We consider the final stage of triple ionization of atoms in a strong linearly polarized laser field. We propose that for intensities below the saturation value for triple ionization the process is dominated by the simultaneous escape of three electrons from a highly excited intermediate complex. We identify within a classical model two pathways to triple ionization, one with a triangular configuration of electrons and one with a more linear one. Both are saddles in phase space. A stability analysis indicates that the triangular configuration has the larger cross sections and should be the dominant one. Trajectory simulations within the dominant symmetry subspace reproduce the experimentally observed distribution of ion momenta parallel to the polarization axis.

The distributions of the momenta of the two electrons liberated in nonsequential double ionization of neon and argon are calculated in the S-matrix formalism assuming a rescattering scenario. Two different forms for the electron-electron correlation are compared: the Coulomb repulsion in the Born approximation and a three-body contact interaction including the ion. The former favors disparate momenta of the two electrons, the latter equal momenta.

We present an effective computational method and quantum results for the three-dimensional propagation of wave packets in the hydrogen atom driven by a train of short unidirectional electric-field pulses. We studied the dynamics of wave packets that are initially in a Stark state with different parabolic quantum numbers and observed quantum localization in the high-frequency domain.

We perform detailed close-coupling calculations for the rubidium isotopes ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ to ascertain the nature of their spinor Bose-Einstein condensates. These calculations predict that the spinor condensate for the spin-1 boson ${}^{87}\mathrm{Rb}$ has a ferromagnetic nature. The spinor condensates for the spin-2 bosons ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb},$ however, are both predicted to be polar. The nature of a spin-1 condensate hinges critically on the sign of the difference between the s-wave scattering lengths for total spins 0 and 2 while the nature of a spin-2 condensate depends on the values of the differences between s-wave scattering lengths for the total spins 0, 2, and 4. These scattering lengths were extracted previously and found to have overlapping uncertainties for all three cases, thus leaving the nature of the spinor condensates ambiguous. The present study exploits a refined uncertainty analysis of the scattering lengths based on recently improved result from experimental work by Roberts et al., which permits us to extract an unambiguous result for the nature of the ground state spinor condensates.

An exactly solvable model of two-component interacting Fermi vapor in two dimensions within the Thomas-Fermi approach has been proposed. We assume a realistic off-diagonal s-wave interaction between fermions in the two hyperfine states. The interaction is taken to be given by a screened Coulomb interaction, which is both physically relevant and analytically tractable. There are two distinct limits in the case of trapped fermionic systems: When the rotating frequency is much less than the trap frequency, the Thomas-Fermi approach may be used for a reasonably large number of particles. In the case of rapidly rotating fermions, an alternative variational approach is used, where the local-density approximation is applied after projecting the system on to the lowest degenerate level. Analytic expressions for the relevant physical quantities are obtained and their significance is discussed in both these cases.

We have investigated the chaotic and frequency-locked population oscillations between two coupled Bose-Einstein condensates with time-dependent asymmetric potential and damping. Under the deterministic perturbation, there exist stable oscillations close to the separatrix solution, which are Melnikov chaotic. Numerical results reveal that, in the nondissipative regime, regular oscillations gradually tend to chaotic with the increase of the trap asymmetry, the long-term localization disappears, and short-term localization can be changed from one of the Bose-Einstein condensates to the other through the route of Rabi oscillation. But in the dissipative regime, stationary chaos disappears and transient chaos is a common phenomenon before the regular stable frequency-locked oscillations, and a proper damping can keep the localization long lived.

The emission characteristics in the fluorescence of two laser-driven dipole-dipole-interacting three-level atoms is investigated. When the light from both atoms is detected separately a correlation of the emission processes is observed in dependence of the dipole-dipole interaction. This opens the possibility to investigate the dipole-dipole interaction through the emission behavior. We present quantum Monte Carlo simulations which are in good agreement with the analytic solutions.

