X-ray photoionization of hydrogen in the presence of a bichromatic laser field is considered. The expressions for the $T$ matrix and the cross sections for the laser-assisted x-ray photoionization are presented. The initial state is the laser-field-dressed hydrogen-atom ground state, while the final state is the improved Coulomb-Volkov wave. The gauge consistency is ensured by working in the $\mathbf{r}\cdot \mathbf{E}$ gauge. It turns out that the matrix elements (the explicit form of which is given in the Appendix) are much simpler in this case. This enables one to consider the symmetry properties of the $T$ matrix and the cross sections analytically. It was shown that the symmetry $(\phi +\pi ,\pi -\theta )\leftrightarrow (\phi ,\theta )$, where $\phi$ is the relative phase between the laser-field components and $\theta$ is the polar angle of the outgoing electron, is exact in our case. In addition to this, there are approximate symmetries $\phi \leftrightarrow -\phi$ and $\phi \leftrightarrow \phi +\pi$. All these symmetries, as well as the behavior of the differential and total cross sections as functions of $\phi$, $\theta$, and the number of exchanged photons, are analyzed in numerous examples. The results presented show the possibility of the coherent phase control of the laser-assisted x-ray photoionization process. It was also shown that in the monochromatic case our model gives results that are in good agreement with the results of previous work.

We consider the hydrogen atom in the orthogonal electric and magnetic fields whose strength is assumed to be small enough for the Coulomb $n$-shell perturbation theory to apply. Appropriate scaling of the two fields leads to a uniform parametrization of the problem by $S$, the combined strength of the two fields, and $\alpha$, the ratio of the two field strengths. The initial six-dimensional phase space $R_6$ is lifted to the standard Kustaanheimo-Stiefel eight-dimensional space and then reduced explicitly to the $S_2\times S_2$ reduced space of the $n$ shell using the Lie transformation to the third order in $S$. At fixed $S$ the system is uniformly tuned between the Zeeman and the Stark limits using the analytic formulas of the perturbation theory. The approach requires application of the invariant theory, group theory, and topology to the analysis of the dynamics on the reduced space $S_2\times S_2$ and subsequent explicit transition to the original $R_6$. In particular we follow the evolution of the four principal periodic orbits (nonlinear normal modes) and corresponding four relative equilibria on $S_2\times S_2$.

In this paper we extend the existing theory of stimulated Raman adiabatic passage (StiRAP) in three-level systems to examine the nature of selective photoexcitation using counterintuitively ordered pulses. Our goal is to develop a version of StiRAP that permits control of product selectivity in a chemical reaction. We analyze the case of selective excitation to one state in a pair of degenerate target states in a four-level system, and find that one cannot control the ratio of the populations in the two states in a resonant two-photon process. However, the extension of the system to include a fifth state and a third laser field makes selective excitation to one of the degenerate states possible. It is found that, subject to reasonable restrictions, one may accomplish complete population transfer to a single target state of a degenerate pair of states in a five-level system.

A theory of the ordered motion of two ions in a Paul trap is derived without using the standard pseudopotential approach. The method relies on the limit cycle theory and the van der Pol–Krylov–Bogoliubov approximation. We evaluate approximate solutions to the equations of motion and discuss stability regions and alignment transition regions for various types of motion. We compare analytical predictions with numerical computations and find a good quantitative agreement.

We have simultaneously spin polarized and subrecoil cooled sodium atoms trapped in a blue detuned optical dipole trap. Temperatures of 1.5 μK and less have been achieved for atoms which have been polarized into any of three $F=1\mathrm{}$ ground-state magnetic sublevels of sodium. The final phase-space density is comparable to the best achieved by an all-optical cooling technique.

We propose a scheme that allows us to laser cool trapped atoms to the ground state of a one-dimensional confining potential. The scheme is based on the creation of a dark state by designing the laser profile, so that the hottest atoms are coherently pumped to another internal level, and then repumped back. The scheme works beyond the Lamb-Dicke limit. We present results of a full quantum treatment for a one-dimensional model.

