We numerically investigate the spatiotemporal dynamics of a circular flow mode in a ring array of Bose-Einstein condensates, which consists of $M$ identical Bose-Einstein condensates that couple to the nearest-neighbor sites by tunneling. Introducing a rotational potential in the Gross-Pitaevskii equation, a series of circular flow modes is resonantly excited. For the initial conditions with uniform density and one-round phase difference of $2\pi \ell \left(l=0,1,\dots ,M-1\right)$, two circular flow modes are excited for each circulation-quantized number $l$. It is shown that these circular flow modes periodically appear in time in the presence of the rotational field and persistently survive with a constant shape even after the external potential is removed, the transitions between the circular flow modes with different quantized number $l$ can be realized by applying the phase-imprinting optical pulses, and the rotational velocity of the circular flow mode can be continuously modulated by adiabatically tuning the scattering length in a magnetic field, i.e., by use of the Feshbach resonance.

The single-vortex problem in a strongly correlated bosonic system is investigated self-consistently within the mean-field theory of the Bose-Hubbard model. Near the superfluid–Mott-insulator transition, the vortex core has a tendency toward the Mott-insulating phase, with the core particle density approaching the nearest commensurate value. If the nearest-neighbor repulsion exists, the charge-density wave order may develop locally in the core. The evolution of the vortex configuration from the strong- to weak-coupling regions is studied. This phenomenon can be observed in systems of rotating ultracold atoms in optical lattices and Josephson-junction arrays.

We study the continuous resonant four-wave mixing in a medium of atoms with a modified double-$\Lambda$ level configuration. Under the far-off-resonance condition for a pair of levels, we reduce the five-level scheme to an effective three-level scheme, with a two-photon coupling between the two lower levels. We derive the exact steady-state solution to the density-matrix equations for the reduced scheme and obtain the wave-mixing equations for the fields in the continuous-wave regime. We show that the upper-level decay may substantially affect the resonantly enhanced wave-mixing process. We demonstrate that this decay shortens the conversion cycle rather than prolongs it.

We show theoretically how two-photon fields generated by spontaneous parametric down-conversion can be used for creating maximally entangled states of multidimensional quantum systems, qudits. Logical states are defined by using different transverse spatial modes of the twin photons. These spatial modes are created by sending the components of the two-photon field through an array of multislits. The present experimental facilities allow generating maximally entangled states up to an eight-dimensional system.

Cross sections have been determined for direct excitation, ionization, and electron transfer in collisions between H, He, Li, and Be nuclei and ${\mathrm{C}}^{5+}\left(1s\right)$ target ions at nuclear energies $1–24$ MeV/nucleon, extending earlier work [Phys. Rev. A 56, 2903 (1997)] to higher energies. Coupled Sturmian pseudostates of principal quantum number at least up to 30 have been included for each angular momentum $s$, $p$, $d$, and $f$ centered on the C nucleus, as well as a $1s$ state centered on the projectile. Detailed basis-convergence studies have been carried out. Cross sections have been compared with the corresponding Born results, and scaling rules have also been examined.

We perform a dynamical symmetry analysis (DSA) of the high-order harmonic generation (HHG) spectrum of an atom interacting with a bichromatic laser field. Within the framework of the conventional Hermitian quantum mechanics (QM), the HHG spectrum calculated using a single Floquet state, or any finite number of Floquet states, is invariant under the inversion of the relative phase of the two-frequency components, $\varphi \to -\varphi$. The asymmetry with respect to the phase inversion seen in the simulated HHG spectra is obtained in the conventional QM only when the Floquet spectrum is continuous and ionization is taken into consideration. However, when the Hamiltonian is complex scaled the description is different. Even a single eigenstate of the complex scaled Floquet operator is enough to describe the breaking of the $\varphi \to -\varphi$ symmetry in the HHG spectra. We find that there is a direct correlation between the strength of the asymmetry with respect to the relative phase inversion and the magnitude of the ionization rate. For illustration purposes, the DSA is accompanied by the results obtained for a one-dimensional effective single-electron model Hamiltonian mimicking xenon atom interacting with strong laser field.

We present an ab initio method of calculation of isotope shift in atoms with a few valence electrons, based on the configuration-interaction calculation of energy. The main motivation for developing the method comes from the need to analyze whether differences in isotope abundance in early universe can contribute to the observed anomalies in quasar absorption spectra. The current best explanation for these anomalies is the assumption that the fine structure constant $\alpha$ was smaller at early epoch. We show that we can calculate the isotope shift in magnesium with good accuracy.

