We measured a series of spectra of diamagnetic helium under fixed classical conditions. We varied the scaled energy from $\varepsilon =-0.40$ to $-0.26$ in steps of 0.02, which corresponds to a gradual increase of the number of chaotic orbits in classical phase space. The classical dynamics of the system is studied using closed-orbit theory. The high resolution of the experiment allows for an investigation of the evolution of the $V_1^1$ orbit and its repeated traversals. Taking only this stable orbit into account, we reconstruct the most pronounced peaks in the energy spectrum recorded at $\varepsilon =-\mathrm{0.36.}$ The accuracy of our experiment, confirmed by agreement with quantum helium calculations of action spectra up to scaled action 25, provides a good testing ground for recently developed uniform semiclassical approximations in closed-orbit theory.

The optical Ramsey method is employed to investigate molecular electron wave-packet dynamics in the angular coordinate. Time-resolved spectra are presented for vibrationally autoionizing Rydberg electron wave packets with principal quantum numbers $n=17\mathrm{}–21,$ excited between the $v^{+}=0\mathrm{}$ and $v^{+}=1\mathrm{}$ ionization limits, in the presence of electric fields in the range 0.7–1.4 kV ${\mathrm{cm}}^{\mathrm{-}1}$. A regular, almost dispersion-free beating in the angular coordinate is observed for wave packets created using light which is polarized perpendicular to the direction of the external dc electric field.

We present results from perturbative calculations on a scheme of coherent control in Mg. The scheme involves the excitation of Mg in the vicinity of an autoionizing resonance lying above the first two ionization thresholds by a two-color field composed of a fundamental frequency and its third harmonic, whose relative phase can be continuously controlled. Four as well as two-photon coherent excitation pathways, involving appropriate combinations of the two frequencies, proceed through the atomic continuum simultaneously contributing to the excitation, while three-photon ionization by the fundamental is also energetically possible. As a result, some of the excitation processes involve above-threshold ionization (ATI). The calculated ionization yields for the various groups of photoelectrons reveal significant modulation as the relative phase of the field component frequencies is varied. The modulation patterns for the different photoelectron groups are mutually shifted due to the multiphoton matrix element phases associated both with the ATI process and the multichannel nature of the final state. The effect is particularly pronounced when the autoionizing state is in near four-photon resonance with the fundamental frequency. The role of an autoionizing state as a final state as well as that of the continuum as an intermediate state in coherent control processes is discussed.

We apply Raman-induced resonance imaging techniques to determine, with a spatial resolution of 12 $\mu \mathrm{m},$ the size of a cloud of atoms in a magneto-optical trap and the location of the centroid with respect to the magnetic-field zero point. These experiments provide a starting point for developing much higher-resolution resonance imaging methods for cold trapped atoms.

The theory of atom guiding in a far blue-detuned hollow laser beam (HLB) is developed for the dipole interaction scheme described by a three-level $\Lambda$ model. The complete kinetic description of atomic motion based on the Fokker-Planck equation for the atomic distribution function is presented. The dipole gradient force, radiation pressure force, and momentum diffusion tensor are then derived. It is found that even for a far-detuned laser beam, the optical potential for a three-level $\Lambda$ atom is not generally reduced to a sum of two independent potentials associated with the two two-level interactions in the $\Lambda$ scheme. The theory developed here is also compared with the experimental guiding of cold ${}^{85}\mathrm{Rb}$ atoms in the HLB. The experimental results are found to be in good agreement with the Monte Carlo simulations based on the three-level $\Lambda$ model. We observe that the guiding efficiency depends strongly on the intensity and the detuning of the HLB and the initial temperature of atoms. In particular, the experimental results show that, at small detunings, the guiding efficiency is deteriorated strongly by the radiation pressure force. The Monte Carlo simulations also indicate that the efficiency of guiding versus detuning depends strongly on the direction of the HLB propagation with respect to that of atomic motion. Under optimal conditions, the guiding efficiency was found to be about 20%.

We study the dynamics of a system involving double autoionization resonance. We find that a strong dipole coupling between two autoionizing states significantly modifies the properties of the medium. Variation of the linear susceptibility and ionization spectra into each continuum are numerically calculated for illustration. Effects of the temporal delay between pulses are also investigated in terms of the ionization yield into each continuum.