We report on the observation of the modification of the two spin-orbit ionization continua of Xe through laser-induced continuum structure (LICS). The radiative decay of the Xe ground state into the two electronic continua that correspond to the two fine-structure levels of the ground state of the ${\mathrm{Xe}}^{+}$ ion can be varied by electromagnetically embedding a bound state of the atom into the two continua. The dressed ${}^2{P}_{1/2}$ continuum, probed from the atomic ground state through three-photon absorption, exhibits a clear induced structure, while the ${}^2{P}_{3/2}$ continuum possesses no observable structure under the present experimental conditions, as manifested through high-resolution photoelectron spectra. The modified ionization ratio is controlled by the wavelength of the dressing field.

We consider the precise quantum state of two trapped, coupled Bose-Einstein condensates in the two-mode approximation. We seek a representation of the state in terms of a Wigner-like distribution on the two-mode Bloch sphere. The problem is solved using a self-consistent rotation of the unknown state to the south pole of the sphere. The two-mode Hamiltonian is projected onto the harmonic-oscillator phase plane, where it can be solved by standard techniques. Our results show how the number of atoms in each trap and the squeezing in the number difference depend on the physical parameters. Considering negative scattering lengths, we show that there is a regime of squeezing in the relative phase of the condensates which occurs for weaker interactions than the superposition states found by Cirac et al. (quant-ph/9706034). The phase squeezing is also apparent in mildly asymmetric trap configurations.

We calculate Raman scattering of light from a Bose condensate of dilute gas confined in a harmonic trap. We examine the changes in the Raman line shape as a function of temperature. The linewidth exhibits a remarkable transition as the system is cooled down from the noncondensed to the condensed phase. We also present results for sidebands arising from deeper traps. We show that all these results on Raman line shapes are especially pronounced in the backward direction.

We calculate the damping of low-lying collective modes of a trapped Bose gas in the hydrodynamic regime, and show that this comes solely from the shear viscosity, since the contributions from bulk viscosity and thermal conduction vanish. The hydrodynamic expression for the damping diverges due to the failure of hydrodynamics in the outer parts of the cloud, and we take this into account by a physically motivated cutoff procedure. Our analysis of available experimental data indicates that higher densities than have yet been achieved are necessary for investigating hydrodynamic modes above the Bose-Einstein transition temperature.

The derivation of the Gross-Pitaevski equation is discussed starting from a bosonic field theory. The one-loop corrections are derived and estimated using the parameter range where the Thomas-Fermi approximation is expected to be good. It is found that it is consistent to neglect mass and interaction renormalization effects when these parameters are estimated using the Gross-Pitaevski results.

Damping in a dilute Bose gas is investigated using a mean-field approximation which describes the coupled oscillations of condensate and noncondensate atoms in the collisionless regime. Explicit results for both Landau and Beliaev damping rates are given for nonuniform gases. In the case of uniform systems, we obtain results for the damping of phonons both at zero and finite temperature. The isothermal compressibility of a uniform gas is also discussed.

We consider interaction of a laser field with surface waves propagating in a thin layer having a width much less than that of the laser field. It is assumed that the laser field interacts concurrently with a two-level transition. We show that generation of the surface waves in this scheme may be described by the completely integrable Thirring model. We use this model for study of the evolution of a steplike pulse. It is found that a leading edge is described asymptotically by a sequence of solitons. The modulation instability leading to the formation of these solitons is treated in a hydrodynamic approximation. For this aim we find a solution to the Whitham equations associated with deformation of the one-phase solution of the Thirring model. We show that the results obtained here can be applied to other physical situations, for instance, the study of the three-wave mixing in a bulk medium.

Beam modes are considered by a high-aperture scalar theory based on the complex source-point method. A different form for the beam mode that avoids nonphysical singularities in intensity is introduced. The amplitude in the focal region is explored for the lowest-order mode. Conditions for oscillation of a high-aperture resonator, such as a microcavity, are derived. The amplitude in the focal region is explored for higher-order modes in systems with cylindrical symmetry. These modes are expressed in terms of Jacobi polynomials.

