We study dipolar bosons in a 1D optical lattice and identify a region in parameter space—strong coupling but relatively weak on-site repulsion—hosting a series of stable charge-density-wave (CDW) states whose low-energy excitations, built from “fractional domain walls,” have remarkable similarities to those of non-Abelian fractional quantum Hall states. Here, a conventional domain wall between translated CDW's may be split by inserting strings of degenerate, but inequivalent, CDW states. Outside these insulating regions, we find numerous supersolids as well as a superfluid regime. The mentioned phases should be accessible experimentally and, in particular, the fractional domain walls can be created in the ground state using single-site addressing, i.e., by locally changing the chemical potential.

We consider a superfluid cloud composed of a Bose-Einstein condensate oscillating within a magnetic trap (dipole mode) where, due to the existence of a Feshbach resonance, an effective periodic time-dependent modulation in the scattering length is introduced. Under this condition, collective excitations such as the quadrupole mode can take place. We approach this problem by employing both the Gaussian and the Thomas-Fermi variational Ansätze. The resulting dynamic equations are analyzed by considering both linear approximations and numerical solutions, where we observe coupling between dipole and quadrupole modes. Aspects of this coupling related to the variation of the dipole oscillation amplitude are analyzed. This may be a relevant effect in situations where oscillation in a magnetic field in the presence of a bias field $B$ takes place, and should be considered in the interpretation of experimental results.

We unveil the relationship existing between the temperature of an ensemble of three-level atoms in a $\Lambda$ configuration, and the width of the emission cone of Stokes photons that are spontaneously emitted when atoms are excited by an optical pulse. This relationship, which is based on the amount of which-way information available about where the Stokes photon originated during the interaction, allows us to put forward a scheme to determine the temperature of atomic clouds by measuring the width of the emission cone. Unlike the commonly used time-of-flight measurements, with this technique, the atomic cloud is not destroyed during each measurement.

We theoretically analyze the temporal dynamics of strongly coupled quantum-dot–cavity system driven by a resonant laser pulse and observe the signature of Rabi oscillation in the time-resolved response of the system (i.e., in the numerically calculated cavity output). We derive simplified linear and nonlinear semiclassical models that approximate well the system's behavior in the limits of high- and low-power driving pulses and describe the role of quantum coherence in the exact dynamics of the system. Finally, we also present time-resolved transmission measurements showing the dynamics of a quantum-dot–cavity system in the presence of a short laser pulse.

In recent developments on the pair density needed to treat the non-Hartree-Fock-like part of interparticle repulsion, the natural orbitals and sign-correct expansion coefficients play a central role. Since, in principle, an infinite number of natural orbitals must be included, the convergence of expectation values due to finite-term approximations is an important issue. Here we discuss quantitatively this convergence problem based on an exactly solvable two-electron model atom, where the Schrödinger wave function for the ground state is expressible in terms of Löwdin's natural orbitals and sign-correct expansion coefficients. Using properly renormalized truncated series expansions for such an exact decomposition, the corresponding expectation values of the Schrödinger Hamiltonian are calculated analytically. A rapid and uniform convergence is found in these expectation values at given values of the coupling in the interparticle repulsion.

Positron scattering from sodium atoms has been studied theoretically with the use of the two-center convergent-close-coupling method. The target has been treated in the framework of a one-active-electron approach. The positronium formation channels are taken into account explicitly utilizing Laguerre-based states. Our calculations are overall in good agreement with the previous theoretical results, and so the discrepancy with experiment at low energies remains unresolved.

Radiative decay from the excited ${}^1{P}_1$ state to metastable ${}^3{P}_2$ and ${}^3{P}_0$ states is expected to limit the attainable trapped atomic population in a magneto-optic trap of ytterbium (Yb) atoms. In experiments we have carried out with optical repumping of ${}^3{P}_{0,2}$ states to ${}^3{P}_1$, we observe an enhanced yield of trapped atoms in the excited ${}^1{P}_1$ state. The individual decay rate to each metastable state is measured and the results show excellent agreement with the theoretical values.

