A many-body theory for interacting bosons is developed within the framework of minimizing the ground-state energy with respect to the two-particle reduced-density matrix (2-RDM) subject to $N$-representability conditions. The $N$-representability conditions, which ensure that the 2-RDM may be derived from an $N$-particle wave function, are imposed through a hierarchy of positivity conditions where the $p$-positivity conditions restrict the metric matrices for $p∕2$-body operators to be positive semidefinite. Using two-positivity, we minimize the ground-state energies of $5–\mathrm{10\hspace{0.17em}000}$ harmonically interacting bosons in a harmonic external potential. The energies and 2-RDMs obtained are in agreement with the exact solution except for round-off errors, which implies that for this class of boson interactions two-positivity conditions alone yield exact results for any interaction strength. The ground-state energies obtained at strong interactions are more accurate than many-body perturbative techniques by many orders of magnitude.

We report a unique feature of magnetic-field Feshbach resonances in which atoms collide with nonzero orbital angular momentum. $p$-wave $\left(l=1\right)$ Feshbach resonances are split into two components depending on the magnitude of the resonant state’s projection of orbital angular momentum onto the field axis. This splitting is due to the magnetic dipole-dipole interaction between the atoms and it offers a means to tune anisotropic interactions of an ultracold gas of atoms. Furthermore this splitting in the $p$-wave Feshbach resonance has been experimentally observed and is reported. A parametrization of the $p$-wave resonance in terms of an effective-range expansion is given.

Electron-impact ejected-electron spectra of $\text{Xe}$ autoionizing levels between the ${}^{2}P_{3∕2}$ and ${}^{2}P_{1∕2}$ ionic limits have been measured for incident energies from 16 to $150\text{eV}$ and angles of ejection $50°$, $90°$, and $130°$ with respect to the incident beam direction. The spectra have been interpreted by the addition and subtraction of spectra at different angles and energies. Using these techniques, the gradual transition has been observed from mainly dipole excitation at high incident energies to the domination of nondipole and exchange excitation processes at the lowest energies.

In this paper we propose a tight-binding molecular dynamics with parameters fitted to first-principles calculations on the smaller clusters and with an environment correction, to be a powerful technique for studying large transition-metal/noble-metal clusters. In particular, the structure and stability of ${\text{Cu}}_n$ clusters for $n=3–55$ are studied by using this technique. The results for small ${\text{Cu}}_n$ clusters $\left(n=3–9\right)$ show good agreement with ab initio calculations and available experimental results. In the size range $10⩽n⩽55$ most of the clusters adopt icosahedral structure which can be derived from the 13-atom icosahedron, the polyicosahedral 19-, 23-, and 26-atom clusters, and the 55-atom icosahedron, by adding or removing atoms. However, a local geometrical change from icosahedral to decahedral structure is observed for $n=40–44$ and return to the icosahedral growth pattern is found at $n=45$ which continues. Electronic “magic numbers” ($n=2$,$8$,$20$,$34$,$40$) in this regime are correctly reproduced. Due to electron pairing in highest occupied molecular orbitals (HOMOs), even-odd alternation is found. A sudden loss of even-odd alternation in second difference of cluster binding energy, HOMO-LUMO (LUMO, lowest unoccupied molecular orbital) gap energy and ionization potential is observed in the region $n\sim 40$ due to structural change there. Interplay between electronic and geometrical structure is found.

For the description of nonsequential double ionization (NSDI) of rare-gas atoms by a strong linearly polarized laser field, the quantum-mechanical $S$-matrix diagram that incorporates rescattering impact ionization is evaluated in the strong-field approximation. We employ a uniform approximation, which is a generalization of the standard saddle-point approximation. We systematically analyze the manifestations of the electron-electron interaction in the momentum distributions of the ejected electrons: for the interaction, by which the returning electron frees the bound electron, we adopt either a (three-body) contact interaction or a Coulomb interaction, and we do or do not incorporate the mutual Coulomb repulsion of the two electrons in their final state. In particular, we investigate the correlation of the momentum components parallel to the laser-field polarization, with the transverse momentum components either restricted to certain finite ranges or entirely summed over. In the latter case, agreement with experimental data is best for the contact interaction and without final-state repulsion. In the former, if the transverse momenta are restricted to small values, comparison of theory with the data shows evidence of Coulomb effects. We propose that experimental data selecting events with small transverse momenta of both electrons are particularly promising in the elucidation of the dynamics of NSDI. Also, a classical approximation of the quantum-mechanical $S$ matrix is formulated and shown to work very well inside the classically allowed region.

