We calculate the dispersive force between a ground-state atom and a nonplanar surface. We present explicit results for a corrugated surface, derived from the scattering approach at first order in the corrugation amplitude. A variety of analytical results in different limiting cases, including the van der Waals and Casimir-Polder regimes, is derived. We compute numerically the exact first-order dispersive potential for arbitrary separation distances and corrugation wavelengths for a rubidium atom on top of a silicon or gold corrugated surface. We discuss in detail the inadequacy of the proximity force approximation, and present a simple but adequate approximation for computing the potential.

Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical transition is examined as a function of the density of the traps. It is shown that traps act as a serious and additional source of quantum decoherence. Furthermore, nontrivial temporal dependence of the standard deviation of the probability distribution of the walker is found when the trapping imperfections are introduced.

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed $A{{}^1\Sigma }_u^{+}$ and $b{{}^3\Pi }_u$ states of the rubidium dimer. The results are based on laser-induced fluorescence and optical-optical double-resonance polarization spectroscopy measurements combined with earlier laser-induced fluorescence data. We used an analytic potential (Hannover form) incorporated in a discrete variable representation of the Hamiltonian matrix for numerical energy-level calculation. A previous vibrational assignment of the $A$ levels is confirmed, and very probable vibrational assignment for the $b$ levels is also obtained. Currently, the rms residual of our fit is $0.053{\text{cm}}^{-1}$ as compared to the typical experimental uncertainties that are estimated to be $0.005{\text{cm}}^{-1}$. Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with ab initio calculations by all electrons and effective core pseudopotential methods. Analysis of the computational results yields an explanation for the ubiquitous single minima in these spin-orbit functions, which can be represented approximately by Morse-type functions.

An exact and general approach to study molecular vibrations is provided by the Watson Hamiltonian. Within this framework, it is customary to omit the contribution of the terms with the vibrational angular momentum and the Watson term, especially for the study of large systems. We discover that this omission leads to results which depend on the choice of the reference structure. The self-consistent solution proposed here yields a geometry that coincides with the quantum averaged geometry of the Watson Hamiltonian and appears to be a promising way for the computation of the vibrational spectra of strongly anharmonic systems.

We investigate experimentally a two-dimensional rocking ratchet for cold atoms, realized by using a driven three-beam dissipative optical lattice. ac forces are applied in perpendicular directions by phase modulating two of the lattice beams. As predicted by the general theory [S. Denisov, Y. Zolotaryuk, S. Flach, and O. Yevtushenko, Phys. Rev. Lett. 100, 224102 (2008)], we observe a rectification phenomenon unique to high-dimensional rocking ratchets, as determined by two single-harmonic drivings applied in orthogonal directions. Also, by applying two biharmonic forces in perpendicular directions, we demonstrate the possibility of generating a current in an arbitrary direction within the optical lattice plane.

We theoretically investigate the above-threshold ionization of hydrogen atom in a few-cycle nonlinear chirped laser pulse by solving one-dimensional time-dependent Schrödinger equation. It is shown that the cutoff of the above-threshold ionization spectrum could be extremely extended by adjusting the chirp parameter. The results can be well explained by the simple-man model.

Recent experimental studies of ${}^{87}\text{R}\text{b}$ spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition within the framework of the semiclassical truncated Wigner approximation. In the process we present a systematic study of the effects of the trap, nonlinearities, finite temperature, and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system by combining results presented here with those presented previously [S. Leslie, J. Guzman, M. Vengalattore, J. D. Sau, M. L. Cohen, and D. M. Stamper-Kurn, Phys. Rev. A 79, 043631 (2009)]. In the process we estimate the contribution of quantum zero-point fluctuations to the domain formation with quantitative accuracy and find discrepancies between the calculations and experiments at the quantitative level, despite the qualitative agreement between theory and experiment. We discuss the possible origins of these discrepancies. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.

Interband Rabi oscillations of gap-soliton matter waves induced by time-dependent periodic forces in combined linear and nonlinear optical lattices are demonstrated. It is shown that under suitable conditions, these oscillations can become long lived. By switching off the external force at proper time, it is possible to create either pure (stationary macroscopically populated) gap-soliton states or linear combination of two gap solitons with appreciably long lifetime.

