We consider high harmonic generation by ultrashort (27–108 fs) laser pulses and calculate the macroscopic response of a collection of atoms to such a short pulse. We show how the harmonic spectrum after propagation through the medium is significantly different from the single-atom spectrum. We use single-atom data calculated by integration of the time-dependent Schrödinger equation and propose a method, based on an adiabatic approximation, to extract the data necessary to perform a propagation calculation.

The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schrödinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.

The production of ${\mathrm{C}}^{Z+},\hspace{0.5em}{\mathrm{N}}^{Z+}$, and ${\mathrm{O}}^{Z+}$ multicharged atomic ions up to $Z=4\mathrm{}$ is investigated using the laser-induced multiple ionization of small molecules in the gas phase in the ${10}^{15}–{10}^{16}-{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ laser intensity range. For molecules built with a single C, N, or O atom and hydrogen atoms such as ${\mathrm{CH}}_4{,\mathrm{\hspace{0.5em}}\mathrm{NH}}_3$, and ${\mathrm{H}}_2\mathrm{O}$, the $Z=3\mathrm{}$ and 4 ion yields are systematically weaker than for molecules built with equivalent atoms such as ${\mathrm{N}}_2{,\mathrm{\hspace{0.5em}}\mathrm{C}\mathrm{O},\mathrm{\hspace{0.5em}}\mathrm{O}}_2{,\mathrm{\hspace{0.5em}}\mathrm{CO}}_2$, and ${\mathrm{N}}_2\mathrm{O}$ using rigorously the same laser excitation conditions. In particular, the ${\mathrm{C}}^{4+}{,\mathrm{\hspace{0.5em}}\mathrm{N}}^{4+}$, and ${\mathrm{O}}^{4+}$ ion production efficiency is more than one order of magnitude lower in the first case. In addition, no significant differences are found for the ion production efficiency between diatomic and linear triatomic molecular species built with the same atoms. This overall behavior remains the same at lower laser intensities in the ${10}^{14}–{10}^{15}-{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ range for lower atomic ions charge states. The experimental results are in good qualitative agreement with recent theoretical models of molecules in strong laser fields. In order to get quantitative agreement, the initial three-dimensional electronic configuration of each molecule has to be included in nonperturbative theories.

Quantum motion of atoms in light fields is described on the basis of adiabatic internal states. Forces arise due to the spatial variation of these states, which is determined by the electric field polarization. In a dark state, these are the only forces present. They are described by a geometric vector and a scalar potential. We give analytical expressions for the geometric potentials in the dark states of a driven $\overrightarrow{j}j-1$ transition and the dark state in the $\overrightarrow{1}1$ system, for arbitrary electromagnetic fields. For systems with velocity selective trapping states, the scalar geometric potential is inversely proportional to the field intensity squared. When the field has nodes the potential diverges. In one dimension, this constitutes an exact realization of the Kronig-Penney model.

Tailored microwave pulses, to guide asymmetric-top molecules from selected rotational states belonging to the vibronic ground state to generalized angular-momentum coherent states, are designed by using optimal control theory. Characteristics that the molecules have to fulfill in order to achieve the goal with feasible pulses are discussed. Properties of the pulses are discussed as well. The further dephasing among the components of the wave packet which, for the simplest coherent state, is a form of dynamical tunneling, can be locked by exploiting the changes that energy levels and eigenfunctions undergo in the presence of an external static electric field with appropriate intensity. For the special case with $M=0\mathrm{}$, periodic fields are more flexible in avoiding dephasing. This is shown by examining properties of quasienergies and dressed states resulting from the diagonalization of a truncated Floquet matrix.

The pure long-range $1_u$ state of an alkali-metal dimer is observed in ${}^{39}{\mathrm{K}}_2$ using photoassociative spectroscopy of ultracold atoms. High-resolution spectra for vibrational levels $v=\overrightarrow{0}7$ are recorded by resonance-enhanced two-photon ionization. Strong rotation-hyperfine couplings are observed. Major molecular constants and a hyperfine structure analysis are presented. This $1_u$ state is useful as an ungerade Franck-Condon “window” at large internuclear distance for studies of highly excited long-range interactions.

We consider a hydrogen atom in a strong static electric field with a weak parallel radio-frequency (rf) field. We compute the photoabsorption spectrum by calculating the spectrum of Floquet states, including their quasienergies and their oscillator strengths. Our calculation is based upon “semiquantal” formulas: we calculate the discrete spectrum of quasienergy states by using a quantum adiabatic approximation combined with semiclassical (Bohr-Sommerfeld) quantization rules. We express this spectrum in a manner consistent with the method of scaled-variable spectroscopy, and then calculate the Fourier transform. These calculated absorption spectra and recurrence spectra are in good agreement with experiments on Li atoms. Additional approximations show that the recurrence spectrum is approximately equal to the product of the recurrence spectrum in a static field times an envelope function. That envelope function is the Fourier transform of a cluster of sidebands surrounding a progenitor level in the rf field. The resulting formula agrees with the low-frequency limit of a formula obtained from a semiclassical treatment.

