We study quantum trajectories of collective atomic spin states of $N$ effective two-level atoms driven with laser and cavity fields. We show that interesting “entangled-state cycles” arise probabilistically when the (Raman) transition rates between the two atomic levels are set equal. For odd (even) $N$, there are $\left(N+1\right)/2$ $\left(N/2\right)$ possible cycles. During each cycle the $N$-qubit state switches, with each cavity photon emission, between the states $\left(|N/2,m⟩\pm |N/2,-m⟩\right)/\sqrt{2}$, where $|N/2,m⟩$ is a Dicke state in a rotated collective basis. The quantum number $m$ $\left(>0\right)$, which distinguishes the particular cycle, is determined by the photon counting record and varies randomly from one trajectory to the next. For even $N$ it is also possible, under the same conditions, to prepare probabilistically (but in steady state) the Dicke state $|N/2,0⟩$, i.e., an $N$-qubit state with $N/2$ excitations, which is of particular interest in the context of multipartite entanglement.

The electromagnetic dispersion in periodic layered media can be tailored and their resonant properties can be considerably improved by utilizing anisotropic materials. Periodic structures with a photonic band edge split into two parts, or so-called split band edge, exhibit superior resonant properties including exceptionally high $Q$ values of transmission resonances and nearly perfect impedance matching at the boundaries, even when the number of unit cells $N$ is not large. A microwave transmission resonance with $Q\sim 220$ is demonstrated in a periodic stack of form-birefringent layers with $N=12$ realized in a waveguide geometry.

An optical realization of a quantum bouncing ball on a truncated lattice is theoretically proposed for light waves propagating near the edge of a circularly curved waveguide array. As compared to the analogous problem of matter waves bouncing on a perfectly reflecting surface under the influence of gravity, where the wave packets basically behave as classical particles, it is shown that the genuine quantum regimes of wave packet collapse and revival are accessible for the discrete optical system.

We present an investigation of resonances with unnatural parities in positron scattering with atomic hydrogen. The method of complex-coordinate rotation is used, together with Hylleraas wave functions to take care of the correlation effects among the three charged particles. States with angular momenta $L=1$ to $L=5$ and parity $(-1{)}^{L+1}$ are calculated. Resonance energies and widths for the states lying below the Ps $(N=2)$, H $(N=3)$, and H $(N=4)$ thresholds are reported.

We study an atomic quantum dot representing a single hyperfine “impurity” atom which is coherently coupled to two well-separated Bose-Einstein condensates, in the limit when the coupling between the dot and the condensates dominates the intercondensate tunneling coupling. It is demonstrated that the quantum dot by itself can induce large-amplitude Josephson-like oscillations of the particle imbalance between the condensates, which display a two-frequency behavior. For noninteracting condensates, we provide an approximate solution to the coupled nonlinear equations of motion which allows us to obtain these two frequencies analytically.

We derive sufficient conditions for infinite-dimensional systems whose entanglement is not completely lost in a finite time during its decoherence by a passive interaction with local vacuum environments. The sufficient conditions allow us to clarify a class of bipartite entangled states which preserve their entanglement or, in other words, are tolerant against decoherence in a vacuum. We also discuss such a class for entangled qubits.

We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels, and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. A possible test for the quantum nature of memories using two nonorthogonal signal states arises naturally. Furthermore, closer inspection of the measurement process in terms of the Stokes operators reveals a security threat for quantum key distribution involving phase reference beams.

We demonstrate that fusion and nucleosynthesis reactions between light and heavy nuclei driven by Coulomb explosion (CE) of nanodroplets will be dominated by intrananostructure collisions within a single, large heteronuclear nanodroplet (with initial radii of $R_0=1000–3000\mathrm{\AA }$) in ultraintense, near-infrared laser fields (peak intensities of $I_M={10}^{20}–{10}^{21}\mathrm{W}{\mathrm{cm}}^{-2}$). A computational and theoretical study of the yields of the intrananodroplet ${}^3\mathrm{T}(d,n){}^4\mathrm{He}$ fusion and ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ nucleosynthesis reactions driven by CE of $({\mathrm{D}}^{+}{\mathrm{T}}^{+}{)}_n$ and $({\mathrm{C}}^{6+}{\mathrm{H}}_4^{+}{)}_n$ heteronuclear nanodroplets provides a manifestation of kinematic overrun effects. The ${}^3\mathrm{T}(d,n){}^4\mathrm{He}$ fusion yield of $Y_{\mathrm{INTRA}}\simeq 200\mathrm{per}$ nanodroplet per laser pulse within a $(\mathrm{DT}{)}_n$ nanodroplet ($n=2\times {10}^9$, $R_0=2700\mathrm{\AA }$) is sufficiently high to warrant experimental observation for a single nanodroplet. The ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ reaction yield within a $({\mathrm{CH}}_4{)}_n$ nanodroplet ($n=3.9\times {10}^8$; $R_0=1790\mathrm{\AA }$) is $Y_{\mathrm{INTRA}}\simeq 4\times {10}^{-4}\gamma$ rays per nanodroplet per laser pulse, so that this intrananodroplet nucleosynthesis is amenable to experimental observation only in an assembly of such nanodroplets. A striking manifestation is provided for the absence of kinematic overrun effects in CE of $({\mathrm{C}}^{6+}{\mathrm{D}}_4^{+}{)}_n$ nanodroplets (with a kinematic parameter ${\eta }_{\mathrm{DC}}=1$), where intrananodroplet ${\mathrm{D}}^{+}+{\mathrm{C}}^{6+}$ collisions and the ${}^{12}\mathrm{C}(d,n){}^{13}\mathrm{N}$ reaction are precluded. CE driven intrananodroplet nuclear reaction involves transient temporal confinement of the heavy nuclei on the $10–20\mathrm{fs}$ time scale, with the heavy nuclei subcluster acting as a target for the expanding light protons or deuterons.

