The operation of cold-atom beam splitters is analyzed in the context of Bose-Einstein condensate interferometry. We introduce two representative geometries of the splitting region and study influence of nonlinearity and nonadiabaticity on the splitting and the recombination of the condensate for both geometries.

We consider the use of a traveling-wave probe to continuously measure the quantum state of an atom in free space. Unlike the more familiar cavity QED geometry, the traveling wave is intrinsically a multimode problem. Using an appropriate modal decomposition, we determine the effective measurement strength for different atom-field interactions and different initial states of the field. These include the interaction of a coherent-state pulse with an atom, the interaction of a Fock-state pulse with an atom, and the use of Faraday rotation of a polarized laser probe to perform a quantum nondemolition measurement on an atomic spin.

We explore the behavior of a system that consists of a photon mode dipole coupled to a medium of two-level oscillators in a microcavity in the presence of decoherence. We consider two types of decoherence processes, which are analogous to magnetic and nonmagnetic impurities in superconductors. We study different phases of this system as the decoherence strength and the excitation density are changed. For a low decoherence we obtain a polariton condensate with comparable excitonic and photonic parts at low densities and a BCS-like state with a bigger photon component due to the fermionic phase-space filling effect at high densities. In both cases there is a large gap in the density of states. As the decoherence is increased, the gap is broadened and suppressed, resulting in a gapless condensate and finally a suppression of the coherence in a low-density regime and a laser at the high-density limit. A crossover between these regimes is studied in a self-consistent way analogous to the Abrikosov and Gor’kov theory of gapless superconductivity [A. A. Abrikosov and L. P. Gor’kov, Sov. Phys. JETP 12, 1243 (1960)].

The phenomenon of optical bistability is studied for the three-level atomic system in V-configuration confined in a unidirectional optical ring cavity, and the effects of quantum interference and coupling field are investigated. The possibility of obtaining optical multistability in the system by controlling quantum interference and coupling field strength is also discussed.

We characterize the different dynamical regimes and bifurcations in the transition from a stationary hexagonal pattern to optical turbulence. In order to characterize the bifurcations we perform linear stability analysis of stationary hexagonal patterns and Floquet analysis of oscillating hexagons. The interplay between space and time leads to a series of bifurcations showing spatial-period multiplying and quasiperiodicity.

The system whose Hamiltonian is a linear combination of the generators of $\mathrm{SU}\mathrm{}(1,1)\mathrm{}$ group with time-dependent coefficients is studied. It is shown that there is a unitary relation between the system and a system whose Hamiltonian is simply proportional to the generator of the compact subgroup of $\mathrm{SU}\mathrm{}(1,1).$ The unitary relation is described by the classical solutions of a time-dependent (harmonic) oscillator. Making use of the relation, the wave functions satisfying the Schrödinger equation are given, for a general unitary representation, in terms of the matrix elements of a finite group transformation (Bargmann function). The wave functions of the harmonic oscillator with an inverse-square potential is studied in detail, and it is shown that through an integral, the model provides a way of deriving the Bargmann function for the representation of positive discrete series of $\mathrm{SU}\mathrm{}(1,1).$

As a consequence of the Aharonov-Bohm effect, there is a quantum-induced attraction between a charged particle and a rigid, impenetrable hoop made from an arbitrarily thin tube containing a superconductor quantum of magnetic flux. This is remarkable because in classical physics there is no force between the two objects, and quantum-mechanical effects (associated with uncertainty-principle energy) generally are repulsive rather than attractive. For an incident spinless charged particle in a P wave (in a configuration with total angular momentum zero) we verify a resonance just above threshold using the Kohn variational principle in its S-matrix form. Even if optimistic choices of parameters describing a model system with these properties were feasible, the temperature required to observe the resonance would be far lower than has yet been attained in the laboratory.

The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.