The oscillation between bound-state configurations in a rapidly autoionizing three-body Coulomb system has been directly observed. Using a 500-fsec laser pulse, calcium atoms are excited to the pure ${4p}_{3/2}15d$ two-electron configuration at an energy greater than 3 eV above the ionization limit. As a result of configuration interaction, the electrons scatter coherently into multiple bound and continuum configurations. The oscillation between the degenerate ${4p}_{1/2}{n}^{\prime }d$ and ${4p}_{3/2}\mathrm{nd}$ modes as well as autoionization into ${4s}_{1/2}\epsilon \mathcal{l},$ ${3d}_{3/2}\epsilon \mathcal{l},$ and ${3d}_{5/2}\epsilon \mathcal{l}$ continua are observed explicitly using bound-state interferometry. The measured time dependence of the ${4p}_{3/2}15d$ character is in excellent agreement with the Fourier transform of the frequency domain excitation cross section. To our knowledge, this is the first experimental demonstration of the equivalence of time and frequency domain spectra in a multiconfigurational system involving bound and continuum channels.

We introduce a notion of “matrix potential” to nonlinear optical systems. In terms of a matrix potential $g$, we present a gauge-field-theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multilevel media. We show that the Bloch part of the equation can be solved identically through $g$ and the remaining Maxwell equation becomes a second-order differential equation with a reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (non-Abelian) symmetry structure of the Maxwell-Bloch equations for various multilevel media in association with symmetric spaces $G/H$. In particular, we associate the nondegenerate two-level system for self-induced transparency with $G/H=\mathrm{SU}\left(2\right)/\mathrm{U}\left(1\right)\mathrm{}$ and three-level $\Lambda$ or $V$ systems with $G/H=\mathrm{SU}\left(3\right)/\mathrm{U}\left(2\right)\mathrm{}$. We give a detailed analysis for the two-level case in the matrix potential formalism, and address various properties of the system including soliton numbers, effective potential energy, gauge and discrete symmetries, modified pulse area, conserved topological, and nontopological charges. The nontopological charge measures the amount of self-detuning of each pulse. Its conservation law leads to a different type of pulse stability analysis that explains earlier numerical results.

The Bäcklund transformation for the three-level coupled Schrödinger-Maxwell equation is presented in the matrix potential formalism. By applying the Bäcklund transformation to a constant-electric-field background, we obtain a general solution for matched pulses (a pair of solitary waves) that can emit or absorb a light velocity solitary pulse but otherwise propagate with their shapes invariant. In the special case, this solution describes a steady-state pulse without emission or absorption, and becomes the matched pulse solution recently obtained by Hioe and Grobe [Phys. Rev. Lett. 73, 2559 (1994)]. A nonlinear superposition rule is derived from the Bäcklund transformation and used for the explicit construction of two solitons as well as non-Abelian breathers. Various features of these solutions are addressed. In particular, we analyze in detail the scattering of “binary solitons,” a specific pair of different wavelength solitons, one of which moves with the velocity of light. Unlike the usual case of soliton scattering, the broader soliton changes its sign after the scattering, thus exhibiting a binary behavior. Surprisingly, the light velocity soliton receives a time advance through the scattering, thereby moving faster than light, which, however, does not violate causality.

In a previous Rapid Communication [Phys. Rev. A 56, R5 (1997)] we reported a semiclassical formula describing oscillator strengths for transitions to a high Rydberg state of a hydrogen atom in an electric field. The formula relates the oscillator strength for an atomic transition into a Rydberg state to the angular distribution of outgoing electron waves and to the density of classical tori. Here we give a derivation of that formula and we suggest some generalizations. We compare the formula with experimental measurements of the absorption spectrum of hydrogen in an electric field. This absorption spectrum consists of quasidiscrete resonances superposed on a smooth background. We find that this background has a hitherto unexplained structure that was visible but not recognized in the experiment. The background absorption is related to electron orbits that directly escape from the atom, and its structure is related to the angular distribution of outgoing electrons.

