We present two methods for measuring the duration of ultrashort high-harmonic pulses produced by an intense laser pulse propagating in an atomic gas. Both methods rely on the nonlinearity of ionization of atomic gases by optical laser pulses. In the first method, the same medium is used for the dual purpose of generating and measuring the high harmonics. The second method uses atomic photoionization in an intense low-frequency laser field to produce the optical analog of a “streak camera” capable of subfemtosecond resolution.

A theory of electron-atom ionizing collisions in the presence of a bichromatic laser field is developed. The incident and scattered electron of high energy is described by Volkov states, the atomic ground state is dressed by the laser field to first order in the electric-field strength, and the atomic continuum state that corresponds to the ejected slow electron is dressed by the laser field to all orders in the field strength, but in an approximate way. It is shown that the dressing of these continuum states is mainly responsible for the different effects that a bichromatic laser field introduces into this process. These effects are more pronounced compared to similar effects recently observed in an analysis of the target dressing in free-free transitions in a bichromatic laser field. The possibility of the coherent phase control is analyzed and it is shown that the triple differential cross section (TDCS) can be changed by almost one order of magnitude by changing the relative phase between the two laser field components. The TDCS as a function of the relative phase, the number of absorbed (emitted) photons, and the laser electric-field strength shows a specific behavior that is mainly determined by the properties of the generalized Bessel functions appearing in our results. It is also shown that these effects are particularly pronounced for rather small scattering angles of the fast electron.

Dual-frequency interferences using appropriate combinations of circular writing beam polarizations are demonstrated to enable full control of the molecular polar order in a polymer. A comparative theoretical and experimental analysis of the all-optical poling process in the cases of linear, cohelical, and counterhelical writing polarizations is achieved. Dynamics, efficiency, phase matching, and tensorial aspects are analyzed. Nearly perfect dipolar and octupolar ordering is achieved using conventional one-dimensional molecules. As a feature of dual-frequency holography with circular polarizations, writing beam phase retardation ΔΦ is coded into a ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ pattern rotation by the same angle. Interestingly, in the case of a fundamental beam with linear polarization, second harmonic generation is independent of the polarization direction.

The influence of laser-induced two-electron excitation processes on the deflection of atoms by a standing-wave laser field is investigated. In particular, isolated-core excitation processes are studied in which, after preparing one valence electron as an electronic Rydberg wave packet, the core electron is driven resonantly by the standing wave. The dynamics of the two electrons are entangled through laser-induced electron correlation effects. A theoretical approach is developed that clearly exhibits the intricate interplay between these correlation effects and the atomic center-of-mass motion that originates from the stimulated light force. Various examples are analyzed that show the manifestations of this interplay in the diffraction pattern of a deflected atom.

This work is concerned with the temporal evolution of the coherent population trapping (CPT) process in the case of additional optical pumping to states not contributing to the CPT superposition states. Special attention is paid to the influence of weak external magnetic fields that can change the laser-atom interaction considerably. The theoretical analysis is completed by experimental observations on a sodium atomic beam, which show good agreement with our theory. The results obtained are of importance for a realistic picture of CPT schemes in practical applications.

We have presented a two-dimensional multiwell model to simulate the inertially confined ionized clusters of which unscreened ions contribute attractive potential wells to other nearby atoms. Dynamics of the intense laser-driven multiwell system has been explored. When the multiwell system is irradiated by an intense laser pulse, it will emit enhanced high-order harmonic radiation in the process of avalanche multiphoton ionization. Three facts, namely, the combined potential configuration lowering potential barrier, intermediate states resonance, and collision heating of electron with ions, are responsible for the avalanche ionization of clusters. And the enhanced high-order harmonic generation is attributed to a higher ionization potential and greater polarizability of the active electron in the clustering multiwell system. We can conclude that the cluster is a highly efficient nonlinear medium for coherent short-wavelength radiation, especially when an ultrashort $(<\mathrm{}100\mathrm{}\mathrm{fs}),$ medium intensity laser pulse is used.

The linear Boltzmann equation for active atoms submerged in the much denser perturber gas contains a collision rate and a kernel. These two quantities are combined into a single entity—the collision operator. The collision operator possesses several interesting properties, the most important being that it is Hermitian. The eigenvalues are negative with the exception of one eigenvalue, which is zero and corresponds to the Maxwellian (steady-state) velocity distribution. A set of functions, closely related to the eigenfunctions of the quantum-mechanical harmonic oscillator, is postulated to approximate the true eigenfunctions. This assumption was a basis of the method of modeling various physical phenomena occurring in the gaseous mixtures, subjected to a radiation field. The eigenvalues of the collision operator were treated as free parameters. In this paper we establish a direct relationship between the eigenvalues and the collision integrals, or transport coefficients, known from the kinetic theory of gases. The generating function approach is employed to derive expressions yielding the eigenvalues. The obtained results form a bridge between kinetic theory, atomic physics, and quantum optics.