A numerical method is developed for a V system driven by two counterpropagating laser fields in a momentum regime where a full quantum-mechanical treatment of the atomic variables is necessary. This method is based on a transformation by which integral equations, reduced from steady-state optical-Bloch-type equations involving the atomic center-of-mass momentum, can be transformed into inhomogeneous tridiagonal vector recurrence equations. The effect of the atomic recoil on the momentum distribution in the absence of the probe field, and, in particular, the absorption spectrum in a copropagating spectrum configuration is analyzed and discussed. Special attention is given to the Rayleigh resonance of subnatural linewidth.

Systematic studies of the temporal coherence properties of high-order harmonic radiation are presented. These complement our previous investigations [Bellini et al., Phys. Rev. Lett. 81, 297 (1998)], where we showed the separation of the far-field pattern of high-order harmonics into two distinct spatial regions with different coherence times. Here we show how the coherence time of the inner and outer regions changes as a function of the harmonic order, the laser intensity, and the focusing conditions. Good agreement with the predictions of the semiclassical model of harmonic generation is obtained.

We formulate exact integral boundary conditions for a solution of the time-dependent Schrödinger equation that describes an atom interacting, in the dipole approximation, with a laser pulse. These conditions are imposed on a surface (boundary) which is usually chosen at a finite (but sufficiently remote) distance from the atom where the motion of electrons can be assumed to be semiclassical. For the numerical integration of the Schrödinger equation, these boundary conditions may be used to replace mask functions and diffuse absorbing potentials applied at the edge of the integration grid. These latter are usually introduced in order to (approximately) compensate for unphysical reflection which occurs at the boundary of a finite region if a zero-value condition is imposed there on the solution. The present method allows one to reduce significantly the size of the space domain needed for numerical integration. Considering the numerical solution for a one-dimensional model, we demonstrate the effectiveness of our approach in comparison with some other numerical methods.

We propose a scheme to measure the cross correlations and mutual coherence of optical and matter fields. It relies on the combination of a matter-wave detector operating by photoionization of the atoms and a traditional absorption photodetector. We show that the double-detection signal is sensitive to cross-correlation functions of light and matter waves.

Starting from the Boltzmann equation, we calculate the frequency and the damping of the collective oscillations of a classical gas confined by a harmonic potential. Both the monopole and quadrupole modes are considered in the presence of spherical as well as axially deformed traps. The relaxation time is calculated using a Gaussian ansatz which explicitly accounts for the occurence of quadrupole deformations in velocity space. Our approach provides an explicit description of the transition between the hydrodynamic and collisionless regimes. The predictions are in very good agreement with the results of a molecular-dynamics simulation carried out in a gas of hard spheres.

The spatial structure of the spinor Bose-Einstein condensates with the spin degrees of freedom is analyzed based on the generalized Gross-Pitaevskii (GP) equation in light of the present spin-domain experiment on $m_F=\pm 1,$ and $0$ of the hyperfine state $F=1\mathrm{}$ of ${}^{23}\mathrm{Na}$ atom gases. The GP solutions in three- and one-spatial dimensional cases reproduce the observed spin-domain structures, revealing the length scale associated with the existence of the weak interaction of the spin-spin channel, other than the ordinary coherence length related to the density-density channel. The obtained domain structure in GP is compared with the result in the Thomas-Fermi approximation. The former solution is found to better describe the observed features than the latter.

We study numerically the stability of axially symmetric vortex lines in trapped dilute gases subject to rotation. For this purpose, we solve numerically both the Gross-Pitaevskii and the Bogoliubov equations for a three-dimensional condensate in spherically and cylindrically symmetric traps, from small to very large nonlinearities. In the stationary case we find that the vortex states with $m=1\mathrm{}$ and $m=2\mathrm{}$ are energetically unstable. In the rotating trap it is found that this energetic instability may only be suppressed for the $m=1\mathrm{}$ vortex line, and that the multicharged vortices are never a local minimum of the energy functional. This result implies that the absolute minimum of the energy is not an eigenstate of the $L_z$ operator, when the angular speed is above a certain value.

We show that the nonequilibrium atomic phase-space density (degeneracy) of a Bose gas confined in the off-resonant optical trap can be manipulated by means of the breathing modes of the atomic oscillations in the trap. This new phenomenon opens a possibility to control the onset of the Bose-Einstein condensation in the atomic cloud loaded in an optical trap. The effect arises from the instability of squeezing oscillations of atomic phase-space distribution, initiated by the nonadiabatic change of the optical potential. The manipulation of the degree of degeneracy of the atomic distribution is achieved by means of dynamical control of the squeezing parameters. The physical consequences of the proposed mechanism are discussed.