We explore the existence and stability of two-dimensional spatial gap solitons with embedded vorticity in a bulk medium with the quadratic $\left({\chi }^{\left(2\right)}\right)$ nonlinearity and a transverse grating represented by periodic modulation of the refractive index. Gap-vortex solitons (GVSs) can be found in total gaps of the underlying spectra of the fundamental-frequency and second-harmonic waves. We demonstrate the existence of a family of stable GVSs, which are built as four-peak complexes, in the lowest total gap. We also consider dynamical effects, such as self-trapping of GVSs from input beams, and delocalization transitions.

Path-integral Monte Carlo simulation of the dipositronium “molecule” ${\text{Ps}}_2$ reveals its surprising thermal instability. Although, the binding energy is $\sim 0.4\text{eV}$, due to the strong temperature dependence of its free-energy ${\text{Ps}}_2$ dissociates, or does not form, above $\sim 1000\text{K}$, except for high densities where a small fraction of molecules are in equilibrium with Ps atoms. This prediction is consistent with the recently reported first observation of stable ${\text{Ps}}_2$ molecules by Cassidy and Mills, Jr., [Nature (London) 449, 195 (2007); Phys. Rev. Lett. 100, 013401 (2008)] at temperatures below 1000 K. The relatively sharp transition from molecular to atomic equilibrium, which we find, remains to be experimentally verified. To shed light on the origin of the large entropy factor in free-energy, we analyze the nature of interatomic interactions of these strongly correlated quantum particles. The conventional diatomic potential curve is given by the van der Waals interaction at large distances; but due to the correlations and high delocalization of constituent particles, the concept of potential curve becomes ambiguous at short atomic distances.

We present an empirical strategy to determine the Hamiltonian dynamics of a two-qubit system using only initialization and measurement in a single fixed basis. Signal parameters are estimated from measurement data using Bayesian methods from which the underlying Hamiltonian is reconstructed, up to three unobservable phase factors. We extend the method to achieve full control Hamiltonian tomography for controllable systems via a multistep approach. The technique is demonstrated and evaluated by analyzing data from simulated experiments including projection noise.

We demonstrate how the matrix-product state formalism provides a flexible structure to solve the constrained optimization problem associated with the sequential generation of entangled multiqubit states under experimental restrictions. We consider a realistic scenario in which an ancillary system with a limited number of levels performs restricted sequential interactions with qubits in a row. The proposed method relies on a suitable local optimization procedure, yielding an efficient recipe for the realistic and approximate sequential generation of any entangled multiqubit state. We give paradigmatic examples that may be of interest for theoretical and experimental developments.

We present a practical scheme by global addressing to deterministically entangle negatively charged nitrogen-vacancy $\left(\text{N-}V\right)$ centers in distant diamonds using a nanomechanical cantilever with the magnetic tips strongly coupled to the $\text{N-}V$ electron spins. Symmetric Dicke states are generated as an example, and the experimental feasibility and challenge of our scheme are discussed.

The majority of research on intense $\left(\sim {10}^{14}\text{W}/{\text{cm}}^2\right)$ ultrashort $\left(<100\text{fs}\right)$ laser-molecule interactions has been focused on studies of ${\text{H}}_2^{+}$ fragmentation, mainly due to its elemental structure. So far the bulk of this work has been conducted using near infrared light while studies at shorter wavelengths are comparatively scarce. We report a detailed investigation of the interaction of 395 nm, 40 fs pulses with an ${\text{HD}}^{+}$ molecular-ion beam, measured using a coincidence three-dimensional momentum imaging technique. This allows us to clearly discriminate dissociation and ionization channels. From the kinetic energy and angular distributions, insight is gained into the intensity dependence of the main breakup processes. We observe the onset of above-threshold dissociation above ${10}^{14}\text{W}/{\text{cm}}^2$, a higher intensity than required for 790 nm due to a smaller transition dipole moment for the low vibrational states probed at 395 nm. Ionization spectra display structure consistent with the above-threshold Coulomb explosion mechanism that we have proposed [B. D. Esry et al., Phys. Rev. Lett. 97, 013003 (2006)].