We observed phonon hopping by using the radial vibrational motion of trapped ions and we investigated the properties of radial mode phonons, which can be used for quantum simulation of the Hubbard model. This study represents an essential step toward realizing a physical implementation of the Bose-Hubbard model with trapped ions.

Low-energy ($E_0$ $=$ 70.8 eV) electron-impact single ionization of a 3$p$ electron in argon has been studied experimentally and theoretically. Our measurements are performed using the so-called reaction microscope technique, which can cover nearly a full 4π solid angle for the emission of a secondary electron with energy below 15 eV and projectile scattering angles ranging from −8° to −30°. The measured cross sections are internormalized across all scattering angles and ejected energies. Several theoretical models were employed to predict the triple-differential cross sections (TDCSs). They include a standard distorted-wave Born approximation (DWBA), a modified version to account for the effects of postcollision interaction (DWBA-PCI), a hybrid second-order distorted-wave plus $R$-matrix (DWB2-RM) method, and the recently developed $B$-spline $R$-matrix with pseudostates (BSR) approach. The relative angular dependence of the BSR cross sections is generally found to be in reasonable agreement with experiment, and the importance of the PCI effect is clearly visible in this low-energy electron-impact ionization process. However, there remain significant differences in the magnitude of the calculated and the measured TDCSs.

We study the inelastic excitations of Xe for electrons with relatively high energies (500 or 750 eV) scattered over large angles, both experimentally and theoretically. In particular, we focus on the shape and intensity of the spectra of inelastically scattered electrons at the sharp dip in the elastic cross section near 135${}^{\circ }$ at 750 eV. Under these conditions, the first Born approximation predicts virtually zero intensity. However, in reality, measurable intensity is observed. Calculations carried out using the relativistic distorted-wave method describe the measurements reasonably well. A comparison is made between the calculations and previously published high-resolution studies. Overall agreement is quite good, especially for the lowest-energy excitations, but substantial differences are found for certain higher levels. The theory reproduces quite well the variations in intensity of the inelastic excitations for measurements near the dip in the elastic-scattering cross section, somewhat surprisingly, as the theories for elastic scattering and inelastic scattering are developed along completely different lines.

We report full quantum scattering calculations for low-energy near-threshold inelastic cross sections in Mg + H and Mg${}^{+}$ + H${}^{-}$ collisions. The calculations include all transitions between the eight lowest adiabatic MgH(${}^2{\Sigma }^{+}$) molecular states, with the uppermost of those diabatically extended to the ionic molecular state in the asymptotic region. This allows us to treat the excitation processes between the seven lowest atomic states of magnesium in collisions with hydrogen atoms, as well as the ion-pair production and the mutual neutralization processes. The collision energy range is from threshold up to 10 eV. These results are important for astrophysical modeling of spectra in stellar atmospheres. The processes in question are carefully examined and several process mechanisms are found. Some mechanisms are determined by interactions between ionic and covalent configurations at relatively large internuclear distances, while others are based on short-range nonadiabatic regions due to interactions between covalent configurations.

We establish a numerical solution to the time-dependent Schrödinger equation employing an adaptive, discontinuous spectral element basis that automatically adjusts to the requested precision. The explicit time evolution is accomplished by a band-limited, gradient-corrected, symplectic propagator and uses separated representations of operators for efficient computation in multiple dimensions. We illustrate the method calculating accurate bound and continuum transition probabilities along with the photoelectron spectra for H(1$s$), He${}^{+}$(1$s$), and Li${}^{2+}$(2$s$) in three dimensions and H${{}_2}^{+}$ in three and four dimensions under a two-cycle attosecond laser pulse with driving frequency of 36 eV and an intensity of $1\times {10}^{15}\text{W}/{\text{cm}}^2$.

