We report the results of a theoretical study of the response of atomic clusters to an intense short laser pulse. Numerical simulations are based on a time-dependent density-functional method for a one-dimensional model of chain of atoms. The electron dynamics is investigated with frozen ion positions. Results concerning the initial stage of ionization, together with high-order harmonic generation are presented.

We describe and characterize a setup for subrecoil stimulated Raman spectroscopy of cold cesium atoms. We study in particular the performances of a method designed for active control and stabilization of the magnetic fields across a cold-atom cloud inside a small vacuum cell. The performance of the setup is monitored by copropagative-beam stimulated Raman spectroscopy of a cold cesium sample. The root-mean-square value of the residual magnetic field is $300\hspace{0.5em}\mu \mathrm{G},$ with a compensation bandwidth of 500 Hz. The shape of the observed spectra is theoretically interpreted and compares very well to numerically generated spectra.

We present a variational solution of the Langevin field equation describing the nonequilibrium dynamics of a harmonically trapped Bose-Einstein condensate. If the thermal cloud remains in equilibrium at all times, we find that the equations of motion for the parameters in our variational ansatz are equivalent to the Langevin equations describing the motion of a massive Brownian particle in an external potential. Moreover, these equations are coupled to a stochastic rate equation for the number of atoms in the condensate. As applications of our approach, we have calculated the collisional damping rates and frequencies of the low-lying collective excitations of a condensate with repulsive interactions, and have obtained a description of the growth and subsequent collapse of a condensate with attractive interactions. We have found good agreement with the available experimental results in both cases.

An appropriate, time-dependent modification of the trapping potential may be sufficient to create effectively collective excitations in a cold-atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions and should allow the creation of both dark solitons and vortices.

We report continuous-wave laser action in two oxide nanopowders doped with ${\mathrm{Ce}}^{3+}$ and ${\mathrm{Pr}}^{3+}$ ions. To our knowledge, these are the first observations of stimulated emission from electrically pumped random media in which scattering and distributed feedback scale lengths are much shorter than a wavelength. The continuous nature of the laser emission in small volumes (on the order of a cubic wavelength) of these low gain systems, and the absence of coherent speckle, provide compelling evidence that these results are mediated by strong Anderson localization of light.

The transport of broadband incoherent radiation through a bleaching medium is analyzed using a different analytical treatment. The principal features of the photodecomposition (bleaching) wave formation are examined for media characterized by uniform initial distribution of decomposing absorbers. Considering a broadband radiation from uniform planar or cylindrical source with stable radiative characteristics, we show that the problem has an asymptotic stationary solution for the case where the absorption spectrum is nonzero within the bandwidth that leads to decomposition. In more general cases the process dynamics can be adequately described by an asymptotic approach to a stationary solution obtained for properly chosen limits of integration over frequency.

We apply the coupled-channel-optical method for positron-hydrogen atom scattering at energies just above the ionization threshold to 40 eV. The rearrangement positronium channels are treated in the close-coupling method that includes the atomic target states. The neglect of the continuum is taken into account via an ab initio optical potential model. Physical observables such as ionization, positronium formation, and total cross sections are presented together with elastic and positronium$\mathrm{}\left(1s\right)\mathrm{}$ differential cross sections.

We apply the complex absorbing potential method to study the resonances of the ground state of hydrogen atom and the low-lying $2S$ and $2P\mathrm{}(m=0\mathrm{})\mathrm{}$ states of lithium atoms in parallel magnetic and electric fields. The behavior of resonance parameters for the ground state of hydrogen atoms in parallel magnetic and electric fields are consistent with those obtained by other methods. We then discuss the extension of the present method to study the resonant low-lying states of lithium atoms.

The ability to perform measurements on a quantum system, combined with the ability to feed back the measurement results via coherent control, allows one to control the system to follow any desired coherent or incoherent quantum dynamics. Such universal dynamical control can be achieved, in principle, through the repeated application of only two coherent control operations and a simple “Yes-No” measurement. As a consequence, a quantum computer can simulate an arbitrary open-system dynamics using just one qubit more than required to simulate closed-system dynamics.

A statistical model serving to estimate the branching ratios in the dissociative recombination of polyatomic molecular ions is described. Simple phase-space assumptions are employed separately for the electronic capture step and the subsequent dissociation and yield predictions in good agreement with existing data on ${\mathrm{H}}_3^{+}.$ Also the vibrational state populations of molecular fragments can be obtained and for ${\mathrm{H}}_3^{+}$ are found to agree well with recent measurements.

A model of discrete dynamics of entanglement of a bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied by an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of subsystems. For some mixed states having different marginal entropies of the subsystems we find an asymmetry in speed of entanglement decay. The entanglement of these states decreases faster, if the depolarizing channel acts on the “classical” subsystem, characterized by smaller marginal entropy.