We study the zero-temperature phase diagram of a gas of bosonic ${}^{87}\text{R}\text{b}$ atoms in two-color superlattice potentials starting directly from the experimental parameters, such as wavelengths and intensities of the two lasers generating the superlattice. In a first step, we map the experimental setup to a Bose-Hubbard Hamiltonian with site-dependent parameters through approximate band-structure calculations. In the second step, we solve the many-body problem using the density-matrix renormalization-group approach and compute observables such as energy gap, condensate fraction, maximum number fluctuations, and visibility of interference fringes. We study the phase diagram as function of the laser intensities $s_2$ and $s_1$ as control parameters and show that all relevant quantum phases, i.e., superfluid, Mott-insulator, and quasi-Bose-glass phase, and the transitions between them can be investigated through a variation of these intensities alone.

Highly precise energy values for the first 14 ${{}^{3}P}^e$ bound states of helium arising out of two electrons having equal azimuthal quantum number are being calculated by using Ritz variational method. The present calculated upper bound energies are lowest yet obtained. Resonance energies and widths for a wide range of resonance states $\left({{}^{3}P}^e\right)$ of helium below $N=3–5$ ionization threshold of ${\text{He}}^{+}$ have also been evaluated by using stabilization method. The present resonance parameters for the region below $N=3–5$ ionization threshold of ${\text{He}}^{+}$ are in excellent agreement with the few available accurate theoretical results. Moreover in the present paper, the resonance parameters of ${{}^{3}P}^e$ resonance states below $N=6$ and 7 ionization thresholds of ${\text{He}}^{+}$ are also reported.

We have performed very accurate quantum mechanical calculations of the five lowest $S$ states of the beryllium atom. In the nonrelativistic part of the calculations we used the variational method and we explicitly included the nuclear motion in the Schrödinger equation. The nonrelativistic wave functions of the five states were expanded in terms of explicitly correlated Gaussian functions. These wave functions were used to calculate the leading ${\alpha }^2$ relativistic correction ($\alpha$ is the fine structure constant) and the ${\alpha }^3$ quantum electrodynamics (QED) correction. We also estimated the ${\alpha }^4$ QED correction by calculating its dominant component. A comparison of the experimental transition frequencies with the frequencies obtained based on the energies calculated in this work shows an excellent agreement.

Charge transfer processes due to collisions of ground-state ${\text{C}}^{3+}\left(1s^{2}2s{}^{2}S\right)$ ions with He atoms are studied using the quantum-mechanical molecular-orbital close-coupling method for energies in the range ${10}^{-4}–2\times {10}^3\text{eV}/\text{u}$. The ab initio adiabatic potentials and radial couplings utilized in the calculations are obtained from the multireference single- and double-excitation configuration interaction approach. Total and state-selective single-electron capture cross sections and rate coefficients are calculated and compared with the available experimental and theoretical data. A good agreement is found between the measured cross sections and the present calculations. However, the previous calculations of total rate coefficients using the Landau-Zener model are one to two orders of magnitude smaller than the present results.

The $R$ matrix with pseudostate (RMPS) method has been employed to perform nonperturbative calculations of the total cross sections for single-photon double photoionization of ground-state Ne. A series of calculations was performed in which the number of pseudostates included in the close-coupling expansion was varied. Within the constraints of currently available massively parallel computers, we were able to achieve reasonably good convergence of the double photoionization cross section for Ne. The final RMPS results in both the length and the velocity gauges are compared to double photoionization cross sections determined from many-body perturbation-theory calculations and synchrotron measurements.

When chromatic dispersion operates together with two-dimensional diffraction, the degenerate optical parametric oscillator exhibits three-dimensional (3D) localized structures in a regime devoid of Turing or modulational instabilities. They consist of single lamella, cylinder, or light drops. These 3D structures are generated spontaneously from a weak random noise. We construct 3D bifurcation diagrams associated with these structures. We show that a single cylinder and a single light drop exhibit an overlapping domain of stability. Finally, for a large input intensity, we identify a self-pulsing behavior affecting the stability of 3D localized structures.