Low energy elastic scattering between clouds of Bose condensed atoms leads to the well known $s$-wave halo with atoms emerging in all directions from the collision zone. In this paper we discuss the emergence of Hanbury Brown and Twiss coincidences between atoms scattered in nearly parallel directions. We develop a simple model that explains the observations in terms of an interference involving two pairs of atoms each associated with the elementary $s$-wave scattering process.

We measure the damping of excitations in cigar-shaped Bose-Einstein condensates of atomic vapor. By using postselection, excitation line shapes of the total population are compared with those of the undamped excitations. We find that the damping depends on the initial excitation energy of the decaying quasiparticle, as well as on the excitation momentum. We model the condensate as an infinite cylinder and calculate the damping rates of the different radial modes. The derived damping rates are in good agreement with the experimentally measured ones. The damping rates strongly depend on the destructive interference between pathways for damping, due to the quantum many-body nature of both excitation and the vacuum modes.

We investigate the ground state properties of normal and superfluid phases of a mixture of Fermi atoms at zero temperature in a quasi-one-dimensional harmonic trap. Assuming pairing occurs in the Hartree-Fock single-particle states (obtained using atomic orbitals approach) we calculate the spectrum of elementary excitations of the system. We find that for strong enough attraction between different kinds of fermions the state consisting of Cooper pairs becomes energetically favorable. For even stronger attraction a discontinuity located at the Fermi surface appears in the spectrum of elementary excitations. At the same time the chemical potential changes its sign and the system goes from the gas of Cooper pairs to the condensed phase of molecular dimers realizing the BCS to Bose-Einstein condensate crossover in one-dimensional space.

In this paper, we examine theoretically the system of periodically poled ${\text{LiNbO}}_3$ waveguide arrays that feature a quadratic nonlinearity and that have recently become accessible to experimental studies. Motivated by these earlier works, we provide a detailed analytical study of the existence, stability, and dynamics of plane wave delocalized solutions, as well as that of strongly localized modes consisting of a few sites. The linear stability of both classes of solutions is quantified as a function of the system parameters, such as the wave vector mismatch parameter or the interchannel coupling strength, using experimentally accessible ranges. Our findings are, in all the cases, corroborated by numerical bifurcation analysis results; furthermore, when the solutions are found to be unstable, typical examples of the instability evolution are shown.

We show how to optimize the process of high-order harmonic generation (HHG) by gating the interaction using the field gradient of the driving pulse. Since maximized field gradients are efficiently generated by self-steepening processes, we first present a generalized theory of optical carrier-wave self-steepened (CSS) pulses. This goes beyond existing treatments, which only consider third-order nonlinearity, and has the advantage of describing pulses whose wave forms have a range of symmetry properties. Although a fertile field for theoretical work, CSS pulses are difficult to realize experimentally because of the deleterious effect of dispersion. We therefore consider synthesizing CSS-like profiles using a suitably phased subset of the harmonics present in a true CSS wave form. Using standard theoretical models of HHG, we show that the presence of gradient-maximized regions on the wave forms can raise the spectral cutoff and so yield shorter attosecond pulses. We study how the quality of the attosecond bursts created by spectral filtering depends on the number of harmonics included in the driving pulse.

A B-spline algorithm has been developed to evaluate the electronic structure of multielectron atoms in a magnetic field. A generalized electron configuration concept, which is crucial to perform the current investigation, was introduced to solve Hartree-Fock equations. The wave functions for electron orbitals of the magnetized multielectron atom are expanded in terms of a B-spline basis in the radial direction and spherical harmonics in the angular direction. The developed algorithm has been applied to calculations of He in a magnetic field. Energy levels of magnetized He in the ground state are presented as a function of magnetic field strength with a range from zero up to $2.35\times {10}^7\mathrm{T}$ and compared with available theoretical data.