One- and two-electron-transfer processes resulting from ${\mathrm{Ne}}^{2+}$ collisions with He are studied, based on a molecular-orbital close-coupling method within the semiclassical representation for the collision energy range of 10 eV/u–10 keV/u. One-electron processes are considered from ground state ${\mathrm{Ne}}^{2+}{(}^{3}P)$ as well as from the metastable ions ${\mathrm{Ne}}^{2+}{(}^{1}D)$ and ${\mathrm{Ne}}^{2+}{(}^{1}S).\mathrm{}$ Two-electron processes are considered only for metastable ${\mathrm{Ne}}^{2+}{(}^{1}D)$ and ${\mathrm{Ne}}^{2+}{(}^{1}S)$ collisions. Previous electron-transfer experimental cross sections show a weak energy dependence, while the present theoretical results for the ground-state ion impact have a pronounced energy dependence, decreasing with decreasing collision energy. However, the theoretical cross sections for the metastable ions are found to be weakly dependent on the collision energy. If the ion beams used in the experiments are assumed to have contained some fraction of metastable ions, then the present results appear to be consistent with the measurements.

A simple qualitative explanation is presented for the observed state selectivity in the associative ionization of ${\mathrm{Xe}}^{*}\left(nf\right)$ to form ${\mathrm{Xe}}_2^{+}.$ It is suggested here that compared to electrons in ${\mathrm{Xe}}^{*}\mathrm{}\left(\mathrm{np}\right)\mathrm{}$ Rydberg states, electrons excited to nf levels are radially localized outside the ${\mathrm{Xe}}^{+}$ ion core for long periods of time due to a larger centrifugal barrier in the effective atomic potential. This enhances the probability that excited Xe atoms in an f state will encounter a ground-state atom at those impact distances that lead to the formation of dimer ions.

Large-angle elastic scattering cross sections were measured for medium energy ${\mathrm{He}}^{+}$ and ${\mathrm{Ne}}^{+}$ ions impact on Ni, Sb, and Hf atoms and the results are compared with those calculated using screened interatomic potentials. As the screened Coulomb potential, we employed the Molière, Ziegler-Biersack-Littmark (ZBL), and that calculated numerically by solving the Poisson equation applied to the Hartree-Fock (HF) atomic model. For ${\mathrm{He}}^{+}$ impact, the ZBL and HF $({\mathrm{He}}^{2+}$ is assumed) potentials reproduced well the observed scattering cross sections but the Molière potential underestimated them significantly. Surprisingly, however, for ${\mathrm{Ne}}^{+}$ impact on Sb and Hf, the observed scattering cross sections were much larger than those calculated from all the above screened interatomic potentials, although ${\mathrm{Ne}}^{10+}$ was assumed for the HF potential. In a large-angle collision, a projectile heavy ion attracts the target electrons to distort the electron cloud and as a result it changes the electric field upon the projectile. The observed scattering cross sections are reproduced well by assuming a simple model that the center of gravity of the target electrons slightly shifts toward the projectile by 0.09–0.12 Å for Hf and 0.066–0.070 Å for Sb from the nucleus.

In this work we study the effects of both atomic description and ion velocity on the surface-plasmon mediated neutralization rates for low energy ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ ions interacting with Al surfaces. The transition rates appear to have a weak velocity dependence for ion velocities below 0.5 a.u. It is also shown that differences in the atomic description of the final neutral helium atoms are responsible for the strong discrepancies between recently published surface plasmon transition rates and earlier multielectron Auger rates. The relevance of the surface collective response during the ion neutralization is illustrated for intermediate and large ion-surface distances. For the case of grazing incidence, we analyze the velocity effects for the corresponding angular distributions of the final neutral He atoms. Earlier calculations had been performed within the fixed ion approximation. We find that although both the collective neutralization rates and the neutralized fractions depend very weakly on the parallel velocity, its effects on the angular distributions are clearly noticeable.

