We present an extension of the strong-field theory of multiphoton ionization due to Reiss aimed at retaining the retardation effects. The time-reversed $S$-matrix approach and a recently proposed strong-field solution to the Schrödinger equation are used in order to obtain analytic expressions for the ionization rates without making the dipole approximation. Photoionization of the hydrogen ground state is used as an example to demonstrate that deviation from the dipole approximation is substantial for high photon orders or, equivalently, highly energetic photoelectrons. As a by-product, an expression is also obtained for the ponderomotive scattering angle of the photoelectron, measured relative to the field propagation direction, in terms of its directed kinetic and binding energies.

We have studied the influence of a strong laser on the dynamics of fast $\mathrm{}(e,2e)\mathrm{}$ collisions in helium, in asymmetric, coplanar geometry. The interaction of the laser field with the unbound electrons is treated in a nonperturbative way. The wave functions of the incident and scattered electrons in the laser field are treated as Volkov waves, while that of the ejected electron moving in the combined field of the residual He${}^{+}$ ion and of the laser is obtained by generalizing the ansatz proposed by Joachain et al. [Phys. Rev. Lett. 61, 165 (1988)] for the case of atomic hydrogen. On the other hand, the interaction of bound electrons with the laser field is treated by using first-order perturbation theory, assuming that the electric-field strength is much less than the atomic unit ${e/a}_0^2\simeq 5\times {10}^9$ V cm${}^{-1}$. The required scattering amplitudes are evaluated by using two different implementations of the Dalgarno and Lewis method. The first approach uses a technique proposed by Zernik and Klopfenstein, based on Laplace transforms and analytic continuation procedures. The second approach is based on a Sturmian basis expansion. The influence of the laser parameters (photon energy and intensity and direction of polarization) on the angular distribution of the ejected electron is analyzed, and several illustrative examples are discussed. We find that in general the triple-differential cross sections are strongly dependent on the dressing of the projectile and the target by the laser field.

STIRAP (stimulated Raman adiabatic passage) has proven to be an efficient and robust technique for transferring population in a three-level system without populating the intermediate state. Here we show that the counterintuitive pulse sequence in STIRAP, in which the Stokes pulse precedes the pump, emerges automatically from a variant of optimal control theory we have previously called “local” optimization. Since local optimization is a well-defined, automated computational procedure, this opens the door to automated computation of generalized STIRAP schemes in arbitrarily complicated $N$-level coupling situations. If the coupling is sequential, a simple qualitative extension of STIRAP emerges: the Stokes pulse precedes the pump as in the three-level system. But, in addition, spanning both the Stokes and pump pulses are pulses corresponding to the transitions between the $N-2$ intermediate states with intensities about an order of magnitude greater than those of the Stokes and pump pulses. This scheme is amazingly robust, leading to almost 100% population transfer with significantly less population transfer to the $N-2$ intermediate states than in previously proposed extensions of STIRAP.

With the goal of providing critically evaluated atomic data for modeling high harmonic generation processes in noble gases, we present calculations of frequency-dependent nonlinear susceptibilities of the ground state of helium, within the framework of Rayleigh-Schrödinger perturbation theory at lowest applicable order. The nonrelativistic, infinite-nuclear-mass, atomic Hamiltonian is decomposed in terms of Hylleraas coordinates and spherical harmonics, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. The mixed Hylleraas and Frankowski basis functions are employed to represent accurately the ground-state and perturbed wave functions. We believe our results for nonlinear susceptibilities of helium are the most accurate (and in many cases, the only) available to date, and they are offered as benchmark data for design of future multiphoton experiments.

We provide a general formulation of the energy eigenvalue problem for a two-electron atomic system interacting with a monochromatic radiation field using interparticle coordinates to describe the internal motion; electron correlation is fully incorporated. No restriction is placed on the total orbital angular momentum of the system. We have applied this formulation using the perimetric combination of interparticle coordinates to the calculation of accurate second- and fourth-order ac shifts and widths of the negative hydrogen ion. In addition, we have obtained estimates of the ac shifts and widths in the nonperturbative regime, using a three-level model Hamiltonian constructed from the zeroth-, first-, and second-order perturbed wave functions. We have used this model to investigate the intensity dependence of absorption profiles in the autoionizing resonance region below the two-electron escape threshold. We have also used the model to estimate the intensity for onset of stabilization (against ionization) at frequencies above the threshold for two-electron escape; the onset intensity increases as the third power of the frequency, in accord with earlier results for atomic hydrogen.

We describe theoretically the generation of ultrashort (subfemtosecond) pulses using high-order harmonics of a laser pulse with a time-dependent degree of ellipticity. The single-atom response is calculated by using a low-frequency strong-field approximation. Propagation effects are taken into account using a method going beyond the slowly varying envelope approximation. Propagation modifies significantly the results obtained in the single-atom response and, in certain conditions, makes the generation of one attosecond pulse possible. We discuss prospects for the observation of these ultrashort pulses.