Since the work of Anderson on localization, interference effects for the propagation of a wave in the presence of disorder have been extensively studied, as exemplified in coherent backscattering (CBS) of light. In the multiple scattering of light by a disordered sample of thermal atoms, interference effects are usually washed out by the fast atomic motion. This is no longer true for cold atoms where CBS has recently been observed. However, the internal structure of the atoms strongly influences the interference properties. In this paper, we consider light scattering by an atomic dipole transition with arbitrary degeneracy and study its impact on coherent backscattering. We show that the interference contrast is strongly reduced. Assuming a uniform statistical distribution over internal degrees of freedom, we compute analytically the single- and double-scattering contributions to the intensity in the weak-localization regime. The so-called ladder and crossed diagrams are generalized to the case of atoms and permit to calculate enhancement factors and backscattering intensity profiles for polarized light and any closed atomic dipole transition.

The multimode emission threshold of class-$B$ ring lasers is analytically investigated taking into account the localized nature of the cavity losses and the inhomogeneous broadening of the amplifying medium. This analysis finds a relevant application to erbium-doped fiber lasers (EDFL’s). The main conclusion is that the predictions of the simplest models are deeply modified both quantitatively and qualitatively. Thus, any attempt to interpret multimode emission in EDFL’s must incorporate the two considered factors. Two main results are: (i) While in homogeneously broadened lasers instabilities are inhibited for values of the mirrors’ reflectivity $\mathcal{R}<0.54ca,$ this limitation disappears as soon as the inhomogeneous width exceeds $0.9$ times the homogeneous width; and (ii) the band of unstable modes is reduced as cavity losses increase.

We report an experimental observation of narrow and high-contrast spectra, which are induced by interacting dark resonances and have been predicted in Phys. Rev. A 60, 3225 (1999). Spectra are measured with cold ${}^{87}\mathrm{Rb}$ atoms produced by a magneto-optical trap. In this experimental system, a coupling laser and a weak probe laser form a three-level Λ-type configuration of electromagnetically induced transparency (EIT); a microwave drives a magnetic-dipole transition between the fourth level and the ground state that is coupled with the excited state by the coupling laser. The observed spectral profile of probe absorption exhibits a very sharp peak emerging inside a narrow EIT dip. Such spectral feature provides more opportunities in manipulating atomic-optical response.

Parr and Liu [Chem. Phys. Lett., 276, 164 (1997)], showed that the electron-electron repulsion functional $V_{\mathrm{ee}}\left[\rho \right]$ can be expressed in terms of its first and second functional derivatives under certain assumptions. Starting from this expansion it is shown that with the same assumptions, the density-functional exchange energy $E_x\left[\rho \right],$ correlation energy $E_c\left[\rho \right],$ and the kinetic contribution to the correlation energy $T_c\left[\rho \right],$ can each be expressed in terms of their first and second functional derivatives only. It is pointed out that some expansions of density functionals proposed in the literature are not compatible with the expressions derived.

By varying $\mathrm{}(x,y,z)\mathrm{}$ within a manifold $\mathcal{M},$ the positive (negaive)-energy eigenvectors of the $2\times 2$ Hamiltonian $H=x{\sigma }_x+y{\sigma }_y+z{\sigma }_z$ (where ${\sigma }_{x,y,z}$ are the Pauli matrices) form a U(1) fiber bundle. For certain $\mathcal{M}$ the bundle has nontrivial topology. For example, when $\mathcal{M}{=S}^2$ the associated bundle has nonzero Chern number indicating that it is topologically nontrivial at the highest level. In this paper we construct a simple $2\times 2$ Hamiltonian whose eigenvector bundle exhibits a more subtle topological nontriviality when $\mathcal{M}$ is a closed three manifold. This nontrivial topology is characterized by nonzero Chern-Simons invariant.

For the implementation of a quantum computer it is necessary to exercise complete control over the Hamiltonian of the used physical system. For nuclear magnetic resonance quantum computing the effectively acting Hamiltonian can be manipulated via pulse sequences. Here we examine a register consisting of N selectively addressable spins with pairwise coupling between each spin pair. We show that complete decoupling of the spins is possible, independent of the particular form of the spin-spin interaction. The proposed method based on orthogonal arrays is efficient in the sense that the effort regarding time and amount of pulses increases only polynomially with the size N of the register. However, the effect of external control errors in terms of inaccurate control pulses eventually limits the achievable precision.

