We consider x-ray-hydrogen atom scattering in the presence of a monochromatic linearly polarized laser field. The S matrix of this process is presented and an expression for the differential cross section (DCS) is derived. We show that the time-dependent Wentzel-Kramers-Brillouin approximation can be applied to the present problem. The presented numerical results for the DCS as a function of the number n of photons exchanged with the laser field show a characteristic behavior. The number n can only be even. For $n=0,\pm 2$ we have pronounced maxima in the DCS, followed by sharp minima at $n=\pm 4.$ After that, we have a plateau that is different for negative and positive values of n. The plateau for negative values of n is much more extended than for the positive ones. The structure of the plateau and the positions of the minima and maxima of the DCS do not depend on the laser field intensity, while the height of the plateaus strongly depends on it. We also analyze the dependence of the matrix elements of the x-ray spectra on the incident x-ray photon energies by using both the saddle-point method and the numerical evaluation, and we show that the shape and position of the plateau are determined by the simple relation $nħ\omega {=I}_0-ħ{\omega }_{\mathbf{K}}.$ This condition connects the number of absorbed or emitted laser field photons n, the laser field photon energy $ħ\omega ,$ the atomic ionization potential $I_0,$ and the energy of the incident x-ray photon $ħ{\omega }_{\mathbf{K}}.$

The laser-cooled ions in a radio-frequency ion show a variety of peculiar line profiles as functions of laser intensity and trap potential. All these line profiles are well reproduced by a calculation based on the present theoretical model, in which the ion motion in a trap in the presence of laser radiation pressure is analyzed. The results give information about collisions of ions, and are utilized for the accurate spectroscopic measurement of the ion responses.

$p+$H collisions in the presence of intense laser fields are investigated by the classical trajectory Monte Carlo method. A prominent feature of these processes is that, in contrast to the usual ionization scheme in field-free ion-atom collisions, the ionization of the target atom is always accompanied by an increase in the total kinetic energy of the colliding proton and the target nucleus. This result is explained in terms of the charge-resonance-enhanced-ionization effect taking place when the internuclear separations reach a range of 4–10 a.u. Also, the energy-gain cross section is evaluated, and its dependence on laser intensities is discussed.

This work investigates the dissociation dynamics of a diatomic molecule under the chirped pulse with the vibrational and rotational degrees of freedom. Results obtained herein are also compared with those of the conventionally used one-dimensional (1D) model. According to the comparison, the 1D model still provides valuable information such as dissociation dynamics. Meanwhile, predictions such as harmonic generation spectrum from the 1D model are impractical.

A description of the common properties for different phenomena is presented: interference stabilization of Rydberg atoms in a strong electromagnetic field and phase locking of an array of cavities. A comparison of master equations is held for the discussed effects. Analytical expressions for basic parameters of the problems involved are used for quantitative analysis. The analogy established is exploited for the interpretation of a decrease in intracavity losses in the system of two coupled cavities with an increase of the extent of mutual coupling at a slight detuning of the cavity lengths. The expediency of the analogy establishment consists of existing difficulties in experimental confirmation of the principles of Rydberg-atom stabilization.

The phenomenon of coherent population trapping in alkali-metal atoms is analyzed by means of a perturbation approach. Closed form transparent solutions are obtained for the coherences existing within the system and the populations of the ground levels and of the excited state. The presence of dark lines and coherent microwave emission from the ground state are made explicit. Experimental results that confirm the theoretical calculations are reported for the case of cesium in a buffer gas. Conclusions are drawn in connection with the application of coherent population trapping to the field of atomic frequency standards.

For ideal Bose atoms in an isotropic harmonic trap, we consider thermodynamic variables obtained from microcanonical, canonical, and grand canonical ensembles, each with certain variables specified and other variables fluctuating. For the first two of these ensembles, we derive recursion relations that link partition functions for different dimensions. We discuss fluctuations in general, and obtain expressions for variances of the atom number N, the chemical potential μ, and the temperature T for small, Gaussian fluctuations in the grand canonical ensemble. Then from our recursion relations and others given elsewhere, we obtain probability distributions for N, for ground-state occupation number $n_0$, for μ, and for T. Below the critical temperature, the shape of the distributions for N, $n_0,$ and μ are definitely not Gaussian for the grand canonical ensemble. For given temperature and small N, we find that the chemical potential values pertaining to the three ensembles differ. We compare the specific-heat function $C_N\mathrm{}\left(T\right)\mathrm{}$ for the three ensembles and propose to use the minimum of ${\mathrm{dC}}_N/dT$ to define the critical temperature to facilitate comparisons with similar configurations of interacting atoms.

In analogy to Glauber’s analysis of optical coherence, we adopt an operational approach to introduce different classes of atomic coherence associated with different types of measurements. For the sake of concreteness we consider specifically fluorescence, nonresonant imaging, and ionization. We introduce definitions of coherence appropriate to them, which we call electronic, density, and field coherence, respectively. We illustrate these concepts in various descriptions of Bose-Einstein condensation, showing that each of these descriptions makes different implicit assumptions on the coherence of the system. We also study the impact of elastic collision on the field and density coherence properties of atom lasers.

We provide a unified investigation of normal modes and sound propagation at zero temperature in Bose-Einstein condensed gases confined in highly asymmetric harmonic traps and interacting with repulsive forces. By using hydrodynamic theory for superfluids we obtain explicit analytic results for the dispersion law of the low-energy discretized modes for both cigar- and disk-shaped geometries, including the regime of large quantum numbers where discrete modes can be identified with phonons. The correspondence with sound propagation in cylindrical traps and the one-dimensional nature of cigar-type configurations are explicitly discussed.