The conventional $J=1/2\mathrm{}\leftrightarrow J=1/2\mathrm{}$ model is successful for the qualitative description of the interaction of sodium atoms and laser light tuned close to the atomic $D_1$ transition. However, time constants for dynamic effects due to optical pumping predicted by the model are about an order of magnitude too short compared to experimental observations. The inclusion of hyperfine states in the quantum-mechanical description of the atom leads to a satisfactory model that also predicts the correct absorption due to atomic diffusion and allows for the description of effects related to population trapping. This hyperfine model is derived in detail and compared with the $J=1/2\mathrm{}\leftrightarrow J=1/2\mathrm{}$ approximation.

Quantum-mechanical transport of atoms in an optical lattice in one dimension is described in an exactly solvable model. The atoms are tightly bound and they are sufficiently cooled so that they are restricted only to the lowest Bloch band in a single adiabatic potential. The coherent spreading of an atomic wave packet by tunneling is counteracted by the localizing effect of photon emission that accompanies optical pumping. The time evolution of the quasimomentum distribution, the coherence length, and the spatial width of the atomic state are evaluated analytically. These quantities depend strongly on the statistics of photon emissions.

We study the connection of the high-frequency Floquet theory (HFFT) and the wave-packet dynamics (WPD) descriptions of laser-atom interactions. The analysis is motivated by the need to ascertain the realm of validity of the current form of the HFFT and extend its scope. We test the general ideas on a one-dimensional atomic model with soft Coulomb potential, frequently considered before. The comparison is carried out in two stages of approximation. In the first stage, we compare WPD predictions for ionization with those from the usual (single-state) form of the HFFT. To make the comparison meaningful, we use as initial conditions for the WPD bound high-frequency “dressed states,” corresponding to the peak intensity of the field. The dressed states play a special role in the HFFT and have direct physical interpretation at high frequencies. We show that, under certain conditions, the decay rates extracted from WPD agree rather well with those from the HFFT. Thus “adiabatic stabilization,” derived originally from the HFFT, results also from WPD. This form of the phenomenon contrasts “dynamic stabilization,” the only form shown so far to follow from WPD. In the next stage of the comparison, we extend the HFFT in two directions: we include results from the second iteration within the theory, and we introduce a multistate HFFT analysis. As a test for the agreement of the HFFT and WPD we compare the results regarding the populations in dressed states. In a variety of circumstances we find striking agreement, indicating the potential of the multistate Floquet analysis. In addition, we study the characteristics of the population trading among the dressed states during the ionization process. Although the individual populations in bound states may fluctuate substantially, their sum decreases rather smoothly in time, as predicted analytically by the HFFT.

In the framework of semiclassical theory we investigate the influence of a low-intensity monochromatic electromagnetic plane wave on a nonrelativistic one-electron atom. The radiation field is switched on adiabatically, while the atom is assumed to be initially in its ground state. We analyze their interaction to the first order of perturbation theory, taking into account retardation effects. In the radiation gauge, the exact first-order correction to the wave function consists of separate orbital and spin contributions which are determined, respectively, by a vector and a scalar linear-response function. Starting from Hostler’s integral representation of the Schrödinger Coulomb Green function in coordinate space, we have derived them, via a generating function, as closed-form contour integrals. Then they have also been written explicitly, as double power series involving linear combinations of Humbert hypergeometric functions ${\Phi }_1$. From the integral representation of the linear-response wave function we have extracted the considerably simpler second-order retardation approach. We have subsequently translated it in a conveniently modified Poincaré gauge, which we call a multipolar gauge, in order to display the contributions of the genuine field-atom multipole couplings. The relevant orbital and spin multipole terms are then recovered by employing directly the generating function of the linear response. Their low- and high-frequency behavior is finally examined.

The interaction of a low-intensity laser field with a nonrelativistic one-electron atom is considered to the first order of perturbation theory and in the electric dipole approximation. The radiation field is turned on adiabatically modifying the initial unperturbed atomic state, which is either an angular-momentum eigenstate $|\mathrm{nlm}〉$ or a Stark state $|{\mathrm{nn}}_{e}m〉$. The first-order correction to the wave function is expressed both in the length and velocity gauges in terms of a vector function called the linear-response vector and depending on the field-free energy eigenstate. We derive in a unifying manner the linear-response vectors in the position representation, as closed-form contour integrals, starting from a unique generating function built up with the Coulomb Green function. The linear-response vectors are then evaluated in momentum space via a Fourier transformation: they are obtained as integral representations and also in explicit form, as generalized hypergeometric functions. With reference to the static limit, we complement earlier results and find the reduced linear-response vectors in momentum space, as Fourier transforms of their coordinate-representation counterparts. The low-frequency behavior of the length-gauge first-order correction to the ground-state wave function is established in coordinate as well as in momentum space. We finally point out the high-frequency limit of the linear response in the velocity gauge.