The rate at which external random thermal fluctuations drive transitions between, and cause decoherence of, the near ground vibrational (harmonic oscillator) quantum states of trapped cold ions is of crucial importance in relation to quantum computing. Presented here is an estimate of these rates, for a single trapped ion, based on a quantum perturbation approach where an external thermal energy reservoir is electrically coupled to the ion. The results are for a general system, and it is shown that the relevant parameter in the interpretation of experimentally observed heating rates is the correlation time of the fluctuations. The rates due to the fluctuating electric field associated with blackbody radiation are also considered and shown to be negligible.

We have observed the microwave ionization of Na $s$ and $d$ states with 8-GHz pulses as short as 600 ps full width at half maximum, i.e., pulses containing five cycles. We find the ionization probability to be strongly dependent on pulse length. For the shortest pulses, ionization probability of $|m|=0\mathrm{}$ and 1 states is approximately zero if a requirement for the minimum number of cycles is not met, even when the microwave amplitude exceeds the long-pulse threshold of ${E=1/3n}^5$. For the $|m|=2\mathrm{}$ states, which are approximately hydrogenic, essentially no ionization occurs with the shortest pulse until the microwave amplitude equals ${1/9n}^4$. We also find that as many as 50% of the $|m|=0\mathrm{}$ and 1 atoms not ionized by the microwaves are left trapped in higher $n$ levels than the one initially excited.

We have measured the energy spectra of electrons resulting from the ionization of K using high-intensity $\left({2\times 10}^{12}{\mathrm{}\mathrm{W}/\mathrm{c}\mathrm{m}}^2\right)$ nanosecond laser pulses at 266 nm. At this wavelength, the energy of one photon is enough to ionize the atom, but the single-photon excitation is suppressed by a Cooper minimum in the ionization cross section. Little direct ionization is observed but, interestingly, a substantial amount of above-threshold ionization (ATI) is detected. The experimental results show that the atom can absorb up to three photons even though the one-photon channel is directly in the continuum. We have calculated the perturbed wave function of the intermediate state at the one-photon level during the laser pulse and discuss what the radial dependence of the wave function implies for the relative strength of the direct and ATI ionization channels. We have also repeated the experiment using femtosecond laser pulses having focused peak intensities near ${2\times 10}^{14}{\mathrm{}\mathrm{W}/\mathrm{c}\mathrm{m}}^2$.

Expressions used for describing the optical preparation of oriented and aligned reagents are derived. For a parallel transition, the probability of orienting and aligning a symmetric top by excitation with circularly polarized radiation is given.

The electron nuclear dynamics theory (END) extended to include a time-dependent external field is briefly described. The dynamical equations, in addition to the full electron nuclear coupling terms, now also contain the interactions of both the nuclei and the electrons with the external field. This extended END theory is applied to the study of vibrational excitations of the simple diatomics HF and LiH. The END results using an intense infrared laser field are compared with those of molecular dynamics as well as those from quantum wave-packet calculations. While the effect of the nonadiabatic electron-nuclear coupling terms on the vibrational dynamics is negligible for the chosen application, the electron-field coupling has a significant impact.

Dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, is considered by applying an accurate method for solving nonlinear systems of differential equations. This method is more general than the adiabatic approximation and, thus, permits one to check the limits of the latter and also to analyze nonadiabatic regimes of motion. An unusual nonadiabatic regime is found when atoms are confined from one side of the $z$ axis but are not confined from another side. The lifetime of atoms in a trap in this semiconfining regime can be sufficiently long for accomplishing experiments with a cloud of such atoms. At low temperature, the cloud is ellipsoidal, being stretched in the axial direction and moving along the $z$ axis. The possibility of employing the semiconfining regime for studying the relative motion of one component through another in a binary mixture of gases is discussed.

A three-level $\Lambda$ scheme is proposed in order to achieve a large (resonant) index of refraction with vanishing absorption. This scheme is based on the selective population of one of the dressed states produced by a strong laser field. For modest values of the density and realistic atomic parameters the present scheme gives the index to absorption ratio $\approx 2500.$ It is to be noted that an off-resonant two-level scheme can also give such a ratio but the index of refraction will be smaller. The present approach to index enhancement is not limited to weak fields, as is the case in some other schemes.

For the description of spectral and radiative decay properties of atoms or molecules, placed in a photonic material, the electromagnetic field in the material must be quantized and active research is taking place in this area. Here a unified account is given of such quantization procedures. Led by the Maxwell example, we consider the canonical formalism and its quantization for a class of linear evolution equations ${\partial }_{t}F=NF-G$, obeying a conservation law for $G=0\mathrm{}$. If $N$ has a nonempty null space (zero is an eigenvalue with associated nonpropagating solutions), an abstract form of the gauge concept makes its appearance and generalizations of the familiar Coulomb and Lorentz gauges are obtained. A canonical formalism is set up and quantized. The application to spatially inhomogeneous nonconducting electrodynamical systems is immediate, including the interaction with matter. Next atomic decay in a medium is considered, in particular in the presence of band gaps. For a simple two-level model with transition frequency in the gap, single-photon decay is inhibited and also a different stable eigenvalue of the combined system is found. An open problem in connection with random dielectrics, showing Anderson localization, is discussed. Finally, a mass renormalization, by means of a Kramers transformation, is presented. In general, the renormalized mass is no longer a scalar quantity.

