We present a quantum-mechanical study of multiple-electron transfer processes in collisions between a highly charged ion and an atom, taking ${\mathrm{Ar}}^{8+}-\mathrm{Ar}$ collisions as an example. We employ time-dependent mean-field theories for this purpose, with different levels of approximation for the exchange effect. The time-dependent single-electron equation is solved directly by a discretization of the three-dimensional Cartesian coordinate into a uniform mesh. Calculations for various physical situations specified by the incident energy and the impact parameter are presented to elucidate the reaction mechanisms. They provide us with intuitive pictures of the electronic dynamics as well as a microscopic understanding of the reaction mechanisms. We also compare results with different treatments of the exchange effect to learn the sensitivity of our results on the possible uncertainty of the theories.

We study the explosion dynamics of rare-gas clusters $({\mathrm{Ar}}_{55},\hspace{0.5em}{\mathrm{Ar}}_{147},\hspace{0.5em}{\mathrm{Xe}}_{55},$ and ${\mathrm{Xe}}_{147})$ in an intense, femtosecond laser pulse via Monte Carlo classical particle-dynamics simulations. Our method includes tunnel and impact ionization as well as ion-electron recombination, and allows us to follow the motion of both ions and free electrons during laser-cluster interaction. Our simulation results show that ionization proceeds mainly through tunnel ionization by the combined fields from ions, electrons, and laser while the contribution of electron-impact ionization is secondary. The ions are ejected in a stepwise manner from outer shells and accelerated mainly through their mutual Coulomb repulsion. Taking a spatial laser intensity profile into account, we show that the Coulomb explosion scenario leads to the same charge dependence of ion energy, i.e., quadratic for lower charge states and linear for higher ones, as that observed in experiments with larger clusters. This indicates that Coulomb explosion may be a dominant cluster explosion mechanism even in the case of large clusters. We also find that the ion energy is higher in the direction parallel to laser polarization than in the direction perpendicular to it. When ions are emitted along the direction of laser polarization, their charge changes in phase with the laser field, and this leads to an efficient acceleration.

We generalize the kinetic theory of the magneto-optical trap (MOT) to investigate the finite-linewidth effect of cooling lasers. Our results confirm that the polarization-gradient cooling mechanism in the low-velocity domain of the MOT originates from a two-photon process and that the Doppler cooling mechanism in the high-velocity domain stems from a one-photon process. We find that, when we increase the linewidth of the cooling lasers, the cooling temperature increases monotonically and the atomic cloud radius initially decreases quadratically and later increases.

We extend earlier models of the growth of a Bose-Einstein condensate c.w. [Gardiner et al., Phys. Rev. Lett. 79, 1793 (1997); e-print cond-mat/9801027; Phys. Rev. Lett. 81, 5266 (1998)] to include the full dynamical effects of the thermal cloud by numerically solving a modified quantum Boltzmann equation. We determine the regime in which the assumptions of the simple model of Gardiner et al. [Phys. Rev. Lett. 81, 5266 (1998)] are a reasonable approximation, and compare our results with those that were earlier compared with experimental data. We find good agreement with our earlier modeling, except at higher condensate fractions, for which a significant speedup is found. We also investigate the effect of the final temperature on condensate growth, and find that this has a surprisingly small effect. The particular discrepancy between theory and experiment found in our earlier model remains, since the speedup found in these computations does not occur in the parameter regime specified in the experiment.

We study the dynamics of condensate formation in an inhomogeneous trapped Bose gas with a positive interatomic scattering length. We take into account both the nonequilibrium kinetics of the thermal cloud and the Hartree-Fock mean-field effects in the condensed and the noncondensed parts of the gas. Our growth equations are solved numerically by assuming that the thermal component behaves ergodically and that the condensate, treated within the Thomas-Fermi approximation, grows adiabatically. Our simulations are in good qualitative agreement with experiment, however important discrepancies concerning details of the growth behavior remain.

All stationary solutions to the one-dimensional nonlinear Schrödinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or gray density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schrödinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.

All stationary solutions to the one-dimensional nonlinear Schrödinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper treated the repulsive case. Our solutions take the form of bounded, quantized, stationary trains of bright solitons. Among them are two uniquely nonlinear classes of nodeless solutions, whose properties and physical meaning are discussed in detail. The full set of symmetry-breaking stationary states are described by the $C_n$ character tables from the theory of point groups. We make experimental predictions for the Bose-Einstein condensate, and show that, though these are the analog of some of the simplest problems in linear quantum mechanics, nonlinearity introduces surprising phenomena.

We use a Thomas-Fermi approximation that includes the leading kinetic terms due to fluid motion to estimate analytically the critical velocity for the formation of vortex pairs in harmonically trapped Bose-Einstein condensates. We find rough agreement between this analytical estimate and recent experiments on trapped sodium gas condensates.