We present the results of analytical and numerical calculations of the amplitude and temporal shape of photon echoes produced in optically thick absorbing media. In particular, we are interested in echo output signals that mimic the temporal shape of one of the input pulses (the data pulse). Echo recall efficiencies of temporally structured data pulses exceeding unity can be obtained in optically thick media while preserving the information content of the data pulse. We find that the relationship between the maximum echo efficiency and the Beer’s length at which that maximum is attained is nearly linear. This linear relation holds well beyond the optimal absorption length predicted by linear theory for both two-pulse photon echoes and three-pulse stimulated photon echoes. These results have significance in the development of optical coherent transient memory and processing systems, where previous calculations predicted recall efficiencies of only a few percent.

The Bogoliubov equations of the quasiparticle excitations in a weakly interacting trapped Bose condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasiparticle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasiparticle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function, which can be observed by off-resonance inelastic light scattering.

We describe an atomic interferometer based on Raman transitions between two hyperfine states. We show how atom count probabilities at the output of the interferometer can be used to reconstruct the joint multiparticle state of a two-mode Bose-Einstein condensate. Two data collection schemes are compared, via numerical solution for the density matrix from the probability data and analytical estimates of the errors are made. In the first scheme, only the phase of the interferometer is varied. We prove that state reconstruction is impossible for the case of a balanced beam splitter; otherwise, the problem is ill-conditioned. In the second scheme, both the phase and transmission parameters are varied, the $Q$ function can be measured directly, and the reconstruction of the state is well conditioned.

We derive coupled equations of motion for the condensate (superfluid) and noncondensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock-Popov approximation for the time-dependent condensate wave function, and thermodynamic local equilibrium for the noncondensate atoms. In the special case of a uniform weakly interacting gas, our hydrodynamic equations are shown to be consistent with the two-fluid equations of Landau. The collective modes in a parabolically trapped Bose gas include the analog of the out-of-phase second-sound mode in superfluid ${}^4\mathrm{He}$.

Thermal fluctuations of the normal component induce dephasing—reversible damping of the low-energy collective modes of a confined Bose-Einstein condensate. The dephasing rate is calculated for the isotropic oscillator trap, where the Landau damping is expected to be suppressed. This rate is characterized by a steep temperature dependence. It is weakly amplitude dependent, and is sensitive to the total number of atoms in the trap. The value of the rate belongs to the range of the damping rates observed by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)]. We suggest that a reversible nature of the damping caused by the thermal dephasing in the isotropic trap can be tested by the echo effect. A reversible nature of the Landau damping is also discussed, and a possibility of observing the echo effect in an anisotropic trap is considered as well. The parameters of the echo for the isotropic trap are calculated in the weak echo limit. Results of the numerical simulations of the echo are also presented.

Various aspects of the phase dynamics of an atom-laser scheme based on binary collisions are investigated. Analytical estimates of the influence of elastic atom-atom collisions on the laser linewidth are given, and linewidths achievable in a recently proposed atom-laser scheme [M. G. Moore and P. Meystre, Phys. Rev. A 56, 2989 (1997)] are evaluated explicitly. The extent to which a relative phase can be established between two interfering atom lasers as well as the properties of this phase are also investigated.

We demonstrate a method of inducing neutron spin rotation in a field-free region of space. A multilayer mirror (“spin splitter”) is used as an optically active element, providing a longer path length for one spin eigenstate of a polarized neutron than for the other. This produces a relative phase shift between the two eigenstates, which is interpreted, quantum mechanically, as precession of the neutron spin. We show that the spin precession of our technique is equivalent to Larmor precession in a magnetic field, though our method has no such classical analog and occurs on shorter (e.g., 20 nm) length scales. We also demonstrate a “phase spin-echo” interferometer based on a pair of multilayer spin splitters.

A special kind of atomic beam splitter using a four-level atomic system in combination with polarized light fields is demonstrated. These specific atom optical elements are used to operate an atom interferometer where the beam-splitting mechanism acts selectively on specific paths only and therefore allows for several different interferometer geometries. Based on a Ramsey-Bordé configuration, the experimental data show considerably better accuracy and a contrast enhanced by 65% compared to the two-level interferometer. Our concept appears to be especially interesting in the context of metrological aspects in matter-wave interferometry.

I derive the quantum phase-noise limit to the sensitivity of a Mach-Zehnder interferometer in which the incident quantum particles enter via both input ports. I show that if the incident particles are entangled and correlated properly, then the phase sensitivity scales asymptotically like the Heisenberg-limited $\Delta \phi =O(1/N),$ for large $N,$ where $N$ is the number of particles incident per unit time. (In a one-input-port device, the sensitivity can be at best $\Delta \phi =1/\sqrt{N}.$) My calculation applies to bosons or fermions of arbitrary integer or half-integer spin. Applications to optical, atom-beam, and atom-laser gyroscopes are discussed—in particular, an atom-laser can be used to obtain the required entanglements for achieving this Heisenberg-limited sensitivity with atomic matter waves.