A recently introduced hierarchy of states of a single-mode quantized radiation field is examined for the case of centered Gaussian-Wigner distributions. It is found that the onset of squeezing among such states signals the transition to the strongly nonclassical regime. Interesting consequences for the photon-number distribution, and explicit representations for them, are presented. The effects of nonideal detection are also carefully analyzed.

Spontaneous pulsations and polarization multistability resulting from the nonlinear interaction of two standing waves with an active medium in a single-longitudinal-mode Fabry-Pérot gas laser with a weakly anisotropic cavity have been studied at different cavity anisotropies and different transitions between the working levels with and without an axial magnetic field applied to the active medium. As predicted theoretically, a series of polarization dynamical phenomena have been observed experimentally in the He-Ne $(\lambda =1.15\mathrm{}\mu$m) laser in the case of orthogonal elliptically polarized eigenstates of the cavity. Periodic oscillations of two qualitatively different forms (distorted sinusoids and large spikes), the transition between two stationary orthogonal elliptically polarized waves in the vicinity of the line center tuning which occurs through the region with polarization instability, as well as switches between the orthogonally polarized components when the output is nonstationary have been found. It is shown that the diversity of nonstationary polarization phenomena in gas lasers with weakly anisotropic cavities is due to spontaneous pulsations of intensities, ellipticities, and azimuths of two emitted waves, caused by the competition of the nonlinear active medium and empty cavity anisotropies. The results of the theoretical modeling are in quantitative agreement with the experimental results.

Amplification without population inversion in a resonant V-type atomic medium is analyzed using the theory of quantum trajectories. A global view of the dynamics underlying the amplification is provided by a quantum stochastic process governing an interplay between coherence and decoherence. The quantum trajectories decompose into distinct “gain cycles” and “loss cycles” which determine, respectively, the emission and absorption spectra that might be calculated from perturbation theory. Two methods for calculating net gain are developed, motivated by complementary views of the exchange of energy between an atom and a probe field. One time averages the energy radiated continuously by the induced dipole, while the other determines probabilities for discontinuous energy exchange through the emission and absorption of individual quanta. In the latter case, the emission and absorption probabilities are evaluated as sums over probabilities for classical records that define the unobservable exchange of a quantum with the probe field in terms of observable scattering events. Quantum trajectories for a V-type medium driven by a coherent field are compared with those for a medium driven incoherently. Two relationships which connect amplification to population inversion in the latter case are shown to be lacking in the former; hence the possibility for amplification without population inversion arises from the following: (1) a decoupling of the rate of gain-cycle (loss-cycle) initiation from the time-averaged population in the initial state for gain (loss), and (2) loss of the symmetry that the final state for emission be the initial state for absorption and vice versa. The specific influences of these general observations vary from model to model. The details are worked out for the resonant V-type medium, where the quantum trajectory analysis sheds light on the meaning of “without population inversion” and “cancellation of absorption by quantum interference.”

We study the level shifts and depopulation of Rydberg states, confined between two parallel metallic plates, due to blackbody radiation. After the derivation of the formal equations for the level shift and the depopulation, we present, as an example, specific calculations for the Rb $24s$ state as a function of plate distance $L$ at three different temperatures 10, 85, and 205 K.

Transverse pattern formation in a three-level cascade laser is analyzed in the case of a cavity resonator limited by infinite plane-parallel mirrors. The two generated fields present in general different spatial profiles, which are coupled to each other through their nonlinear interaction with the amplifying medium. Close to the lasing threshold, the spatiotemporal dynamics can be described by two coupled amplitude equations of either the Ginzburg-Landau or Newell-Whitehead-Segel types, depending on the values of the field detunings. For small detunings, the dynamics can also be described by universal model equations that take the form of coupled complex Swift-Hohenberg equations. These equations yield traveling-wave solutions whose stability can be analyzed by means of phase equations. Numerical simulations confirm the validity of the Swift-Hohenberg approach and show the influence of the coupling between the two cascaded fields in the pattern-forming process.

The temporal behavior of a polarization self-modulated laser is investigated theoretically and experimentally. The self-phase-locking of the eigenstates of such a laser is described theoretically by a set of coupled nonlinear differential equations governing the amplitudes and phases of the eigenstates. This permits us to reproduce the temporal signals obtained experimentally for different locations of the active medium with respect to the nodes and antinodes of the eigenstates. This proves unambiguously that such lasers are passively phase locked. This is confirmed experimentally and theoretically by the fact that the eigenstates can be unlocked by slightly altering the eigenstate spectrum, thus leading to a loss of the specific temporal behavior of such a polarization self-modulated laser.