The recent prediction of a total zero angular momentum bound state of the spin-polarized atomic tritium trimer [D. Blume, B. D. Esry, Chris H. Greene, N. N. Klausen, and G. J. Hanna, Phys. Rev. Lett. 89, 163402 (2002)] was verified. Searches using our smooth exterior complex scaling finite element method gave no evidence for any zero or nonzero angular momentum shape resonances of the system.

Blinder [Phys. Rev. A, 43, 13 (1991)] has given an explicit diagonal form for the nonrelativistic Coulomb propagator. His result is an infinite series involving Whittaker, Laguerre, Hermite, and error functions. However, he notes that at the nucleus, only error functions remain in the infinite series. Here, an off-diagonal generalization of Blinder’s result at the nucleus is constructed. By relating this result to the Green function, it is then shown that one is led in this latter representation to an explicit sum of Blinder’s infinite series. Finally, contact is established between the present off-diagonal study and the recent work of Chibisov et al. [Phys. Rev. Lett. 84, 451 (2000)] on the Coulomb Green function.

We investigate the effect of imperfections in realistic detectors upon the problem of quantum state and parameter estimation by continuous monitoring of an open quantum system. Specifically, we have reexamined the system of a two-level atom with an unknown Rabi frequency introduced by Gambetta and Wiseman [Phys. Rev. A 64, 042105 (2001)]. We consider only direct photodetection and use the realistic quantum trajectory theory reported by Warszawski, Wiseman, and Mabuchi [Phys. Rev. A 65, 023802 (2002)]. The most significant effect comes from a finite bandwidth, corresponding to an uncertainty in the response time of the photodiode. Unless the bandwidth is significantly greater than the Rabi frequency, the observer’s ability to obtain information about the unknown Rabi frequency, and about the state of the atom, is severely compromised. This result has implications for quantum control in the presence of unknown parameters for realistic detectors, and even for ideal detectors, as it implies that most of the information in the measurement record is contained in the precise timing of the detections.

We use a Heisenberg spin-1∕2 chain to investigate how chaos and localization may affect the entanglement of pairs of qubits. To measure how much entangled a pair is, we compute its concurrence, which is then analyzed in the delocalized (localized) and in the chaotic (nonchaotic) regimes. Our results indicate that chaos reduces entanglement and that entanglement decreases in the region of strong localization. In the transition region from a chaotic to a nonchaotic regime localization increases entanglement. We also show that entanglement is larger for strongly interacting qubits (nearest neighbors) than for weakly interacting qubits (next and next-next neighbors).

Relativistic energy-consistent small-core lanthanide pseudopotential multireference configuration-interaction (MRCI) studies yield 15 bound states for ${\text{Ce}}^{-}$. These include twelve bound states with $5d$ attachment with the following electron affinities (in meV with corresponding $J$ in parentheses): 530 (7∕2), 421 (9∕2), 332 (7∕2), 276 (9∕2), 242 (9∕2), 229 (11∕2), 168 (5∕2), 101 (11∕2), 96 (7∕2), 84 (13∕2), 62 (3∕2), 18 (5∕2). The remaining three bound states result from $6p$ attachment with the following electron affinities: 156 (9∕2), 80 (5∕2), 8 (7∕2). Considering averaged coupled pair functional-type corrections to the MRCI value as well as possible finite basis set errors the final relativistic result for the electron affinity of Ce is $0.58\pm 0.1\text{eV}$. The present results are compared to experimental measurements, as well as to data from other theoretical calculations.

We report beam-loss photoassociation (PA) spectra of cold collisions within a slow, bright Na atom beam near the $D_1$ resonance line. The high collimation and brilliance of the atomic beam permits the detection of atomic fluorescence loss resulting from the photoassociation of cold sodium atoms. The results show that even at high PA laser intensities, where strong coupling of the colliding atoms to the optical field might obscure spectral features, vibrational and rotational progressions are surprisingly well resolved. We attribute the conservation of narrow spectral features to the properties of the saturated line shapes and to the unconventional collision energy distribution in one-dimensional (1D) single-beam collisions compared to 3D collisions in a gas cell.