We consider how to probe the quantum degeneracy of a dilute noncondensed Bose gas by measuring quantum statistical properties of a transmitted light field. In particular, we use the sensitivity of the quantum correlations of a squeezed vacuum transmitted by a dispersive dielectric slab to differential changes in the dielectric transmission coefficient as a function of frequency. This result is applied to the transmission of squeezed light from a degenerate optical parametric oscillator by a dilute, inhomogeneous noncondensed Bose gas. We find that the pronounced sensitivity to differential dispersion and absorption can be used to distinguish between classical and quantum gas statistics, due to the influence of bosonic particle bunching on the dielectric response, including the influence of resonant van der Waals interactions. The transition from classical to quantum gas behavior is predicted to result in an overall reduction in noise in the transmitted spectrum of homodyne photocurrent fluctuations.

We investigate a nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement backaction noise alone.

All existing atomic mirrors are conceptually similar to metallic mirrors in standard optics in the sense that they are constructed with repulsive potentials and thus produce an imaginary “refraction index.” Here a different kind of mirror for atoms that is similar to a multilayer dielectric mirror in standard optics is proposed. We show that a periodic attractive laser potential can reflect atoms of certain momenta due to the presence of gaps in the spectrum of energies, as in the photonic band-gap structures in light optics. Spontaneous emission and gravitational effects are also analyzed.

Light reflected from a conical mirror produces an intensity gradient that can be used to focus atoms to a single spot. Within the Raman-Nath approximation the position of the focal plane, peak atomic density, and spot size have been determined for a range of field strengths. Theoretical estimates of the field strength needed to focus atoms using a conical lens are found to be three to four orders of magnitude lower than that needed for focusing atoms using standing-wave fields.

We consider the conditions under which solitary waves can exist in elongated clouds of Bose-Einstein condensed atoms. General expressions are derived for the velocity, characteristic size, and spatial profile of solitary waves, and the low- and high-density limits are examined.

Present experiments with Bose condensed gases can be largely described by a semi-ideal two-gas model. In this model, the condensate is influenced only by the mean-field repulsion among condensed atoms, while the thermal cloud is considered an ideal gas confined by an effective potential that consists of the external trap and the mean-field repulsion by the condensate. This simple, intuitive model provides explicit analytical expressions for the density distributions of the condensate and the thermal component. It describes the reduction of the condensate fraction relative to that of an ideal gas as a consequence of the positive chemical potential due to interactions in the condensate.

In view of ongoing experiments to trap ultracold spin-polarized ${}^6\mathrm{Li},$ we study various properties of an interacting Fermi gas in a harmonic trap, taking the discrete nature of the unperturbed harmonic trap levels into account exactly. As ${}^6\mathrm{Li}$ has a rather large and negative scattering length, we focus on the effects of the attractive atom-atom interaction on several thermodynamic properties, and on the momentum and density distributions. The dependence of the chemical potential, the specific heat, and the density and momentum distributions on the number of particles in the trap is obtained. We also calculate the energy of the gas. Comparison is made with results of a semiclassical calculation and with the properties of a noninteracting gas. We find that the effect of the interactions is rather large for realistic trap frequencies. Hence it is important to include these interactions in any quantitative predictions relevant for experiments.

We present two gapless mean-field theories for trapped Bose-Einstein condensates, and compare them to the better known Hartree-Fock-Bogoliubov (HFB)-Popov approach. The proposed theories are based on suitable inclusion of the simplest anomalous average of the Bose field operator. This leads to an effective interaction between two atoms which is both temperature and density dependent, as opposed to the HFB-Popov approach, for which it is constant. These theories are compared to the HFB-Popov approach for a trapped one-dimensional condensate of 2000 atoms. The density profiles and excitation frequencies of the proposed theories differ from the corresponding HFB-Popov ones by at most a few percent.

In this work we develop a quantum theory of second-order nonlinear optical processes such as parametric fluorescence and second-harmonic generation (SHG), generated by a strong electromagnetic field in an active medium placed in a microcavity. Fields are quantized and expanded in terms of a suitable set of cavity normal modes. In the first part of this work we consider a single many-level quantum system (an atom or molecule), which interacts with all the radiation field modes (spontaneous emission). We show how vacuum fluctuations affect both SHG and parametric processes. For SHG, we demonstrate that the presence of the microcavity allows the introduction of the concept of coherence length, even for a medium made of a single molecule. In the second part of this paper we discuss the case of a uniform distribution of emitting dipoles. For this configuration we calculate the differential extinction coefficient, and discuss the dependence of the emitting power on the microcavity’s parameters. Finally we suggest the possibility of realizing a micro-optical parametric oscillator.

We observed quantum interference effects in steady-state optical absorption in a $V$-type three-level system of ${\mathrm{Pr}}^{3+}:{\mathrm{YAlO}}_3$ where a hyperfine transition between two upper levels was homogeneously broadened by pure dephasing. This $V$-type system was excited by a single driving radio-frequency (rf) field and two probe laser fields (quantum-beat scheme). The probe absorption was constructively or destructively affected by the phase of the driving rf field. In contrast, under two-laser excitation without application of the rf, no absorption change due to electromagnetically induced transparency (EIT) was observed. A comparison of observations and theoretical predictions revealed that the quantum-beat scheme generates quantum interference even when the dephasing rate between the two upper levels is comparable with the Rabi frequency of the probe laser, and completely destroys EIT.

The theory in which the laser is interpreted as a nonlinear amplifier and filter is applied to the calculation of its spectral density in the case of a homogeneous medium. The method is extended to an injected laser in which the source term includes both the spontaneous emission and the injected signal. Linewidth narrowing or widening, spectral amplification or attenuation are described, using simple semiclassical formulas.