We study the drag on an object moving through a trapped Bose-Einstein condensate, and show that finite compressibility leads to a mutual drag, which is subsequently suppressed by the formation of a vortex ring.

The focusing of atoms after interacting with both far-detuned and resonant standing wave fields in the thin-lens regime is considered. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\theta :$ the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible $\left(\theta \gg 1\right).$ Within the diffraction theory analytical expressions show that the focused atoms in the far-detuned case have an approximately constant background density $0.5\left(1-0.635{\theta }^{-1/2}\right)$ while the peak density behaves as $3.83{\theta }^{1/2},$ the focal distance as ${\theta }^{-1}(1+1.27\mathrm{}{\theta }^{-1/2})$ $L_T/2\mathrm{}\pi ,$ the depth of focus as ${0.304L}_T{\theta }^{-3/2},$ and the focal spot size $0.0592\lambda {\theta }^{-3/4},$ where $L_T$ is the Talbot distance and λ is the wavelength of the light. Focusing by the resonant standing wave field leads to a new effect, a Rabi-like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied quantitatively with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin-lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.

We investigate theoretically an array of traps containing Bose-Einstein condensates, taking into account tunneling of atoms between adjacent traps and atom-atom interactions within each trap. After an expansion valid in the limit of a large number of atoms, we end up studying a variation of the problem of phonons in a one-dimensional lattice. Analysis of these fictitous phonons and their vacua shows that the fluctuations in atom numbers and phases of the condensates behave qualitatively as in the much-studied case of two traps.

A second-order expansion of the Gross-Pitaevskii equation in the interaction parameter determines the thermodynamic critical angular velocity ${\Omega }_c$ for the creation of a vortex in a small axisymmetric condensate. Similarly, a second-order expansion of the Bogoliubov equations determines the (negative) frequency ${\omega }_a$ of the anomalous mode. Although ${\Omega }_c=-{\omega }_a$ through first order, the second-order contributions ensure that the absolute value $|{\omega }_a|$ is always smaller than the critical angular velocity ${\Omega }_c.$ With increasing external rotation $\Omega ,$ the dynamical instability of the condensate with a vortex disappears at ${\Omega }^{*}=|{\omega }_a|,$ whereas the vortex state becomes energetically stable at the larger value ${\Omega }_c.$ Both second-order contributions depend explicitly on the axial anisotropy of the trap. The appearance of a local minimum of the free energy for a vortex at the center determines the metastable angular velocity ${\Omega }_m.$ A variational calculation yields ${\Omega }_m=|{\omega }_a|$ to first order (hence ${\Omega }_m$ also coincides with the critical angular velocity ${\Omega }_c$ to this order). Qualitatively, the scenario for the onset of stability in the weak-coupling limit is the same as that found in the strong-coupling (Thomas-Fermi) limit.

We study the generation of microwave pulses due to optical rectification in a traveling-wave geometry. A system of evolution equations is derived which describes the mutual propagation of both optical and microwave fields. Overlap integrals and optimization criteria are given, and analytical expressions to determine the generated microwave pulse are derived. It is observed that in non-velocity-matched geometries two microwave pulses are generated initially. Both are the exact image of the optical signal. One pulse stays attached to the optical wave, while the other propagates at the microwave group velocity and is subject to absorption and dispersive broadening. In contrast, in velocity-matched configurations a single signal is generated which is proportional to the first derivative of the optical pulse. It is found that for increased conversion efficiencies the action of the generated voltage on the optical wave via the electro-optic effect can no longer be neglected, and results in an effective cubic nonlinearity acting on the optical wave.

The electromagnetic field operators in the Heisenberg picture are found in both the minimal and multipolar forms of nonrelativistic quantum electrodynamics within the electric dipole approximation. These are made up of free- and source-field terms. The free electric- and magnetic-field operators in the two formalisms differ since the creation/annihilation operators are manifestly distinct. Their explicit forms in the Heisenberg picture are given. However, the source fields are formally the same when expressed in terms of dipole moment operators at positive retarded time. The cancellations that lead to this equivalence are presented. In many applications it is necessary to express the operators at retarded time in terms of creation and annihilation operators at the initial time. Explicit expressions for the fields up to second order in terms of the transition dipole moments are given. These enable the formulas for induced dipole moments to be derived within the context of quantum electrodynamics whereas previous derivations have been based on semiclassical electrodynamics.