from the measured intensity of the $L\alpha$ x rays, produced due to ionization of the $L_2$ and $L_3$ subshells of the target element by the Kp $(p=\alpha ,\beta )$ x rays of an exciter ${(E}_{L_3}<E_{K\alpha }<E_{L_2}$ and $E_{L_2}<E_{K\beta }<E_{L_1},$ $E_{L_q}$ is the $L_q$-subshell ionization threshold for the target element), by subtracting the contribution of those produced by direct ionization of the $L_3$ subshell. In view of very small magnitude of this difference and the errors associated with the measurements, we infer that the deduced $f_{23}$ value must have been associated with enormously large error as compared to the quoted one, ∼7%, thus making the measurements inconsequent.

In the preceding Comment [Phys. Rev. A 65, 036501 (2002)], Kumar et al. claim that $f_{23}$ values obtained by Şimşek [Phys. Rev. A 62, 052517 (2000)] for Dy, W, and Bi must be associated with an enormously large error. For this reason, we have rechecked all the calculations used to obtain the $f_{23}$ yield. As a result, we have found out that the error analysis was inaccurate as claimed by the writers of the Comment, but there is no typographical error in the Eq. (4) of our paper contrary to the claim of Kumar et al. In addition, the method of using equivalent Al target to estimate the additional excitation by 59.5-keV photons scattered from primary target is accurate.

Coulomb fragmentation processes in collisions of ${\mathrm{Kr}}^{8+}$ ions with nitrogen molecules were studied at projectile energies between 19 and 171 eV/u. At low impact energies $(\lesssim 50\hspace{0.5em}\mathrm{eV}/\mathrm{u})$ and small impact parameters, the electron distribution of the fragmenting molecular ${\mathrm{N}}_2^{q+}$ ion becomes strongly polarized. This is due to the presence of the slow highly charged projectile during the fragmentation process. Microscopic calculations simultaneously incorporating electron transfer and molecular dissociation give insight into the dynamics of this newly found polarization effect.

We use a generalized Gross-Pitaevskii equation for the condensate and a semiclassical kinetic equation for the noncondensate atoms to discuss the scissors mode in a trapped Bose-condensed gas at finite temperatures. Both equations include the effect of collisions between the condensate and noncondensate atoms. We solve the coupled moment equations describing oscillations of the quadrupole moments of the condensate and noncondensate components to find the collective-mode frequencies and collisional damping rates as a function of temperature. Our calculations extend those of Guéry-Odelin and Stringari at $T=0\mathrm{}$ and in the normal phase. They complement the numerical results of Jackson and Zaremba, although Landau damping is left out of our approach. Our results are also used to calculate the quadrupole response function, which is related to the moment of inertia. It is shown explicitly that the moment of inertia of a trapped Bose gas at finite temperatures involves a sum of an irrotational component from the condensate and a rotational component from the thermal-cloud atoms.

Vector momenta of electrons and ions have been measured for strong-field (25 fs, 0.25 to 1.0 ${\mathrm{P}\mathrm{W}/\mathrm{c}\mathrm{m}}^2$) double ionization of Ar using a “reaction microscope.” Correlated two-electron momentum distributions along the field direction ${(P}_{1\parallel }{,P}_{2\parallel })$ are explored at different transverse momenta $P_{1\perp }$ of one of the electrons. Whereas a distinct ${(P}_{1\parallel }{,P}_{2\parallel })$ correlation, strongly varying with $P_{1\perp }$ is observed for nonsequential double ionization at small light intensity, only a weak, but still significant correlation is found at large intensity where sequential ionization dominates.

Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via one- and two-bit gate operations. How this works can be understood by comparing the system with a three-level atom exhibiting a macroscopic dark period. In addition, a dynamical explanation is given for a scheme based on atoms inside an optical cavity in the strong-coupling regime and we show how spontaneous emission by the atoms can be highly suppressed.

Equilibrium geometries and electronic-structure properties of ${\mathrm{Na}}_n\mathrm{Li}$ and ${\mathrm{Li}}_n\mathrm{Na}$ $(n=1\mathrm{}–12)$ clusters are obtained using ab initio molecular-dynamics method with the generalized gradient approximation for the exchange-correlation potential. The resulting geometries show that Li atoms become trapped inside the Na cage, while Na prefers to be on the periphery of Li clusters. The comparison of total binding energies indicates a high degree of stability for clusters with eight atoms. We also report polarizabilities for both series of ${\mathrm{Na}}_n\mathrm{Li}$ and ${\mathrm{Li}}_n\mathrm{Na}$ clusters. Polarizabilities are calculated by a finite field method. Our calculations demonstrate that Li impurity reduces polarizabilities of ${\mathrm{Na}}_n$ clusters while the doping of Na in ${\mathrm{Li}}_n$ clusters increases the polarizabilities.

