We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a $F=1$ ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.

Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic “perturbative” equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed.

We report detailed spectroscopic measurements of the $X\left(0\right)\left[{}^1\Sigma ^{+}\right](v=0)\to B\left(1\right)\left[{}^3\Pi \right](v=5)$ transition in PbO. Using a Stark-modulated laser absorption technique, we have measured the hyperfine constant of ${}^{207}\mathrm{Pb}\mathrm{O}$ in the $B\left(1\right)$ state, as well as the $B\left(1\right)(v=5)$ rotational constant, $X\text{−}B$ isotope shifts, etc. The hyperfine constant of the $B\left(1\right)$ state is of interest as a benchmark for calculations of PbO electronic structure related to experiments to search for the electric dipole moment of the electron.

Fullerenelike nanostructures of silicon with two and four carbon atoms substituted on the surface of ${\mathrm{Si}}_{60}$ cages, as well as inside the cage at various symmetry orientations, have been studied within the generalized-gradient approximation to density-functional theory. Full geometry optimizations have been performed without any symmetry constraints using the GAUSSIAN 03 suite of programs and the Los Alamos National Laboratory 2 double-$\zeta$ basis set. For the silicon atom, the Hay-Wadt pseudopotential with the associated basis set are used for the core electrons and the valence electrons, respectively. For the carbon atom, the Dunning-Huzinaga double-$\zeta$ basis set is employed. Electronic and geometric properties of the nanostructures are presented and discussed in detail. It was found that optimized silicon-carbon fullerenelike cages have increased stability compared to the bare ${\mathrm{Si}}_{60}$ cage and the stability depends on the number and orientation of carbon atoms, as well as on the nature of bonding between silicon and carbon atoms.

High-order harmonic generation (HHG) from a single hydrogen atom is studied analytically and numerically in the regime of small Keldysh parameter. The HHG spectra from different Coulomb-like model potentials, such as soft-core and/or one-dimensional (1D) potentials are compared to the three-dimensional (3D) Coulomb potential. It is shown, using analytic arguments, that the famous plateau in the HHG spectrum owes its existence to the Coulomb singularity, whereas soft-core potentials give spectra that fall off exponentially with increasing frequency. The idea is demonstrated numerically on a 3D soft-core potential that has the same long-range asymptotic behavior and ground-state energy as hydrogen. In addition, a number of widely used 1D Coulomb-like potentials are discussed. It is shown that in order that a 1D potential be a reasonable substitute for the 3D Coulomb potential, it must have a cusp singularity. A specific potential satisfying this criterion is proposed.

We report on an investigation of the beam profile of an atom laser extracted from a magnetically trapped ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. The transverse momentum distribution is magnified by a curved mirror for matter waves and a momentum resolution of $1∕60$ of a photon recoil is obtained. We find the transverse momentum distribution to be determined by the mean-field potential of the residing condensate, which leads to a nonsmooth transverse density distribution. Our experimental data are compared with a full three-dimensional simulation of the output coupling process and we find good agreement.

We have observed two-photon quantum interference in a Michelson interferometer. For the first time, we experimentally demonstrated two-photon quantum interference patterns, which show the transition from nonsubwavelength interference fringes to the general subwavelength interference. At the same time, a photon bunching effect was also shown by a postselection. The ∣1, 1⟩ state with a single photon in a mode corresponding to each arm of the interferometer was exclusively postselected by using path difference between two arms.

Electromagnetically induced transparency (EIT) resonance in a $\Lambda$ configuration is obtained when the frequencies of two fields are close to resonance with two of the transitions and their frequency difference matches the frequency of the third transition. In this situation the spectrum of one swept field as a probe gives a simple transparency feature. However, when an additional field drives the third transition the EIT feature associated with the probe is split. This perturbed EIT is illustrated for both single and bichromatic driving fields. In the single-driving-field case a density matrix treatment is shown to be in reasonable agreement with experiment, and in both single and bichromatic cases the structure in the spectrum can be explained using the dressed-state formalism. The dressed states can also be used to account for subharmonic resonances observed in the strong-probe regime.

The effect a perturbing field has on an electromagnetically induced transparency within a three-level $\Lambda$ system is presented. The perturbing field is applied resonant between one of the lower levels of the $\Lambda$ system and a fourth level. The electromagnetically induced transparency feature is split and this is measured experimentally for both single and bichromatic driving fields. In the single-driving-field case a density matrix treatment is shown to be in reasonable agreement with experiment and in both single and bichromatic cases the structure in the spectrum can be explained using a dressed-state analysis.

We study spontaneous emission from a pair of two-level atoms near a nanofiber. We demonstrate a substantial radiative exchange between distant atoms mediated by the guided modes of the nanofiber. The exchange is shown to lead to increased and decreased lifetimes of the subradiant and superradiant states, respectively. Our analysis is based on the full quantization of both the radiation and guided modes of the fiber in the framework of the Heisenberg-Langevin theory and the master equation formalism.

Quantum-optical permutation and parity observables are unitarily exchanged by a 50:50 beam splitter. Bosonic coalescence effects are reexamined from this point of view. We show that photon-number resolving counters behind a beam splitter define a permutation detector for the input optical field. With suitable phase encoding, the detector also enables Heisenberg-limited interferometry.