Using measured cross sections, empirical scaling laws are extracted for projectile stripping induced by collisions with a many-electron target. By scaling both the cross sections and the impact velocities, it is shown that a single universal curve can be used to fit data for single and multiple electron loss from negative ions, neutral particles, and singly or multiply charged positive ions. The scaling applies to projectiles ranging from hydrogen to uranium and collision energies ranging from below $\text{keV}∕\mathrm{u}$ to hundreds of $\text{MeV}∕\mathrm{u}$. At high energies, existing data are consistent with a $v^{-1}$ impact velocity dependence for scaled velocities less than 10. Limited data imply that above 10 the velocity dependence becomes $v^{-2}$. Using our universal curve, cross sections are predicted for electron loss from low-charge-state heavy ions at 20 and $100\text{MeV}∕\mathrm{u}$.

A quantum-classical hybrid (or semiclassical) method is applied to protonium formation $\overline{p}+\mathrm{H}_2{}^{+}\to \overline{p}p+\mathrm{H}$ and dissociation $\overline{p}+\mathrm{H}_2{}^{+}\to \overline{p}+p+\mathrm{H}$ at kinetic energies up to $200\text{eV}$. The electronic motion is accurately solved quantum mechanically, while the motion of the heavy particles $\overline{p}$ and $p$ is described by classical mechanics. The $\overline{p}\text{−}p\text{−}p$ collinear configuration is assumed as a preliminary to three-dimensional calculations, and to assess the validity of the adiabatic approximation. Vibrational excitation to the dissociative continuum is crucial in $\overline{p}p$ formation in contrast to the importance of electron emission for the atomic-hydrogen target. For this reason, $\overline{p}p$ formation occurs efficiently even well beyond the ionization threshold if the target is a molecule.

The dynamics of multiphoton processes in $\mathrm{H}_2{}^{+}$ ions interacting with strong femtosecond fields is investigated by solving the time-dependent Schrödinger equation in the Born-Oppenheimer approximation. We use a spectral method with prolate spheroidal coordinates to represent the electronic wave functions. The theoretical approach is of spectral type in which the electronic and vibrational wave functions are represented with $L^2$ basis functions. In order to check the accuracy of these wave functions we have investigated the cases of the multiphoton ionization and dissociation of $\mathrm{H}_2{}^{+}$ at long wavelengths. First, we calculate the ionization probabilities and the electron spectra at $228\text{nm}$ and $400\text{nm}$, and we compare our results with other calculations when available. The effect of the initial dispersion of the internuclear distance $R$ in the equilibrium region is discussed in the context of short pulses. Then, we study the dissociation of $\mathrm{H}_2{}^{+}$ at $350\text{nm}$ and we compare our results with other recent calculations. Finally, the case of two-photon ionization of $\mathrm{H}_2{}^{+}$ at short wavelength is investigated, and we examine the electronic and vibrational spectra that have been obtained.

We present a theory for the linear dynamics of a weakly interacting Bose gas confined inside a harmonic trap at finite temperature. The theory treats the motions of the condensate and of the noncondensate on an equal footing within a generalized random-phase approximation, which (i) extends the second-order Beliaev-Popov approach by allowing for the dynamical coupling between fluctuations in the thermal cloud, and (ii) reduces to an earlier random-phase scheme when the anomalous density fluctuations are omitted. Numerical calculations of the low-lying spectra in the case of isotropic confinement show that the present theory obeys with high accuracy the generalized Kohn theorem for the dipolar excitations and demonstrate that combined normal and anomalous density fluctuations play an important role in the monopolar excitations of the condensate. Mean-field theory is instead found to yield accurate results for the quadrupolar modes of the condensate. Although the restriction to spherical confinement prevents quantitative comparisons with measured spectra, it appears that the non-mean-field effects that we examine may be relevant to explain the features exhibited by the breathing mode as a function of temperature in the experiments carried out at JILA on a gas of ${}^{87}\mathrm{Rb}$ atoms.

We study rotational motion of an interacting atomic Bose-Einstein condensate confined in a quadratic-plus-quartic potential. We calculate the lowest energy surface mode frequency and show that a symmetric trapped (harmonic and quartic) Bose-Einstein condensate breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We argue that the formation of a vortex is not possible in a noninteracting as well as in an attractive Bose-Einstein condensate confined in a harmonic trap due to the absence of the spontaneous shape deformation, but it can occur which leads to the vortex formation if we add an additional quartic potential. Moreover, the spontaneous shape deformation and consequently the formation of a vortex in an attractive system depends on the strengths of the two-body interaction and the quartic potential.