In this paper, we calculate the effect of radiation trapping on the photon statistics of the light scattered from optical molasses. We propose that an intensity correlation function measurement may be sensitive to the presence of radiation trapping at an on-resonance optical depth as low as 0.1, more than an order of magnitude less than where effects of multiple scattering in cold-atom clouds have been previously observed [T. Walker, D. Sesko, and C. Wieman, Phys. Rev. Lett. 64, 408 (1990); D. Sesko, T. Walker, and C. Wieman, J. Opt. Soc. Am. B. 8, 946 (1991)].

The adiabatic properties of stimulated Raman passage via N intermediate quasidegenerate levels are studied. It is shown that the outcome of the population transfer depends on the geometrical structure of the molecular couplings, in particular, on the signs or phases of the dipole matrix elements that connect the initial and the final states with all the intermediate levels. These phases constitute a molecular Franck-Condon configuration. The majority of the possible configurations disable adiabatic passage through a dark state so that the dynamics is dominated by Rabi oscillations among the different levels. It is shown, however, that adiabatic passage can be regained via nonresonant stimulated Raman for almost all possible configurations.

We investigate the low-lying excitations of a stack of weakly coupled two-dimensional Bose-Einstein condensates, which is formed by a one-dimensional optical lattice. In particular, we calculate the dispersion relations of the monopole and quadrupole modes, both for the ground state as well as for the case in which the system contains a vortex along the direction of the lasers creating the optical lattice. Our variational approach enables us to determine analytically the dispersion relations for an arbitrary number of atoms in every two-dimensional condensate and for an arbitrary momentum. We also discuss the feasibility of observing our results experimentally.

We report on the existence of a different form of solitary waves in a passively mode-locked fiber ring laser. Studying the interaction between bound solitons observed in a passively mode-locked fiber laser revealed that the bound-soliton pair behaves as a unit, and the properties of their interaction have exactly the same features as those of the single-pulse soliton in the laser, which suggests that the observed bound solitons are in fact another form of solitary waves in the laser. Numerical simulation confirmed the existence of a different form of solitons in the laser.

The analytical solution to the time-dependent Schrödinger equation for tunneling using cutoff plane-wave initial conditions is in general given by the sum of two types of terms that exhibit a transient behavior. The time evolution of the probability density for the $\delta$ potential is compared with the free case to investigate in this case the role of these transient terms for the delay time. We find, by a dynamical calculation, that the delay time arises from the interference between these transient terms and we show that at very long times it goes into the phase delay time, given by the energy derivative of the phase of the transmission amplitude.

The behavior of the ground-state hyperfine coherence formed in coherent population trapping (CPT) is studied. Using potassium atoms cooled with a magneto-optical trap, a pure hyperfine CPT state was prepared in a magnetic field, and hyperfine coherent effects in an open system were experimentally studied with off-Raman resonance oscillations (ORRO). Comparisons were made to full numerical simulations and to a pseudo-three-level model. The frequency and phase of ORRO can be manipulated by changing the relative frequency and phase of the lasers.

We analyze the dynamics of a vertical-cavity surface-emitting laser with optical feedback operating in the low-frequency fluctuation regime. By focusing on the fast pulsing dynamics, we show that the two linearly polarized modes of the laser exhibit two qualitatively different behaviors: they emit pulses in phase just after a power dropout and they emit pulses out of phase after the recovery process of the output power. As a consequence, two distinct statistical distributions of the fast pulsating total intensity are observed, either monotonically decaying from the noise level or peaked around the mean intensity value. We further show that gain self-saturation of the lasing transition strongly modifies the shape of the intensity distribution.

The s-wave scattering length for elastic collisions between ${}^{87}\mathrm{Rb}$ atoms in the state $|{f,m}_f〉=|1,1〉$ is measured in the vicinity of a Feshbach resonance near 1007 G. Experimentally, the scattering length is determined from the mean-field-driven expansion of a Bose-Einstein condensate in a homogeneous magnetic field. The scattering length is measured as a function of the magnetic field and agrees with the theoretical expectation. The width of the resonance is determined to be 0.20(3) G, the position of the zero crossing of the scattering length is found at 1007.60(3) G.