The electron impact single ionization cross sections on a number of targets with atomic number $Z=1–92$ in the H and Li isoelectronic sequences are calculated using a modified version of the recently propounded relativisitic improved binary-encounter dipole (MRIBED) model [M. A. Uddin et al., Phys. Rev. A 70, 032706 (2004); 71, 032715 (2005)]. The modified RQIBED (MRIBED) model along with a $Z$-dependent factor in it is found remarkably successful in the applications to H- and Li-like systems and also valid for the ionization of a filled $s$ orbit including the He-like targets.

Radiative lifetimes of hydrogenic atoms in a homogeneous magnetic field of moderate strength are calculated on the basis of classical radiation. The modifications of the Keplerian orbits due to the magnetic field are incorporated by classical perturbation theory. The model is complemented by a classical radiative decay calculation using the radiated Larmor power. A recently derived highly accurate formula for the transition rate of a field-free hydrogenic state is averaged over the angular momentum oscillations caused by the magnetic field. The resulting radiative lifetimes for diamagnetic eigenstates classified by $n,m$ and the diamagnetic energy shift $C$ compare well with quantum results.

We present a detailed study of laser cooling of neutral atoms with an electric-dipole transition between a $J_g=0$ ground state and a $J_e=1$ excited state, for both broad- and narrow-line transitions. We focus on the novel effects arising from the multidimensional nature of the laser configuration and point out under which conditions these features can be observed in practice. Our analysis also shows that qualitative differences in multidimensional laser cooling properties exist between the broad- and the narrow-line transitions.

We consider high-order harmonic generation by a linearly polarized laser field and a parallel static electric field. We first develop a modified saddle-point method which enables a quantitative analysis of the harmonic spectra even in the presence of Coulomb singularities. We introduce a classification of the saddle-point solutions and show that, in the presence of a static electric field which breaks the inversion symmetry, an additional classification number has to be introduced and that the usual saddle-point approximation and the uniform approximation in the case of the coalescing saddle points have to be modified. The theory developed offers a simple and accurate explanation of the static-field-induced multiplateau structure of the harmonic spectra. The longer quantum orbits are responsible for a long extension of the harmonic plateau, while the larger initial electron velocities are the reason of lower harmonic emission rates.

We present a model for the collisional properties of a mixture of ${}^{133}\mathrm{Cs}$ and ${}^{87}\mathrm{Rb}$ atoms in a magnetic trap at $\mu \mathrm{K}$ temperatures. The experimental sequence we model corresponds to a selective evaporation of the Rb atoms using a radio-frequency field, leading to sympathetic cooling of the Cs atoms or, if selective evaporation is carried out fast, to a difference in temperature between the two atomic species. In the latter case, the two atomic clouds reached an equilibrium temperature starting from an Rb temperature lower than that of Cs. By supposing that each atomic cloud was in thermal equilibrium we modeled this rethermalization process through differential equations for the two atomic temperatures. An alternative approach was based on the Monte Carlo simulations of the individual collisional processes. The sympathetic cooling and the rethermalization were analyzed in terms of the inter-species collisional cross-section.

We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (nonintegrable) model of a spinor (three-component) model of the Bose-Einstein condensate, based on a system of three nonlinearly coupled Gross-Pitaevskii equations. The stability of the solitons is studied by means of direct simulations and, in a part, analytically, using linearized equations for small perturbations. Global stability of the solitons is considered by means of an energy comparison. As a result, ground-state and metastable soliton states of the FM and polar types are identified. For the special integrable version of the model, we develop the Darboux transformation (DT). As an application of the DT, analytical solutions are obtained that display full nonlinear evolution of the modulational instability of a continuous-wave state seeded by a small spatially periodic perturbation. Additionally, by dint of direct simulations, we demonstrate that solitons of both the polar and FM types, found in the integrable system, are structurally stable; i.e., they are robust under random changes of the relevant nonlinear coefficient in time.

We analyze the effect of injected atomic coherence on transverse patterns of a broad area laser by means of the semiclassical two-level Maxwell-Bloch equations. A single longitudinal mode is considered. The injected atomic coherence forces a spatially homogeneous profile to appear and locks the field phase to a single value. Above a pump threshold value a very rich scenario of patterns is developed. Near threshold we find stationary patterns such as rhombic and hexagonal lattices. Well above threshold nonstationary patterns such as complex highly ordered vortex lattices traveling along the cross section, and nearly traveling waves appear.

We describe a simple method of the beat-note interferometer that directly and dynamically measures the phase shift of light pulses induced by highly dispersive samples. Using the method, we show intuitively that the storage and retrieval of light pulses in a medium due to the effect of electromagnetically induced transparency is a coherent process and, quantitatively, that there is no observable phase shift caused by the process. This method is sensitive enough that it can be used to measure the phase of a light pulse with energy on the order of a dozen photons.

The multipartite state in the Rigolin’s protocol [Phys. Rev. A 71, 032303 (2005)] for teleporting an arbitrary two-qubit state is just a product state of $N$ Einstein-Podolsky-Rosen pairs in essence, not a genuine multipartite entangled state, and this protocol in principle is equivalent to the Yang-Guo protocol [Chin. Phys. Lett. 17, 162 (2000)].

