A closer examination of Eberly “revivals,” Berry “quantum fractals,” and Schleich “carpets” exposes a simple unitary-cyclic group structure in the dynamics of wave packets for rotorlike systems with quadratic spectra. Quantum quasifractal patterns are revealed to be permeated by self-similar “X-braid” structures seen by Hofstadter in Zeeman-perturbed band structures and in other spectra related to circle maps. The patterns are shown to correspond to revival dynamics in the flow of energy or information through these N-level systems with X-braids being directly related to quantum beats or elementary U(2) resonance transfer. $C_N$-group analysis and Farey arithmetic discretely catalog X-braid hierarchy and suggest the possibility of homocyclic nanostructures or $C_N$ circuits that are base-N digital quantum computing registers. The phase dynamics corresponds to a fairly sophisticated integer arithmetic that includes an output of all rational numbers resolvable by a given energy input. $C_N$ circuits automatically give all factors of N. The dynamics of a $C_6$ device is discussed in detail.

We study the entanglement in the quantum Heisenberg $\mathrm{XY}$ model in which the so-called W entangled states can be generated for 3 or 4 qubits. By the concept of concurrence, we study the entanglement in the time evolution of the $\mathrm{XY}$ model. We investigate the thermal entanglement in the two-qubit isotropic $\mathrm{XY}$ model with a magnetic field and in the anisotropic $\mathrm{XY}$ model, and find that the thermal entanglement exists for both ferromagnetic and antiferromagnetic cases. Some evidences of the quantum phase transition also appear in these simple models.

During a molecular vibration, an atom changes continuously its position. Just as the emitted photoelectron waves, the electromagnetic waves absorbed by the atom in the different positions are strictly coherent and have different well-defined phases. These phases depend on the relation between the instantaneous internuclear distance and the photoelectron, respectively, photon wavelengths. We predict that the interference of these coherent waves strongly influences the vibrational profile of the photoelectron spectra of core electrons in a molecule. This effect increases with increasing x-ray photon frequency and results in a deformation and broadening of the vibrational profile. In the case of surface adsorbed molecules, the vibrational profile depends strongly on the direction of the photoelectron ejection and photon momentum, and the orientational sensitivity of a vibrational profile can even be used as a tool to define the orientation of adsorbed molecules.

By combining a total-angular-momentum representation, the smooth-exterior complex dilation technique and a three-dimensional finite-element code, a study of some resonances in a model of an electronic surface of the van der Waals complex NeICl was performed. For zero angular momentum, our results show good agreement with earlier calculations. Using the present formalism we believe that we are able to report a fully quantum-mechanical calculation of predissociation widths for a triatomic molecule.

The one-loop self-energy correction to the hyperfine splitting of the $1s$ and $2s$ levels in H-like low-$Z$ atoms is evaluated to all orders in $Z\alpha .$ The results are compared to perturbative calculations. The residual higher-order contribution is evaluated. Implications to the specific difference of the hyperfine-structure intervals $8\Delta {\nu }_2-\Delta {\nu }_1$ in ${\mathrm{He}}^{+}$ are investigated.

Single, double, triple, quadruple, and quintuple capture of electrons in ${}^{15}{\mathrm{N}}^{7+}+\mathrm{N}\mathrm{e}$ collision at the energy of 105 keV have been investigated using recoil-ion momentum spectroscopy. Relative cross sections, stabilization ratios, ratios between single- and multiple-electron capture, along with the branching ratios of subprocesses involved in multiple capture, have been obtained and compared with calculations by the extended classical over-barrier model [A. Niehaus, J. Phys. B 19, 2925 (1986)] and the semiempirical scaling laws [N. Selberg et al., Phys. Rev. A 54, 4127 (1989)]. For single capture, n state relative populations and projectile scattering angle distributions are given. In the case of double capture, we find the autoionizing double capture dominates and populates the symmetric ${\mathrm{N}}^{5+}{(3l3l}^{\prime })$ and near-symmetric ${\mathrm{N}}^{5+}{(3l4l}^{\prime })$ state, while the true double capture mainly gives rise to ${\mathrm{N}}^{5+}{(2\mathrm{lnl}}^{\prime })$ $\mathrm{}(n>\mathrm{}2\mathrm{})\mathrm{}$ configurations. The relative cross sections and stabilization ratios for double electron capture are evaluated. In the more than two-electrons capture, we have obtained stabilization ratios and branching ratios of different subprocesses. The configurations populated by more than two-electron captures have been identified. Our results also show that the electron-electron correlation is important in multiple electron capture.