We discuss the dissipative dynamics of vortex arrays in trapped Bose-condensed gases and discuss the lifetime of the vortices as a function of trap anisotropy and temperature. In particular, we distinguish two regimes of dissipative dynamics, depending on the relative strength of the mutual friction between the vortices and the thermal component, and the friction of the thermal particles on the trap anisotropy. We study the effects of heating of the thermal cloud by the escaping vortices on the dynamics of the system.

We investigate the effects of self-phase and cross-phase ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinearities, in the process of traveling-wave second-harmonic generation. We derive a semiclassical analytical solution for the field intensities, comparing this with the numerically obtained fully quantum solutions. We also investigate the effects of the cross-phase modulation on the quantum statistical properties of the fields. We find that, as the ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ components increase, there are qualitative changes to both the field intensities and the quantum statistics.

Measurements of the ion energies resulting from irradiation of Xe clusters with 800 nm laser pulses in the intensity range $2\times {10}^{15}–5\times {10}^{16}{\mathrm{Wcm}}^{\mathrm{-}2}$ are reported. The maximum ion energies as a function of mean cluster size and laser intensity were determined at a constant laser-pulse duration of ∼65 and 90 fs respectively—a factor of 3 shorter than previous scaling studies. Comparisons made between experimental results and numerical simulations of the laser-cluster interaction have shown the importance of considering a distribution of cluster sizes. We have found the addition of a log-normal size distribution to simulations using the nanoplasma model of cluster excitation improves the agreement between numerical and experimental data.

We propose a method for the measurement of attosecond beating structures that result from the superposition of harmonics of laser radiation. It utilizes the phase control of the excitation probability of atoms through different interfering channels. The channels consist of multiphoton excitation by the fundamental frequency and single-photon excitation by the superposition of the harmonic fields, or alternatively, by each harmonic or frequency interval within the bandwidth of each harmonic. The method is sensitive to the relative phase of the harmonics, including phases introduced by chirp, and thus allows evaluation of the temporal structure of the superimposed harmonic fields. An experimental setup for the implementation of the method based on freestanding transmission grating is suggested as well.

The calculation of cross sections for inelastic and charge-exchange atomic collisions encounters a principal difficulty. The coordinates used to describe the collision event are usually not appropriate for the description of the collision partners long before and after the collision. As a consequence, the coupling matrix elements that govern inelastic transitions can remain nonzero for large internuclear distance. We present a simple procedure to deal with this situation in the framework of a full quantum-mechanical treatment. It applies to radial as well as rotational coupling mechanisms. We demonstrate the practical applicability by numerical examples.

We study the quasienergy spectrum and the nonadiabatic time dynamics of the open quantum system, which incorporates the two-level atom dipole coupled to both the quantized mode and the polychromatic classical field. Both the numeric calculations and the original perturbation technique are applied to track the quasilevel positions against the strength of the classical field. The first-order perturbation theory predicts the singular behavior of the system including the infinitely large squeezing of the quantized mode quadratures at certain values of the field strength. The singularity is removed here by allowing for the nonadiabatic transitions among the quasienergy states and the higher perturbations as well.

We discuss optimal disentanglement processes of states of two two-level systems that belong to (i) the universal set, (ii) the set in which the states of one party lie on a single great circle of the Bloch sphere, and (iii) the set in which the states of one party commute with each other, by teleporting the states of one party (on which the disentangling machine is acting) through three particular types of separable channels, each of which is a mixture of Bell states. In the general scenario, by teleporting one party’s state of an arbitrary entangled state of two two-level parties through some mixture of Bell states, we have shown that this entangled state can be made separable by using a physically realizable map $\tilde{V}$ acting on one party’s states, if $\tilde{V}\mathrm{}\left(I\right)=I,\tilde{V}\left({\sigma }_j\right)={\lambda }_j{\sigma }_j,$ where ${\lambda }_j>~0$ (for $j=1,2,3)$ and ${\lambda }_1+{\lambda }_2+{\lambda }_3<~1.$