We study the long-time dynamics of two entangled ions coupled by a single vibrational mode and two lasers with different frequencies as proposed by Mølmer and Sørensen [Phys. Rev. Lett. 82, 1835 (1999)]. It is shown that the time development involves collapses and revivals well known from the dynamics of a single atom in a cavity or in a trap. The revival time is found to be insensitive to the details of the initial collective vibrational state. Therefore, revival and collapse phenomena are obtained for coherent, thermal as well as other vibrational states.

Dissipative effects on the nonadiabatic transition for the two- and three-level systems are studied. When the system is affected by a strong dissipation through the diabatic states, the exact transition probability is enumerated making use of the effective master equation. In the two-level system, we consider the case where the external field is swept from not only a negative large value but also from the resonant field, and the exact transition probabilities in these cases are derived. The transition probabilities are derived for the three-level system where the three diabatic states form only one avoided-level crossing point. These probabilities are compared with that in the pure quantum case obtained by Carroll and Hioe.

We reconsider the relativistic scattering of electrons by an atom, being approximated by a static potential, in an extremely powerful electromagnetic plane wave of frequency $\omega$ and linear polarization $\varepsilon .$ Since to a first order of approximation spin effects can be neglected, we first describe the scattered electron by the Gordon solution of the Klein-Gordon equation. Then we investigate the same scattering process by including the spin effects, using for the electron the Volkov solution of the Dirac equation. For sufficiently energetic electrons, the first-order Born approximation can be employed to represent the corresponding scattering matrix element. We compare the results of the differential cross sections of induced and inverse bremsstrahlung, evaluated from both approximations, for various parameter values and angular configurations and we find that in most cases the spin effects are marginal, even at very high laser power. On the other hand, we recover the various asymmetries in the angular distributions of the scattered electrons and their respective energies due to the laser-induced drift motion of the electrons in the direction of propagation of the radiation field, thus confirming the findings of our previous work [Phys. Rev. A 59, 2105 (1999); Laser Physics 10, 163 (2000)].

We describe how closed-orbit theory can be applied to the photoabsorption dynamics of asymmetric doubly excited atoms, and demonstrate the method using He and Yb. Closed classical orbits are found to exist and are explained in terms of electron correlation and core scattering. In He, where long range electron correlation alone influences the orbits, the results give insight into the role of electron correlation on closed classical orbits.

We report the demonstration of a sensitive absolute-gravity gradiometer based on light-pulse atom-interference techniques. The gradiometer consists of two absolute accelerometers operated in a differential mode. We report a differential acceleration sensitivity of $4\times {10}^{-9}g/{\mathrm{Hz}}^{1/2}$ and an inferred differential acceleration accuracy of less than ${10}^{-9}g.\mathrm{}$ This corresponds to a gravity-gradient sensitivity of $4E/{\mathrm{Hz}}^{1/2}$ ${(1E=10\mathrm{}}^{-9}{\mathrm{s}}^{\mathrm{-}2})$ and an accuracy of better than $1E$ for a 10-m separation between accelerometers. We demonstrate that the instrument can be used to detect nearby masses in a vibrationally noisy environment and characterize instrument sensitivity to spurious acceleration and rotation noise.

The mean ground-state occupation number and condensate fluctuations of interacting and noninteracting Bose gases confined in a harmonic trap are considered by using a canonical ensemble approach. To obtain the mean ground-state occupation number and the condensate fluctuations, an analytical description for the probability distribution function of the condensate is provided directly starting from the analysis of the partition function of the system. For the ideal Bose gas, the probability distribution function is found to be a Gaussian one for the case of the harmonic trap. For the interacting Bose gas, using a unified approach the condensate fluctuations are calculated based on the lowest-order perturbation method and on Bogoliubov theory. It is found that the condensate fluctuations based on the lowest-order perturbation theory follow the law $〈{\delta }^2{N}_0〉\sim N,$ while the fluctuations based on Bogoliubov theory behave as $N^{4/3}.$