It is shown that the population Rabi oscillations in a lossless two-level atom, interacting with a monochromatic electromagnetic field, in general, are convergent in time. The well-known continuous oscillations take place because the restricted choosing of initial conditions, that is, when the atom is chosen on ground or excited level before the interaction, simultaneously having a definite value of momentum there. The convergence of Rabi oscillations in atomic wave-packet states is a direct consequence of the Doppler effect on optical transition rates (Rabi frequencies): it gradually leads to “irregular” chaotic-type distributions of momentum in ground and excited energy levels, smearing the amplitudes of Rabi oscillations. Conjointly with Rabi oscillations, the coherent accumulation of momentum on each internal energy level monotonically diminishes too.

We present a detailed study of the multiphoton ionization and high-order harmonic generation (HHG) processes of rare-gas atoms (He, Ne, and Ar) in intense pulsed laser fields by means of a self-interaction-free time-dependent density-functional theory (TDDFT) recently developed. The time-dependent exchange-correlation potential with proper short- and long- range potential is constructed by means of the time-dependent optimized effective potential (TDOEP) method and the incorporation of an explicit self-interaction-correction (SIC) term. The TDOEP-SIC equations are solved accurately and efficiently by the time-dependent generalized pseudospectral technique. In this study, all the valence electrons are treated explicitly and nonperturbatively and their partial contributions to the ionization and HHG are analyzed. The results reveal instructive and qualitatively different behavior from each subshell orbital. Moreover, we found that the HHG yields from Ne and Ar atoms are considerably larger than that of the He atom in strong fields. Three main factors are identified for accounting the observed phenomena: (a) the binding energy of the subshell valence electron, (b) the orientation of the valence electron orbital (with respect to the electric-field polarization), and (c) the effect of multiphoton resonant excitation. In particular, we found that the ${\mathrm{np}}_0$ valence electrons (in Ne and Ar) with lowest binding energies and electron orbital orientation parallel to the electric-field direction, make the dominant contributions to both ionization and HHG processes in sufficiently strong fields.

We propose and study resonant ladder schemes of inversionless lasing on a fast-decaying transition when the population inversion is not possible or very difficult to achieve. The driving field on a neighboring, slowly decaying transition is not imposed externally, but is self generated in the same active medium. Inversionless lasing in such schemes avoids the problem of driving-field absorption and leads to considerable reduction in the required pumping rate. Applications of such schemes include inversionless ultraviolet and soft x-ray lasing in gas lasers and inversionless generation of coherent mid/far-infrared emission on intersubband (interlevel) transitions in multiple quantum-well or quantum-dot laser diodes.

The possibility that time can be regarded as a discrete dynamical variable is reexamined. We study the dynamics of the free particle and find in some cases superluminal propagation.

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.

We generalize the recent work of Massar and Popescu dealing with the amount of classical data that is produced by a quantum measurement on a quantum state ensemble. In the previous work it was shown that quantum measurements generally contain spurious randomness in the outcomes and that this spurious randomness can be eliminated by carrying out collective measurements on many independent copies of the system. In particular it was shown that, without decreasing the amount of knowledge the measurement provides about the quantum state, one can always reduce the amount of data produced by the measurement to the von Neumann entropy $H\left(\rho \right)=-\mathrm{Tr}\rho \log \rho$ of the ensemble. Here we extend this result by giving a more refined description of what constitutes equivalent measurements (that is, measurements which provide the same knowledge about the quantum state) and also by considering incomplete measurements. In particular, we show that one can always associate a positive operator-valued measure (POVM) having elements $a_j$ with an equivalent POVM acting on many independent copies of the system, which produces an amount of data asymptotically equal to the entropy defect of an ensemble canonically associated with the ensemble average state ρ and the initial measurement ${(a}_j).\mathrm{}$ In the case where the measurement is not maximally refined this amount of data is strictly less than the amount $H\left(\rho \right)$ obtained in the previous work. We also show that this is the best achievable, i.e., it is impossible to devise a measurement equivalent to the initial measurement ${(a}_j)$ that produces less data. We discuss the interpretation of these results. In particular, we show how they can be used to provide a precise and model-independent measure of the amount of knowledge that is obtained about a quantum state by a quantum measurement. We also discuss in detail the relation between our results and Holevo’s bound, at the same time providing a self-contained proof of this fundamental inequality.