We consider propagation of density wave packets in a Bose-Einstein condensate. We show that the shape of initially broad, laser-induced, density perturbation changes in the course of free time evolution so that a shock wave front finally forms. Our results are well beyond predictions of commonly used zero-amplitude approach, so they can be useful in extraction of a speed of sound from experimental data. We discuss a simple experimental setup for shock propagation and point out possible limitations of the mean-field approach for description of shock phenomena in a Bose-Einstein condensate.

We describe the resonant interaction of an atom with a strongly focused light beam by expanding the field in multipole waves. For a classical field, or when the field is described by a coherent state, we find that both intensity pattern and photon statistics of the scattered light are fully determined by a small set of parameters. One crucial parameter is the overlap of the field with the appropriate dipole wave corresponding to the relevant dipole transition in the atom. We calculate this overlap for a particular set of strongly focused longitudinally polarized light beams, whose spot size is only $0.1{\lambda }^2$, as discussed by S. Quabis et al. [Appl. Phys. B 72, 109 (2001)].

We report on a joint experimental and theoretical study of 50-eV electron-impact ionization of rubidium. Comparison of the experimental data with theoretical predictions from various models shows good qualitative agreement, as long as distortion and channel-coupling effects in the projectile-target interaction are accounted for. The remaining differences between experiment and theory indicate the need for further studies of this collision system.

We study triatomic systems in the regime of large negative scattering lengths which may be more favorable for the formation of condensed trimers in trapped ultracold monoatomic gases as the competition with the weakly bound dimers is absent. The manipulation of the scattering length can turn an excited weakly bound Efimov trimer into a continuum resonance. Its energy and width are described by universal scaling functions written in terms of the scattering length and the binding energy $B_3$ of the shallowest triatomic molecule. For $a^{-1}<-0.0297\sqrt{m{B}_3∕{\hslash }^2}$, the excited Efimov state turns into a continuum resonance.

The possibility of Bloch oscillations for a degenerate and superfluid Fermi gas of atoms in an optical lattice is considered. For a one-component degenerate gas the oscillations are suppressed for high temperatures and band fillings. For a two-component gas, Landau criterion is used for specifying the regime where robust Bloch oscillations of the superfluid may be observed. We show how the amplitude of Bloch oscillations varies along the crossover from BCS to Bose-Einstein condensation.

In this paper we investigate the dispersive and absorptive properties of a system of three-level cascade atoms driven by a strong coherent field. Three characteristic features are found. First, for the same set of atom-light interaction parameters, the indices of refraction are large at three different frequencies where the absorption vanishes. These three frequencies are determined by the resonance transition frequencies between dressed states produced by the strong driving field. Second, negative dispersion without absorption, which leads to superluminal light propagation, is achievable in the central resonance structure of the dispersion spectrum. Third, the whole absorption spectrum displays, in general, three pairs of absorption peaks and three pairs of gain (negative absorption) peaks. The minimal spacing between dressed states determines whether the outer adjacent gain peaks are separated from each other.

A propagating exterior complex scaling method, with iterative coupling, has been adapted for the electron impact of charged hydrogenic targets. Using this fully ab initio method for solving the Schrödinger equation, which has no uncontrolled approximations, we present highly accurate total, single-differential, double-differential, and triple-differential cross-section calculations for the electron-impact ionization of hydrogenic targets with nuclear charge $Z⩽4$ (H, ${\text{He}}^{+}$, ${\text{Li}}^{2+}$, ${\text{Be}}^{3+}$). For a fixed scaled energy, the total and differential cross sections begin to converge with respect to increasing $Z$ when scaled by $Z^4$ and $Z^6$, respectively, and converge more rapidly with increasing incident-electron energy. The angular distributions of the differential cross sections change systematically with increasing nuclear charge for energies above the peak total ionization cross section, but for some lower-energy kinematics the triple-differential cross section for charged targets is significantly different from that of atomic hydrogen.

Expanding the wave function in terms of eigenstates, we calculated the population redistribution of high-Rydberg hydrogen atoms under the interactions of external time-dependent electromagnetic fields. Our numerical results show that populations of Rydberg atoms can be driven down to lower $n$ levels with a train of half-cycle pulses. Oscillations of the Rydberg population through both $n$ levels and $l$ levels are observed during these interactions. The approach may have applications in providing an effective mechanism for producing near ground-state atoms from the initially high-Rydberg distributions found in recombining ultracold plasmas such as encountered in the antihydrogen trapping experiments at CERN.

We demonstrate a Raman amplifier for matter waves, where the amplified atoms and the gain medium are in two different hyperfine states. This amplifier is based on a form of superradiance that arises from self-stimulated Raman scattering in a Bose-Einstein condensate.