We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension $D$ benefits from applying basic concepts from number theory, since the set ${\mathbf{Z}}_D^n$ associated with Bell diagonal states is a module rather than a vector space. We find that a partition of ${\mathbf{Z}}_D^n$ into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension $D$. When $D$ is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.

A representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. It stems from noting that the 0’s in a product qubit state do not contribute to the number. They serve only as place holders. The representation is based on the distribution of four types of systems on an integer lattice. The four types, labeled as positive real, negative real, positive imaginary, and negative imaginary, are represented by creation and annihilation operators acting on the system vacuum state. Complex rational number states correspond to products of creation operators acting on the vacuum. Various operators, including those for the basic arithmetic operations, are described. The representation used here is based on occupation number states and is given for bosons and fermions.

Here we describe a simple mechanical procedure for compiling a quantum gate network into the natural gates (pulses and delays) for an Ising quantum computer. The aim is not necessarily to generate the most efficient pulse sequence, but rather to develop an efficient compilation algorithm that can be easily implemented in large spin systems. The key observation is that it is not always necessary to refocus all the undesired couplings in a spin system. Instead, the coupling evolution can simply be tracked and then corrected at some later time. Although described within the language of NMR, the algorithm is applicable to any design of quantum computer based on Ising couplings.

We analyze the quantum entanglement at the equilibrium in a class of exactly solvable one-dimensional spin models at finite temperatures and identify a region where the quantum fluctuations determine the behavior of the system. We probe the response of the system in this region by studying the spin dynamics after projective measurement of one local spin which leads to the appearance of the “decoherence wave.” We investigate time-dependent spin correlation functions, the entanglement dynamics, and the fidelity of the quantum information transfer after the measurement.

We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation we have to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.

We report on the state-selective detection of near-dissociation ultracold KRb molecules in the ground $X{}^1\Sigma ^{+}$ state and the metastable $a{}^3\Sigma ^{+}$ state. The molecules are produced by photoassociation of ultracold atoms followed by radiative decay into high vibrational levels of the $X$ and $a$ states. Detection utilizes resonance-enhanced one-color two-photon ionization, followed by time-of-flight mass spectroscopy. Scanning the detection laser frequency over the range $582–625\mathrm{nm}$, we observe transitions from the $v^{″}=86–92$ levels of the $X$ state, which are bound by up to $30{\mathrm{cm}}^{-1}$, and the $v^{″}=17–23$ levels of the $a$ state, which are also bound by up to $30{\mathrm{cm}}^{-1}$. The measured vibrational spacings are in excellent agreement with those previously measured and those calculated from the relevant potential curves. Relative vibrational populations are also consistent with Franck-Condon factors for decay from the photoassociated levels.

The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. Definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.

We study an ultracold Bose-Fermi atomic mixture in a one-dimensional optical lattice. When boson atoms are heavier then fermion atoms the system is described by an adiabatic Holstein model, exhibiting a Peierls instability for commensurate fermion filling factors. A bosonic density wave with a wave number of twice the Fermi wave number will appear in the quasi-one-dimensional system, due to the opening of a gap at the Fermi energy in the fermion spectrum.

We have performed a measurement of the Casimir-Polder force using a magnetically trapped ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. By detecting perturbations of the frequency of center-of-mass oscillations of the condensate perpendicular to the surface, we are able to detect this force at a distance $\sim 5\mu \mathrm{m}$, significantly farther than has been previously achieved, and at a precision approaching that needed to detect the modification due to thermal radiation. Additionally, this technique provides a limit for the presence of non-Newtonian gravity forces in the $\sim 1\mu \mathrm{m}$ range.

The squeezing spectrum of the fluorescent light is investigated for a laser-driven three-level atom of the $\Lambda$ configuration when quantum interference of the decay channels is accounted for. We show that when the two atomic transitions contribute to the detected fluorescence field, squeezing at certain frequency intervals is obtained in both the weak- and the high-Rabi-frequency regimes even for equally decay rates of the transitions. Unlike in two-level atoms in free space, squeezing can be obtained in both the in-phase and out-of-phase quadrature spectra although in different spectral regions. We also show that the squeezing spectrum can be controlled by an adequate selection of the Rabi frequencies and atomic detunings. Another remarkable effect is that squeezing can be achieved with proper relative phases of the driving fields. We provide an analytical description in the dressed basis which accounts for the main features of the squeezing spectra obtained from the numerical work.

Maps of the dynamics of an optically injected solid-state $\mathrm{Nd}:\mathrm{Y}\mathrm{V}{\mathrm{O}}_4$ laser are presented. Experimental maps showing different dynamical regions are generated automatically from measured intensity time series by plotting the maxima of intensity. Corresponding numerical maps and a bifurcation diagram are calculated with a rate equation model of an injected class B laser. Intensity time series inside different regions in the maps are examined. The experimental and numerical maps are shown to be in good agreement with each other if the linewidth enhancement factor $\alpha$ is used as a fitting parameter in the model. As a result, experimental estimates for an effective $\alpha$ are given for a $\mathrm{Nd}:\mathrm{Y}\mathrm{V}{\mathrm{O}}_4$ laser. The effects of noise on the dynamics are also discussed.