We investigate the geometric phases and the Bargmann invariants associated with multilevel quantum systems. In particular, we show that a full set of “gauge-invariant” objects for an n-level system consists of n geometric phases and $\frac{1}{2}\left(n-1\right)\left(n-2\right)$ algebraically independent four-vertex Bargmann invariants. In the process of establishing this result, we develop a canonical form for $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}$ matrices that is useful in its own right. We show that the recently discovered “off-diagonal” geometric phases [N. Manini and F. Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analyzed in terms of the basic building blocks developed in this work. This result liberates the off-diagonal phases from the assumption of adiabaticity used in arriving at them.

We show that the width of the wave packet of a class of generalized nonlinear Schrödinger equations (NLSE) trapped in an arbitrary time-dependent harmonic well in any dimensions is universally determined by the same Hill’s equation. This class of generalized NLSE is characterized by a dynamical O(2,1) symmetry in absence of the trap. As an application, we study the dynamical instabilities of the rotating as well as nonrotating Bose-Einstein condensates in one and two dimensions. We also show exact extended parametric resonance in a nonrelativistic Chern-Simons theory producing a gauged NLSE.

Owing to the operator nature of the quantum dynamical variables, classical canonical transformations for integrating the equations of motion cannot be extended to the quantum domain. In this paper, a general procedure is developed to construct the sequences of quantum canonical transformations for integrating the Schrödinger equations. The sequence is made of three elementary canonical transformations that constitute a much larger class than the unitary transformations. In conjunction with the procedure, we also developed a factorization technique that is analogous to the method of integration factor in classical integration. For demonstration, with the same procedure we integrate nine nontrivial models, including the centripetal barrier potential, the Kratzer’s molecular potential, the Morse potential, the Pöschl-Teller potential, the Hulthén potential, etc.

Quantum cloning machines for equatorial qubits are studied. For the case of a one to two phase-covariant quantum cloning machine, we present the networks consisting of quantum gates to realize the quantum cloning transformations. The copied equatorial qubits are shown to be separable by using Peres-Horodecki criterion. The optimal one to M phase-covariant quantum cloning transformations are given.

We study the application of decoupling techniques to the case of a damped vibrational mode of a chain of trapped ions, which can be used as a quantum bus in linear ion trap quantum computers. We show that vibrational heating could be efficiently suppressed using appropriate “parity kicks.” We also show that vibrational decoherence can be suppressed by this decoupling procedure, even though this is generally more difficult because the rate at which the parity kicks have to applied increases with the effective bath temperature.

We calculate the quantum revival time for a wave packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The dependence of the revival time on various parameters of the driven system is shown analytically. As an example of an application of our approach, we compare the analytically obtained values of the revival time for various modulation strengths with the numerically computed ones in the case of a driven gravitational cavity. We show that they are in very good agreement.

The dynamics of ${\mathrm{H}}_2^{+}$ in short intense laser pulses with wavelengths of 532 nm and 800 nm is considered in two approaches, including and not including the motional degree of freedom of the two nuclei. In the situation with moving nuclei, referred to as the non-Born-Oppenheimer approach, the ionization is substantially increased with respect to the case with no motional degree of freedom of the nuclei, and consequently the nuclear separation also increases with rising laser intensity. This separation is accompanied by complex relative accelerations of the nuclei due to a strongly varying mutual shielding via the laser-driven electron. In the harmonic spectrum the irregularity of the electronic dynamics induced by the nuclear motion leads to a broadening of the harmonic peaks. In particular, the correlated nuclear motion is shown to lead to an earlier onset of the harmonic cutoff than for fixed nuclei, but also to a wider cutoff regime with significantly higher harmonics.

We consider a model of N two-dimensional bosons in a harmonic trap with translational and rotational invariant, weak two-particle interaction. We present in configuration space a systematical recursive method for constructing all wave functions with angular momentum L and corresponding energies and apply it to $L<~6$ for all N. The lower and the upper bounds for interaction energy are estimated. We analytically confirm the conjecture of Smith et al. that the elementary symmetric polynomial is the ground state for repulsive δ interaction for all $N>~L$ up to $L<~6.$ Additionally, we find that there exist vanishing-energy solutions for $L>~N\left(N-1\right),$ signaling the exclusive statistics. Finally, we consider briefly the case of attractive powerlike potential $r^k,$ $k>\mathrm{}-2,$ and prove that the lowest-energy state is still the one in which the whole angular momentum is absorbed by the center-of-mass motion.

We investigate the quantum dynamics and statistics of an atom laser by taking into account binary atom-atom collisions. The rotating wave approximation Hamiltonian of the system is solved analytically. We show that the nonlinear atom-atom interactions could yield periodic quadrature squeezing effects in the atom laser output beam, although the input radio frequency field is in a Glauber coherent state.