In this paper the dynamics of wave fields in a cavity, part of which is filled with a dielectric, are investigated. The wave equation is solved approximately using the method of multiple time scales. Phase modulations of the cavity modes in an adiabatic case are given up to the first order. A simple effective field Hamiltonian operator is derived and then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic time dependence of the refractive index of the dielectric can lead to suppression of the Rabi oscillations of atomic inversion.

When a chain of two two-level atoms is placed in a photonic band-gap crystal, trapped photon-atom dressed states can form in the neighborhood of the chain due to emission and reabsorption of the photon by atoms in the chain. For a long chain such states form a quasicontinuum inside the forbidden frequency band. We examine the density of states as a function of the chain length and separation between atoms. The pattern of excitation for atoms in the chain forms a “lattice wave,” which may be used to understand the propagation of excitation along the chain.

Purification schemes for multiparticle entangled states cannot be treated as straightforward extensions of those two-particle ones because of the lack of symmetry they possess. We propose purification protocols for a wide range of mixed entangled states of many particles. These are useful for understanding entanglement, and could be of practical significance in multiuser cryptographic schemes or distributed quantum computation and communication. We show that operating locally on multiparticle entangled states directly is more efficient than relying on two-particle purification.

We have observed changes in the polarization of an evanescent wave propagating in a resonant atomic vapor. The effect can be interpreted as an effective dichroism and birefringence of the vapor, the phenomenon characteristic of anisotropic media. In this case it arises from the Goos-Hänchen shift, which is different for light polarized parallel and perpendicular to the incident plane. We have also observed Faraday rotation of the evanescent wave.

A method devised to measure separate absolute rates for deexcitation of metastable hydrogenic atoms and ions via radiative and nonradiative processes is applied in a pilot study of 6.6-keV ${\mathrm{He}}^{+}\mathrm{}\left(2s\right)-\mathrm{Ar}$ ${\to \mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$-… collisions. An absolute total deexcitation cross section ${\sigma }_{\mathrm{de}}^{\mathrm{tot}}=(7.6\mathrm{}\pm 1.2)\times {10}^{-16}\hspace{0.5em}{\mathrm{cm}}^2$ was measured by attenuation. The cross section for nonradiative deexcitation was then measured independently. A radiative branching ratio $R_{\mathrm{BR}}=(70\mathrm{}\pm 8)\%$ was determined, without requiring absolute photon detection calibrations. The measured radiative deexcitation cross section agrees with the result of a semiclassical calculation when competing capture and ionization processes are taken into account.

It is demonstrated that the structures in the low-energy cross sections for excitation to certain levels of atoms by ions originate from a shift from direct excitation at high and intermediate energies to pronounced two-center molecular mechanisms at lower energies. The molecular mechanisms dominate at small internuclear separations, whereas the direct mechanism is driven by the familiar dipole long-range coupling. The demonstration is based on maps of the excitation probabilities over the collision velocity and impact parameter, which display two typical regions. System specific details determine the separation between the two regions and give rise to a plateau, an oscillation or a hidden shoulder in the excitation cross sections. Maps of classical-trajectory Monte Carlo method results show similar qualitative features, but the details of these maps differ considerably from those of the quantal calculations.

Ion time-of-flight mass spectroscopy was used to study the relaxation dynamics of HCl following photoexcitation in the vicinity of the Cl $K$ threshold $\left(\approx 2.8\mathrm{keV}\right).\mathrm{}$ Detailed observations of molecular fragmentation mediated by postcollision interaction between a photoelectron and an Auger electron are presented, evidenced by the recapture of Cl $K$ photoelectrons by either ${\mathrm{Cl}}^{n+}$ or ${\mathrm{H}}^{+}$ dissociation fragments.

The dynamics of small $(<~55\mathrm{atom})$ argon clusters ionized by a high-intensity, femtosecond laser pulse have been studied using classical particle dynamics simulations. The evolution of both ions and electrons during the laser pulse is examined. These simulations show that the space-charge and impact ionization of electrons, liberated from individual atoms in the cluster, have a very important effect on the ion energies resulting from the cluster explosion.

We show, through numerical simulations, that it is, in principle, possible to follow in time the structure and the population dynamics of an atomic system “dressed” by a strong time-varying laser field. The proposed time-resolved spectroscopy scheme exploits the properties of the currently developed sources of coherent extreme ultraviolet radiations, generated via high-order harmonic conversion. With pulse durations within the femtosecond range, it is possible to conceive two-color pump-probe schemes that would help to shed light on issues currently under discussion about the dynamics of strong-field photoionization.

We investigate theoretically the influence of magnetically tunable Feshbach collision resonances on the photoassociation spectra of ultracold atoms. As an example we consider recently predicted resonances for ${}^{85}\mathrm{Rb}$ atoms. For excitation to the ${}^{85}{\mathrm{Rb}}_2{\mathrm{\hspace{0.5em}}0}_g^{-}{(S}_{1/2}{+P}_{1/2})$ electronic state, we predict that the photoassociation rate is resonantly enhanced by at least two orders of magnitude. We find that photoassociation could serve as a useful probe with which to study Feshbach resonances in ultracold collisions. In turn, these resonances should be very important to Bose-condensed gases, and more generally, to coherent atom optics.