The wave function of a two-level atom driven by a low-frequency laser pulse is obtained in analytical form and is used to determine the power spectrum of the dipole moment of the atom for different initial atomic states. The solution goes over some known approximate solutions and gives the energy of the two dressed states, the position of the hyper-Raman lines, the amplitudes both of the hyper-Raman lines and of the odd harmonics, and the position of the cutoff. The form of the hyper-Raman spectrum results independently of the initial atomic state and shows an onset and a cutoff of the emission.

We describe the use of time-resolved inner-electron ionization as a method of detecting the time evolution of Rydberg wave packets. The method is sufficiently sensitive that it can be used to monitor wave packets for extended times, and its Fourier transform provides a cross correlation between constituent eigenstates, allowing the phases of the constituent eigenstates at the core to be retrieved. These phases, and the easily determined amplitudes of the constituent eigenstates, can be used to construct the wave function of the wave packet.

Observations of a doubly driven V system probed to a fourth level in an N configuration are reported. A dressed-state analysis is also presented. The expected three-peak spectrum is explored in a cold rubidium sample in a magneto-optic trap. Good agreement is found between the dressed-state theory and the experimental spectra once light shifts and uncoupled absorptions in the rubidium system are taken into account.

We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving field is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mollow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving field. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are $180°$ out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we show that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.

We analyze the effect of squeezing the channel in binary communication based on Gaussian states. We show that for coding on pure states, squeezing increases the detection probability at fixed size of the strategy, actually saturating the optimal bound already for moderate signal energy. Using Neyman-Pearson lemma for fuzzy hypothesis testing we are able to analyze also the case of mixed states, and to find the optimal amount of squeezing that can be effectively employed. It results that optimally squeezed channels are robust against signal mixing, and largely improve the strategy power by comparison with coherent ones.

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-$N$ expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.

Sympathetic cooling of two atomic isotopes is experimentally investigated. Using forced evaporation of a bosonic ${}^7\mathrm{Li}$ gas in a magnetic trap, a sample of $1.3\times {10}^5$ ${}^6\mathrm{Li}$ fermions has been sympathetically cooled to $9\left(3\right)\mathrm{}\hspace{0.5em}\mu \mathrm{K},$ corresponding to $2.2\left(0.8\right)\mathrm{}$ times the Fermi temperature. The measured rate constant for two-body inelastic collisions of the ${}^7\mathrm{Li}$ $|2,2〉$ state at low magnetic field is ${1.0}_{-0.5}^{+0.8\mathrm{}}\times {10}^{-14}\hspace{0.5em}{\mathrm{cm}}^3{\mathrm{s}}^{-1}.$

We report studies of spectral line shapes of ultracold $(T=1\mathrm{}\hspace{0.5em}\mu \mathrm{K})$ ${}^{88}\mathrm{Sr}$ in the presence of a laser beam tuned to the red of the ${}^{1}S{-}^{1}P$ transition, as functions of laser intensity and polarization, using the relevant currently available potential curves. These studies predict that, at high enough intensities of the probe laser, for temperatures near the recoil limit, an extra, in principle unexpected, peak appears on the red side of each line in the photoassociation spectrum. We show that the appearance of this extra peak is due to a near-zero-energy resonance of the dressed ground state. We also emphasize that the correct relative position of this peak can only be calculated if multichannel effects are taken into account.