We discuss topological phase transitions in ultracold Fermi superfluids induced by interactions and artificial spin-orbit fields. We construct the phase diagram for population-imbalanced systems at zero and finite temperatures, and analyze spectroscopic and thermodynamic properties to characterize various phase transitions. For balanced systems, the evolution from Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate superfluids in the presence of spin-orbit effects is only a crossover as the system remains fully gapped, even though a triplet component of the order parameter emerges in the helicity basis. However, for imbalanced populations, spin-orbit fields induce a triplet component for the order parameter in the helicity basis, and may produce nodes in the quasiparticle excitation spectrum leading to bulk topological phase transitions of the Lifshitz type. Additionally a fully gapped phase exists, where a crossover from indirect to direct gap occurs, but a topological transition to a gapped phase possessing Majorana fermion edge states does not occur.

We experimentally study the effect of disorder on trapped quasi-two-dimensional (2D) ${}^{87}$Rb clouds in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The disorder correlation length is of the order of the Bose gas characteristic length scales (thermal de Broglie wavelength, healing length) and disorder thus modifies the physics at a microscopic level. We analyze the coherence properties of the cloud through measurements of the momentum distributions for two disorder strengths as a function of its degeneracy. For moderate disorder, the emergence of coherence remains steep but is shifted to a lower entropy. In contrast, for strong disorder, the growth of coherence is hindered. Our study is an experimental realization of the dirty boson problem in a well controlled atomic system suitable for quantitative analysis.

A previous fully relativistic time-dependent close-coupling method [Phys. Rev. A 81, 063431 (2010)], developed to study the photoionization of highly charged atomic ions, is substantially modified to include the full electromagnetic-field potential. Expansion of a one active electron wave function for the time-dependent Dirac equation in spin-orbit eigenfunctions yields close-coupled equations for bispinor radial wave functions. A spherical Bessel function expansion is then used to go beyond the Lorentz gauge dipole approximation to include higher order radiation field operators in both the Lorentz and Coulomb gauges. We test the high-order close-coupling method on the single photoionization of U${}^{91+}$.

We theoretically investigate time-resolved photoemission originating from two different shells ($1s$ and $2p$) of a fully correlated atomic two-electron model system ionized by an extreme-ultraviolet attosecond light pulse. The parameters of the model system are tuned such that the ionization potentials of the $1s$ and $2p$ electrons have values close to those of the $2s$ and $2p$ levels in a neon atom, for which a relative time delay has been measured in a recent attosecond streaking experiment by Schultze et al. [Science 328, 1658 (2010)]. Up to now theoretical efforts could account only for delays more than a factor of 2 shorter than the reported experimental value. By solving the time-dependent Schrödinger equation numerically exactly we explore the influence of correlations on the time delay previously implicated as one of the potential sources of discrepancies. We investigate the influence of the interplay between electron interactions and the probing streaking infrared field on the extracted relative delays between the two emission channels. We find that for our model system the inclusion of electronic correlation only slightly modifies the time shifts, as compared to a mean-field treatment. In particular, the correlation-induced time delay is contained in the Eisenbud-Wigner-Smith time delay for the photoionization process.

Experiments on one- and two-photon laser excitation of ${}^{232}$Th${}^{+}$ ions in a radio-frequency ion trap are reported. As the first excitation step, the strongest resonance line at 402 nm from the $\left(6d^{2}7s\right)J=3/2$ ground state to the $\left(6d7s7p\right)J=5/2$ state at 24874 cm${}^{-1}$ is driven by radiation from an extended-cavity diode laser. Spontaneous decay of the intermediate state populates a number of low-lying metastable states, thus limiting the excited state population and fluorescence signal obtainable with continuous laser excitation. We study the collisional quenching efficiency of helium, argon, and nitrogen buffer gases, and the effect of repumping laser excitation from the three lowest-lying metastable levels. The experimental results are compared with a four-level rate equation model, which allows us to deduce quenching rates for these buffer gases. Using laser radiation at 399 nm for the second step, we demonstrate two-photon excitation to the state at 49 960 cm${}^{-1}$, among the highest-lying classified levels of Th${}^{+}$. This is of interest as a test case for the search for higher-lying levels in the range above 55 000 cm${}^{-1}$ which can resonantly enhance the excitation of the ${}^{229}$Th${}^{+}$ nuclear resonance through an inverse two-photon electronic bridge process.

The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional (3D) inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.