We study the behavior of cesium atoms confined in far-detuned laser traps and submitted to blue Sisyphus cooling. First, in a single focused yttrium aluminum garnet (YAG) beam, the atomic cloud has a rod shape with a $6-\mu \mathrm{m}$ transverse waist radius, a temperature of $2\mu \mathrm{K}$, and a transient density of 10${}^{12}{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$. For this sample, we have not detected any influence of photon multiple scattering on the atomic temperature, in contrast to previous measurements in isotropic samples. Second, the YAG laser is used to produce a $29-\mu \mathrm{m}$ period hexagonal optical lattice in which we directly observe the localization of the atoms by absorption imaging. Equilibrium densities on the order of ${10}^{13}{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$ are achieved in this structure.

Losses from a cesium magneto-optical trap induced by an additional laser ionizing the atoms in the ${6P}_{3/2}$ state have been measured as a function of the intensity and frequency of the ionizing laser. The absolute cross section for ionization of the ${6P}_{3/2}$ state has been derived as a function of the wavelength of the ionizing laser. Our values are compared with previous ones and available theoretical predictions. A simple model describing the photoionization processes has been developed.

We have observed Bose-Einstein condensation of large numbers of ${}^{87}\mathrm{Rb}$ atoms in a magnetic time-averaged orbiting potential (TOP) trap. Over $1.5\times {10}^9$ atoms are captured in the trap and evaporatively cooled to produce condensates containing up to $2\times {10}^5$ atoms. We discuss special considerations relating to the production of large Bose-Einstein condensates in a TOP trap, and present measurements of the condensate fraction for this case.

We have determined the scattering lengths for collisions between the different isotopes of two potassium atoms in singlet and triplet molecular states of ${\mathrm{K}}_2$. We show that for the two bosonic species ${}^{39}\mathrm{K}$ and ${}^{41}\mathrm{K}$ the scattering lengths are positive, hence, leading to stable condensates. The fermionic isotope ${}^{40}\mathrm{K}$ also has positive scattering lengths, but the triplet value is nearly zero, hence, a quasi-non-interacting fermionic gas. We also give results for the interspecies collisions. We conclude that double condensates of ${}^{39}\mathrm{K}$ and ${}^{41}\mathrm{K}$ are possible for purely spin-polarized atoms, and sympathetic cooling between the bosonic ${}^{39}\mathrm{K}$ and the fermionic ${}^{40}\mathrm{K}$ will be efficient due to low spin-flip rates and a sizable interspecies scattering length.

The different time-dependent distances of two arbitrarily close quantum or classical statistical states to a third fixed state are shown to imply an experimentally relevant notion of state sensitivity to initial conditions. A quantitative classification scheme of quantum states by their sensitivity and instability in state space is given that reduces to the one performed by classical mechanical Lyapunov exponents in the classical limit.

We present a method for the direct computation of the Wigner function by solving a coupled system of linear partial differential equations. Our procedure is applicable to arbitrary binding potentials. We introduce a modified spectral tau method that uses Chebyshev polynomials as shape functions to approximate the solution. Since two differential equations are solved simultaneously, the resulting linear equation system is overdetermined. We approximate its solution by a least-squares method. We prove the stability and convergence of our scheme. As an application, we compute numerically the Wigner function for the harmonic oscillator. Our calculations show excellent agreement with known analytic results.

We generalize our modified spectral method for the solution of the coupled real partial differential equations in phase space for the stationary Wigner function of an energy eigenstate. This generalization allows us to apply our algorithm to arbitrary high-order partial derivatives without increasing the numerical costs. This is possible since we can derive a sum factorization formula converting a multiple sum into a simple product. We apply our method to evaluate the Wigner function of the Morse oscillator and an asymmetric double-well potential, and compare our results with the exact solution when it is known.

We give common eigenkets of three compatible observables {$P_1{+P}_2{+P}_3,$ $({\mu }_2{Q}_2+{\mu }_3{Q}_3)/({\mu }_2+{\mu }_3)-Q_1,$ $Q_3-Q_2$}, which are composed of three particles’ coordinate $Q_i$ and momentum $P_i,$ where ${\mu }_i{=m}_i{/(m}_1{+m}_2{+m}_3).\mathrm{}$ This set of operators are so-called Jacobi coordinates and momenta. By compatible we mean such observables can be simultaneously determined. Using the technique of integration within an ordered product of operators, we prove that the common eigenkets are complete and orthonormal, and hereby qualified for making up a representation. Applying this representation to solving some new three-body problems is also shown.

Energy and time entangled photons at a wavelength of 1310 nm are produced by parametric down-conversion in a ${\mathrm{KNbO}}_3$ crystal and are sent into all-fiber interferometers using a telecommunications fiber network. The two interferometers of this Franson-type test of the Bell inequality are located 10.9 km apart from one another. Two-photon fringe visibilities of up to 81.6% are obtained. These strong nonlocal correlations support the nonlocal predictions of quantum mechanics and provide evidence that entanglement between photons can be maintained over long distances.