We report results of analysis of collisions between in-phase spatial solitons in a three-wave system, which includes competing ${\chi }^{\left(2\right)}:{\chi }^{\left(3\right)}$ nonlinearities and birefringence. The character of the collisions is quantified by a critical value of the initial tilt of the colliding solitons, $Q$, which separates quasielastic passage and merger (solitons with phase shift $\pi$ bounce from each other). If $Q$ is very close to $Q_{\text{cr}}$, the solitons may fuse into a double-peak state. $Q_{\text{cr}}$ is smaller for relatively large negative mismatch of the ${\chi }^{\left(2\right)}$ interactions. With the increase of the ${\chi }^{\left(3\right)}/{\chi }^{\left(2\right)}$ ratio, the system quickly transits from the behavior governed by the ${\chi }^{\left(2\right)}$ nonlinearity to a regime dominated by the ${\chi }^{\left(3\right)}$ terms.

We present a fully ab initio quantum investigation of the frequency comb structure and coherence within each order of the high-order harmonic generation (HHG) spectrum in the high-frequency vuv-xuv regime. The HHG spectrum driven by a train of equal-spacing short laser pulses is calculated by propagating the time-dependent Schrödinger equation accurately and efficiently by means of the time-dependent generalized pseudospectral method. We explore the comb structure and coherence by varying the laser pulse separation $\tau$, the number of pulses $N$, and the laser intensity. We find that a nested comb structure appears within each of the harmonics, ranging from the first harmonic all the way to the cutoff harmonic, and this global pattern persists regardless of the values of $\tau$ and $N$ used. The comb structure of the harmonics originates from quantum interferences among induced dipole pulses. Finally, the frequency comb structure prevails even in the presence of appreciable ionization.

We investigate the orientation dependence of molecular high-order harmonic generation (HHG) both numerically and analytically. We show that the molecular recollision electronic wave packets (REWPs) in the HHG are closely related to the ionization potential as well as the particular orbital from which it ionized. As a result, the spectral amplitude of the molecular REWP can be significantly different from its reference atom (i.e., with the same ionization potential as the molecule under study) in some energy regions due to the interference between the atomic cores of the molecules. This finding is important for molecular orbital tomography using HHG [J. Itatani et al., Nature 432, 867 (2004)].

We calculate the radio-frequency spectrum of balanced and imbalanced ultracold Fermi gases in the normal phase at unitarity. For the homogeneous case the spectrum of both the majority and minority components always has a single peak even in the pseudogap regime. We furthermore show how the double-peak structures observed in recent experiments arise due to the inhomogeneity of the trapped gas. The main experimental features observed above the critical temperature in the recent experiment of Schunck et al. [Science 316, 867 (2007)] are recovered with no fitting parameters.

We demonstrate theoretical stationary and dynamical generation of Bell states in a system of two parallel double quantum dots with one mobile electron each (proposed as two charge qubits) driven by an external potential difference applied to the second of the double dots. For coherent dynamics, it is shown that each one of the four Bell states is obtained through a suitable nonentangled initial condition as well as through the control of the time-dependent external electric field. We analyze dissipative effects on such state formation, due to the coupling with a thermal bath of phonons. Via a Markovian master equation approach, which includes the electron-phonon interaction, we found that Bell-state probabilities are preserved for very low temperature but are adversely affected as the temperature increases. In addition, we include concurrence and charge distribution calculations in order to characterize the double-dot array. This electrostatic mechanism could be of interest in quantum-computation, -information, and -communication schemes.

Nuclear deformation effects on the binding energies in heavy ions are investigated. Approximate formulas for the nuclear-size correction and the isotope shift for deformed nuclei are derived. Combined with direct numerical evaluations, these formulas are employed to reanalyze experimental data on the nuclear-charge-distribution parameters in ${}^{238}\text{U}$ and to revise the nuclear-size corrections to the binding energies in H- and Li-like ${}^{238}\text{U}$. As a result, the theoretical uncertainties for the ground-state Lamb shift in ${{}^{238}\text{U}}^{91+}$ and for the $2p_{1/2}-2s$ transition energy in ${{}^{238}\text{U}}^{89+}$ are significantly reduced. The isotope shift of the $2p_j-2s$ transition energies for ${{}^{142}\text{N}\text{d}}^{57+}$ and ${{}^{150}\text{N}\text{d}}^{57+}$ is also evaluated including nuclear size and nuclear recoil effects within a full QED treatment.