In this paper we present a detailed theoretical analysis of a recent quantum-nondemolition experiment in optics using cold atoms in a magneto-optical trap as a nonlinear medium. A signal beam and a meter beam from two independent lasers are coupled within a Λ-type three-level scheme in the $D1\mathrm{}$ line of ${}^{87}\mathrm{Rb}$ atoms. The experimental results for the relevant quantum correlations of the fields, that represent up to now the best achievements for a single back-action evading measurement, are found in a remarkably good agreement with the theoretical predictions from a fully quantum model for three-level atoms in a doubly resonant cavity.

Positive and negative subnatural-width resonances (SNWR) were observed in the absorption and fluorescence of rubidium vapor under excitation by two copropagating optical waves with variable frequency offset. The two optical fields resonantly couple Zeeman sublevels, belonging to the same ground-state hyperfine level (GSHL), to an intermediate excited state. The SNWR present opposite signs depending on which GSHL participates in the interaction with the two optical waves. For both Rb isotopes an increase in the transparency with reduced fluorescence occurs for the lower GSHL while the absorption and fluorescence are increased for the upper GSHL. The influence of external magnetic field, polarization, and intensity of applied optical fields on the SNWR is examined. The narrowest observed resonance has a width of 10 kHz (full width at half maximum). The origin of the SNWR is discussed in terms of coherent processes involving ground-state Zeeman sublevels.

We report the polarization measurement of a very high order (59th and 61st order, $\sim$17 nm) harmonic. A Mo-Si multilayer mirror is used as a polarizer with reflectivity of 60% and polarization analyzing power close to unity around a wavelength of 17 nm. We observe that for these high harmonics in Ne there is no rotation of the polarization ellipse with respect to the fundamental laser polarization, even though the harmonics are in the plateau. For linear and slightly elliptical laser polarization the harmonics still remain linearly polarized. These findings are supported by a full theoretical simulation, which includes spatiotemporal integration and phase matching of the emitted harmonic radiation.

We present a method to calculate the dynamics of very-low-temperature Bose-Einstein condensates in time-dependent traps. We consider a system with a well-defined number of particles, rather than a system in a coherent state with a well-defined phase. This preserves the $U\left(1\right)\mathrm{}$ symmetry of the problem. We use a systematic asymptotic expansion in the square root of the fraction of noncondensed particles. In lowest order we recover the time-dependent Gross-Pitaevskii equation for the condensate wave function. The next order gives the linear dynamics of noncondensed particles. The higher order gives corrections to the time-dependent Gross-Pitaevskii equation including the effects of noncondensed particles on the condensate. We compare this method with the Bogoliubov–de Gennes approach.

The longitudinally multimode class-$B$ laser with inhomogeneous broadening is known to behave as a chain of coupled oscillators, each being associated with one mode. If emission occurs along the two eigenstates of polarization, we show theoretically and experimentally that the waves propagating in the spectrum are characterized by two dispersion curves associated with oscillations in phase and in opposite phase of two close modes with different polarizations. These curves may be viewed as the analogs of the “acoustical” and “optical” branches in one-dimensional diatomic crystals.

In centrosymmetric media, in addition to the third- and fifth-order nonlinearity, a cascaded ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}:{\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinearity contributes to the nonlinear refraction. The described effect takes place when the input beam is involved in nearly phase-matched third-harmonic generation. The nonlinear phase shift produced by this new cascaded nonlinearity is comparable to the nonlinear phase shift caused by the direct third-order nonlinearity ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}.$ A new analytical approach, low depletion approximation, was developed and used to study the cascaded third-order processes in the conditions of not very high third-harmonic conversion coefficients. At higher conversion coefficients the effect was studied by numerical simulations. The presence of a seeded third-harmonic wave gives another possibility of controlling the additional phase shift of the fundamental wave. The conditions for stationary copropagation of the fundamental and the generated wave are presented.