We describe an experiment in which a physical qubit represented by the polarization state of a single photon was probabilistically encoded in the logical state of two photons. The experiment relied on linear optics, postselection, and three-photon interference effects produced by a parametric down-conversion photon pair and a weak coherent state. An interesting consequence of the encoding operation was the ability to observe entangled three-photon Greenberger-Horne-Zeilinger states.

We proposed a method for the creation of spatially separated spin entaglement by means of adiabatic passage of an external gate voltage in a triple-quantum-dot system.

The lowest $E{}^3\sum ^{+}\left(6{}^{3}S_1\right)$ Rydberg state of the CdKr van der Waals complex was investigated using supersonic-expansion beam and the optical-optical double-resonance methods. Well-defined vibrational levels $A{}^{3}0_{v^{″}=9}^{+}\left({}^3\Pi \right)$ and $B{}^{3}1_{v^{″}=1}^{+}\left({}^3\sum ^{+}\right)$ were used as intermediate states being excited from the $X{}^{1}0^{+}\left({}^1\sum ^{+}\right)$ ground state. Two types of bound-bound excitation spectra of the $E{}^3\sum ^{+}\leftarrow A{}^{3}0^{+}$ and $E{}^3\sum ^{+}\leftarrow B{}^{3}1$ transitions were observed and recorded. The analyses of the spectra suggest an existence of two, well-defined minima in the $E{}^3\sum ^{+}$-state potential-energy (PE) curve: an inner PE well $E_1$ with $D_{\mathrm{e}}^{\prime }\left(E_1\right)=1656{\text{cm}}^{-1}$ and an outer well $E_2$ with $D_{\mathrm{e}}^{\prime }\left(E_2\right)=27{\text{cm}}^{-1}$, separated from each other by a positive-energy barrier. Combination of bound-bound spectra excited from different intermediate states enabled probing of the $E{}^3\sum ^{+}$-state potential in a relatively large range of internuclear separations $R$ and hence it led to a complete determination of spectroscopical parameters of the $E{}^3\sum ^{+}$-state PE curve. The height of the barrier and its approximate location were also determined. The experimental results of this investigation coincide well with the results of ab initio calculation of Czuchaj and co-workers [Chem. Phys. 248, 1 (1999); Theor. Chem. Acc. 105, 219 (2001)].

The first three electronically excited states in the alkaline-earth-metal atoms magnesium, calcium, and strontium comprise the $\left(nsnp\right){}^{3}P_J^o\left(J=0,1,2\right)$ fine-structure manifold. All three states are metastable and are of interest for optical atomic clocks as well as for cold-collision physics. An efficient technique—based on a physically motivated potential that models the presence of the ionic core—is employed to solve the Schrödinger equation for the two-electron valence shell. In this way, radiative lifetimes, laser-induced clock shifts, and long-range interaction parameters are calculated for metastable Mg, Ca, and Sr.

We have studied the decay of hollow atoms formed in ${\text{Ne}}^{10+}{\text{−}\mathrm{C}}_{60}$ collisions at low energy $\left(E=100\text{keV}\right)$. The decay products of hollow atoms, i.e., the scattered projectiles and the number of ejected electrons from autoionization cascades, have been measured. The projectile energy loss has been analyzed as a function of the final charge state, in order to differentiate collisions at large distance, near the ${\mathrm{C}}_{60}$ through the electronic clouds and inside the ${\mathrm{C}}_{60}$ cage. For scattered projectiles ${\text{Ne}}^{8+}$ where two electrons are stabilized $\left(s=2\right)$, up to 16 ejected electrons have been observed, and lower energy loss compared to projectiles with more stabilized electrons $\left(s>2\right)$ has been measured. These results are interpreted by the formation and relaxation of completely neutralized compact hollow atoms passing very close to the ${\mathrm{C}}_{60}$ molecule (into the electron clouds). The observed large number of ejected electrons is explained by a direct filling of the $N$ shell during the interaction time and a fast decay via quasicomplete autoionization cascades.

For mixtures of Bose and Fermi alkali-metal atoms, the fermion degrees of freedom can be integrated out in their finite temperature partition function. The final result can be expanded as a power series in the boson density. Under appropriate conditions, the pairwise interaction between the bosons can be changed from positive to negative by the fermion-mediated term at a low enough temperature. The boson cloud may then collapse. For attractive fermion-boson interactions, there is also a collapse of the fermion cloud. This transition is first order (discontinuous) because the leading-order nonlinear interaction term between the bosons is third order in boson density with a negative coefficient. We discuss the finite-temperature phase diagram of this transition. Our result may provide for an explanation of recent experimental observations by Modugno and co-workers.