We report here the measurements of the complete valence shell binding energy spectra and the valence-orbital momentum profiles of butanone using the binary $(e,2e)$ electron momentum spectroscopy. The impact energy was $1200\mathrm{eV}$ plus the binding energy and the symmetric noncoplanar kinematics was used. The experimental momentum profiles of the valence orbitals are compared with the theoretical momentum distributions calculated using Hartree-Fock and density functional theory methods with various basis sets. The experimental measurements are generally described by theoretical calculations except for summed $4a^{″}$, $15a^{\prime }$, $3a^{″}$, and $14a^{\prime }$ orbital and summed $8a^{\prime }$, $7a^{\prime }$, and $6a^{\prime }$ orbitals.

The existence of stable orbital motion in a static attractive inverse square potential is predicted for nonpolar molecules with anisotropic polarizability interacting with a charged nanotube or nanowire. A simple three-degree-of-freedom model is constructed to illustrate the underlying physics and the binding characteristics. Numerical results using the diatomic molecule ${\mathrm{I}}_2$ as an example are also presented.

Mixing-demixing transition in one-dimensional mixtures of fermions and bosons is numerically investigated by changing various parameters such as number densities of each component, fermion-boson interactions, boson-boson interactions, and hopping energies. In most cases we found clear evidence of the mixing-demixing transitions and identified the roles of each microscopic parameter in the transitions. Several phase diagrams were obtained.

The dynamics of a fiber laser passively mode-locked through nonlinear polarization rotation is theoretically investigated. The model is based on an iterative equation for the nonlinear polarization rotation and the phase plates and on a scalar differential equation for the gain, the Kerr nonlinearity, and the dispersion. It is demonstrated that depending on the orientation of the phase plates, the laser can be continuous, mode-locked, or $Q$-switched. In the latter case, an additional equation for the gain dynamics must be taken into account. Hysteresis dependence of the operating regime versus the orientation angles of the phase plates is shown. A large bistability domain between the $Q$-switch and the continuous regimes is demonstrated. This model allows us to obtain the main features observed in passively-mode-locked fiber lasers.

An optical frequency standard based on an ensemble of neutral calcium atoms laser-cooled to $12\mu \mathrm{K}$ has been realized. By using ultracold atoms, one major previous source of uncertainty, the residual Doppler effect, was reduced. We show that cold collisions contribute a negligible amount to the uncertainty. The influence of a temporal evolution of the phase of the laser pulses used to interrogate the clock transition was measured and corrected for. The frequency of the clock transition at $657\mathrm{nm}$ was referenced to the caesium fountain clock of PTB utilizing a femtosecond comb generator with a fractional uncertainty of $1.2\times {10}^{-14}$. The transition frequency was determined to be $(455986240494144\pm 5.3)\mathrm{Hz}$, making the calcium clock transition one of the most accurately known optical transitions. A frequency stability of $3\times {10}^{-15}$ at $100\mathrm{s}$ averaging time was achieved and the noise contributions that limit to the observed stability were analyzed in detail. Additionally, the natural linewidth of the clock transition has been determined.

The experimental characterization of the electronic states correlated to the asymptote of ground state Na (3S) and Rb (5S) atoms was expanded by spectroscopic data on $a{}^3\Sigma ^{+}$ state levels using a high resolution Fourier transform spectroscopy technique. The hyperfine splitting of the $a{}^3\Sigma ^{+}$ state levels was partially resolved and analyzed for both $\mathrm{Na}{}^{85}\mathrm{Rb}$ and $\mathrm{Na}{}^{87}\mathrm{Rb}$ isotopomers. Transitions to high lying levels of the $a{}^3\Sigma ^{+}$ and $X{}^1\Sigma ^{+}$ states were recorded simultaneously which enables one to determine long range parameters of the molecular potentials. Coupled channels calculations based on the Fourier grid method were finally applied for deriving accurate potential energy curves of the $a{}^3\Sigma ^{+}$ and $X{}^1\Sigma ^{+}$ states capable of a reliable description of cold collisions between Na and Rb atoms in their ground states. Scattering lengths and Feshbach resonances were calculated for some quantum states.

We discuss absolute doubly differential cross sections (DDCS’s) for the energy and angular distributions (20°–160°) of secondary electrons produced in the collisions of 6.0- and $10.0\text{−}\mathrm{MeV}∕\mathrm{u}$ ${\mathrm{He}}^{2+}$ ions with water vapor. Details of our experiments were reported in our previous paper [D. Ohsawa et al., Nucl. Instrum. Methods Phys. Res. B 227, 431 (2005)], which mainly considered the total uncertainty $(\pm 13\%)$, as well as absolute DDCS data $(7–10000\mathrm{eV})$ by $6.0\text{−}\mathrm{MeV}∕\mathrm{u}$ ${\mathrm{He}}^{2+}$ ions. All DDCS data, including the newly obtained data $(20–12000\mathrm{eV})$ by $10.0\text{−}\mathrm{MeV}∕\mathrm{u}$ ${\mathrm{He}}^{2+}$ ions, are compared with classical theories after being corrected for relativistic effects. Based on the Rudd model and the Rutherford cross section, the experimental results are discussed by taking account of the momentum spread of the bound electrons. This paper mainly describes the analysis of low-energy electrons and binary encounter peaks at high energies, as well as details of relativistic corrections.

A comprehensive set of experimental data is presented for the electron impact ionization differential cross sections of sodium, magnesium, potassium, and calcium. A coplanar symmetric geometry was chosen for these $(e,2e)$ coincidence studies, the energies ranging from near threshold to around fifteen times the first ionization potential. The results reveal a complex structure in both angle and energy which depends on the chosen target. Similarities and differences in the overall structure are found for the targets which have been studied. The results are compared to the measured cross section for helium over the same incident energy regime. The calcium results are also compared to recent theoretical calculations using a distorted wave Born approximation and the convergent close coupling method. Clear discrepancies are found between both theories and with experiment.