The electric field polarization structure of three-dimensional monochromatic electromagnetic fields is investigated, with particular reference to the three-dimensional standing waves that are commonly used in laser cooling. Two parameters are introduced for describing the polarization at a field point, one of which is a generalization of the Stokes ellipticity parameter while the other describes the rotation of linear polarization (or the polarization ellipse) for small displacements. The two parameters are shown to be simply related to the density and flux of intrinsic angular momentum (spin) in the field. Additional parameters are introduced to provide measures of the polarization gradients on straight line trajectories in three-dimensional standing waves and the implications for laser cooling are discussed.

In an experiment using a Paul trap, we create a ${\mathrm{H}}_2^{+}$ ion cloud by electron ionization of the background gas at ${10}^{-9}$-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the $r$ or $z$ direction, we observe a narrow resonance at some distance from the motional resonance center if the amplitude of the exciting field exceeds a threshold value. The threshold value decreases with increasing ion number. Since the narrow resonance does not shift with ion number, we interpret it as a collective resonance of the center of mass of the ion cloud. The resonance shape exhibits the typical form of a driven anharmonic oscillator. The conclusions drawn from the experiments are supported by detailed analytical and numerical computations.

The results of a theoretical study of Cs atoms in a strong and static electric field are compared to experiment. The atoms are excited from the ground state to $m=0\mathrm{}$ or $m=1\mathrm{}$ states above the classical ionization threshold. Regularities in the spectra seem to be caused by simple physical mechanisms. The systems are studied in the time domain using two different methods, recurrence spectroscopy and the ejected time dependent flux, and in the energy domain using two different methods, photoionization cross section and expectation values of the energy shift operator. Each of these methods provides some additional insight into the dynamics.

Recent experiments with atomic clocks and hydrogen gas samples have shown discrepancies between theory and experiment. There are serious disagreements with respect to four different parameters: two different frequency shift parameters and a line broadening cross section relating to the H maser, and a longitudinal relaxation rate observed in a hydrogen gas sample. We study the changes in the short-range singlet and triplet potentials that would be needed to eliminate the above discrepancies. We find that no such changes can remove all four discrepancies simultaneously. In addition, we investigate a possible role of spin-dipole interactions, which have been neglected in previous calculations.

Quantum systems subject to time periodic fields of finite amplitude λ have conventionally been handled either by low-order perturbation theory, for λ not too large, or by exact diagonalization within a finite basis of $N$ states. An adiabatic limit, as λ is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as $N\to \infty ,$ the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high-order resonances). This paper deals with the highly nontrivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude λ. The mathematical radii of convergence of perturbation theory in λ approach zero. There is no adiabatic limit of the wave functions when λ is turned on arbitrarily slowly. However, the quasienergy becomes independent of $\lambda \mathrm{}\left(t\right)\mathrm{}$ in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit $N\to \infty ,$ the conventional approaches are appropriate in almost all physically interesting situations.

We report on measurements of trap-loss collisions between ultracold Rb atoms that are confined in a magneto-optical trap. Both isotopes, ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb},$ have been studied over a wide range of trap laser intensities and detunings. The trap-loss collisional rate constant exhibits variations over three orders of magnitude. At low intensities and/or large detunings, the trap loss is dominated by ground-state hyperfine-changing collisions, while at high intensities and small detunings, collisions involving excited atoms are more important. We see significant differences between the isotopes in both regimes. At large detunings, the ability of the trap to recapture products of a hyperfine-changing collision is significantly diminished. This finding is supported by our numerical simulations of the recapture process. The trap loss rates due to collisions with room-temperature background gas have also been measured. A surprisingly large increase in this rate is seen when the confining power of the trap is reduced.

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation.

We analyze the recently proposed method [H. Paul et al., Phys. Rev. Lett. 76, 2464 (1996)] for reconstructing the quantum state of a light field from multiple coincidences measured at the outputs of a passive multiport. We show that applying a large multiport the reconstruction of a pure state becomes possible using avalanche photodiode-type detectors. The presented simulations show that the photon chopping scheme is appropriate for the indirect measurement of the photon statistics of a weak nonclassical signal.