The behavior of collective oscillations of a trapped boson-fermion mixed condensate is studied in the sum-rule approach. Mixing angle of bosonic and fermionic multipole operators is introduced so that the mixing characters of the low-lying collective modes are studied as functions of the boson-fermion interaction strength. For an attractive boson-fermion interaction, the low-lying monopole mode becomes a coherent oscillation of bosons and fermions and shows a rapid decrease in the excitation energy towards the instability point of the ground state. In contrast, the low-lying quadrupole mode keeps a bosonic character over a wide range of the interaction strengths. For the dipole mode the boson-fermion in-phase oscillation remains to be the eigenmode under the external oscillator potential. For weak repulsive values of the boson-fermion interaction strengths we found that an average energy of the out-of-phase dipole mode stays lower than the in-phase oscillation. Physical origin of the behavior of the multipole modes against boson-fermion interaction strength is discussed in some detail.

Grazing collisions with background gas are the major cause of trap loss and trap heating in atom traps. To first order, these effects do not depend on the trap density. In collisionally opaque trapped atom clouds, however, scattered atoms with an energy E larger than the effective trap depth ${\mathcal{E}}_{\mathrm{eff}},$ which are destined to escape from the atom cloud, will have a finite probability for a secondary collision. This results in a contribution to the heating rate that depends on the column density $〈\mathrm{nl}〉$ of the trapped atoms, i.e., the product of density and characteristic size of the trap. For alkali-metal atom traps, secondary collisions are quite important due to the strong long-range interaction with like atoms. We derive a simple analytical expression for the secondary heating rate, showing a dependency proportional to $〈\mathrm{nl}〉\hspace{0.5em}{\mathcal{E}}_{\mathrm{eff}}^{1/2}.$ When extrapolating to a vanishing column density, only primary collisions with the background gas will contribute to the heating rate. This contribution is rather small, due to the weak long-range interaction of the usual background gas species in an ultrahigh-vacuum system—He, Ne, or Ar—with the trapped alkali-metal atoms. We conclude that the transition between trap-loss collisions and heating collisions is determined by a cutoff energy $200\hspace{0.5em}\mu \mathrm{K}<~{\mathcal{E}}_{\mathrm{eff}}<~400\hspace{0.5em}\mu \mathrm{K},$ much smaller than the actual trap depth $\mathcal{E}$ in most magnetic traps. Atoms with an energy ${\mathcal{E}}_{\mathrm{eff}}<E<\mathrm{}\mathcal{E}$ escape into the Oort cloud: a mechanism of effective traploss in the microkelvin range of trap temperatures. We present results of secondary heating rates for the alkali-metal atoms Li through Cs as a function of the effective trap depth, the column density of the trap, and the species in the background gas. The predictions of our model are in good agreement with the experimental data of Myatt for heating rates in high-density ${}^{87}\mathrm{Rb}$-atom magnetic traps at JILA, including the effect of the rf shield and the composition of the background gas. It is shown that collisions with atoms from the Oort cloud also contribute to the heating rate. For ${}^{85}\mathrm{Rb}$ the calculated heating rate is below the experimentally observed value at JILA, supporting the idea that inelastic collisions in the trap are the major source of heating.

We propose an alternative formulation for atomic side mode dynamics from superradiant light scattering of trapped atoms. A detailed analysis of the recently observed superradiant light scattering from trapped Bose gases [S. Inouye et al., Science 285, 571 (1999)] is presented. We find that scattered light intensity can exhibit both oscillatory and exponential growth behaviors depending on densities, pump pulse characteristics, temperatures, and geometric shapes of trapped gas samples. The total photon scattering rate as well as the accompanying matter wave amplification depend explicitly on atom number fluctuations in the condensate. Our formulation allows for natural and transparent interpretations of subtle features in the experimental data, and provides numerical simulations in good agreement with most important aspects of the experimental observations.

We study coherent photoassociation, phenomena analogous to coherent optical transients in few-level systems, which may take place in photoassociation of an atomic Bose-Einstein condensate but not in a nondegenerate gas. We develop a second-quantized Hamiltonian to describe photoassociation, and apply the Hamiltonian both in the momentum representation and in the position representation (field theory). The solution of the two-mode problem, including only one mode each for the atomic and molecular condensates, displays analogs of Rabi oscillations and rapid adiabatic passage. A classical version of the field theory for atoms and molecules is used to demonstrate that, in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of density fluctuations. Experimental complications, including spontaneous emission and unwanted “rogue” photodissociation from a photoassociated molecule, are analyzed. A two-color Raman scheme is studied as a method to set up an effective two-mode scheme with reduced spontaneous-emission losses. We discuss photoassociation rates and photoassociation Rabi frequencies for high-lying vibrational states in alkali dimers both on the basis of molecular-structure calculations, and by comparing with an experiment [Wynar et al., Science 287, 1016 (2000)].

We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of a vortex line as a function of the local gradient of the trap potential, the line curvature, and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for two-dimensional (2D) and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shaped condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shaped condensate than in a disk-shaped one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.

In this paper, we present a very simple approach to input-output relations in optical cavities, limiting ourselves to one- and two-photon states of the field. After field quantization, we derive the nonunitary transformation between inside and output annihilation and creation operators. Then we express the most general two-photon state generated by inside creation operators, through base states generated by output creation operators. After renormalization of coefficients of the inside two-photon state, we calculate the outside photon-number probability distribution in a general case; then we treat with some detail the single-mode and symmetrical cavity case. We found that the statistics of emitted photons may exhibit either quantum or classical behavior, depending both on source properties and on cavity characteristics.

The problem of the quantum-limited or intrinsic linewidth of a good-cavity laser is revisited. Starting from the Scully-Lamb master equation, we present a fully analytical treatment to determine the correlation function and the spectrum of the cavity field at steady state. For this purpose, we develop an analytical approximation method that implicitly incorporates the microscopic fluctuations of both the phase and intensity of the field, and, in addition, takes full account of the saturation of the nonlinear gain. Our main result is a simple formula for the quantum-limited linewidth that is valid from near to far above threshold and also includes the presence of thermal photons. Close to the threshold, the linewidth is twice as large as predicted by the standard phase-diffusion treatment neglecting intensity fluctuations, and even 50% above threshold the increase is still considerable. In general, quantum fluctuations of the intensity are present and continue to influence the linewidth as long as the photon-number distribution is not strictly Poissonian. This inherent relationship is displayed by a formula relating the linewidth and the Mandel Q parameter. More than 100% above treshold the linewidth is found to be smaller than predicted by the standard treatment, since the simple phase-diffusion model increasingly overestimates the rate of phase fluctuations by neglecting gain saturation. In the limit of a very large mean photon number the expected perfectly coherent classical field is obtained.

We study the entrainment of coupled solid-state lasers by an external injected field. We show that the total output intensity exhibits unexpected nonmonotonic behavior as a function of the injected field and find the critical amplitude marking the transition to the low-intensity branch. In addition, we also show that substantial partial entrainment can be achieved for injected fields much weaker than that required for full entrainment.

We study high-order harmonic generation resulting from a two-color scheme involving a circularly polarized high-frequency field and a weak linearly polarized low-frequency field. Although the low-frequency field is not intense enough to ionize the atom, it can accelerate the electron more efficiently. As a result, the application of this field can generate harmonics with much higher energy compared to the monochromatic case. For a hydrogenlike atom irradiated by a Nd:YAG (yttrium aluminum garnet) laser of intensity $1.9\times {10}^{14}\hspace{0.5em}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ and a ${\mathrm{CO}}_2$ laser of intensity $7.6\times {10}^{12}\hspace{0.5em}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ the cutoff occurs at the 241st harmonic-order corresponding to a photon energy of 281 eV, which is three times higher than that of the monochromatic case.

The fluorescence of a single dipole excited by an intense light pulse can lead to the generation of another light pulse containing a single photon. The influence of the duration and energy of the excitation pulse on the number of photons in the fluorescence pulse is studied. The case of a two-level dipole with strongly damped coherences is considered. The presence of a metastable state leading to shelving is also investigated.

Simple schemes to realize quantum teleportation and dense coding for continuous variables are proposed, in that entangled EPR beams are produced by combining two bright amplitude squeezed beams. The measurement of the “Bell state” is accomplished by means of direct detection for photocurrents and two rf power splitters. As a local oscillator and balanced homodyne detector are not needed, the proposed system is easy to realize experimentally.

The calculations of Compton profiles and various $〈p^n〉$-expectation values are carried out for a few closed-shell atomic systems within Perdew-Burke-Ernzerhof (PBE), Perdew-Wang 1991 (PW91) and Becke-Lee-Yang-Parr (BLYP) generalized-gradient approximations. The calculated Compton profiles and the moments are compared with their local-density approximation (LDA) and more accurate available theoretical or experimental counterparts in order to investigate the supremacy of generalized gradient approximation (GGA) over LDA in predicting the momentum-space properties. The results show that GGA improves the Compton profiles marginally. The PBE and PW91 values of Compton profiles are practically identical and are slightly better than BLYP. Further comparison of GGA and LDA results with those calculated within self-interaction corrected LDA (SICLDA) formalism demonstrates the importance of proper description of the valence region in the study of Compton profiles. GGA values of the moments of electron momentum density are found to be, in general, more accurate than their LDA counterparts.