We study the multiphoton dissociation of ${\mathrm{H}}_2^{+}$ in a strong midinfrared field using a semiclassical, quasistatic approach. The dissociation is caused by the strong coupling of electronic states. We find a broad resonance far below the frequency of the first vibrational transition. This is caused by the field-induced dynamical distortions of the electronic ground state that shifts the classical oscillator frequency into resonance with the effective driving frequency. Dissociation efficiencies and kinetic fragment energies are calculated as a function of wavelength and vibrational excitation.

Hyperspherical harmonic basis functions, expressed in terms of the Jacobi coordinates and belonging to well-defined irreducible representations of the orthogonal and symmetric groups, were recently introduced. The usefulness of these basis functions is presented and the two-body matrix elements between these functions are evaluated, using the various hyperspherical coefficients of fractional parentage. The appropriate rotation, necessary for this evaluation, is achieved by using the rotational symmetry of these functions. Therefore, the representation matrices of the orthogonal group are sufficient for the calculation of the two-body matrix elements. Thus, the Raynal-Revai and the $T$ coefficients are unnecessary. These results make this basis set suitable for few-body calculations in nuclear, atomic, and molecular physics, as well as for microscopic calculations of collective modes in nuclear physics.

The linearized time-dependent coupled Gross-Pitaevskii equations describing the long-wavelength excitations of Bose-Einstein condensed binary mixtures are solved in harmonic traps for the case where only the binary phase is present. The dispersion law contains two branches whose dependence on the quantum numbers of the modes is the same as for a one-component condensate, but with different prefactors, depending on the ratios of the three $s$-wave scattering lengths of the two atomic species. In the general case where the binary phase in the trap coexists with one or both one-component phases, the mode spectrum depends on the geometry of the interphase boundaries due to the boundary conditions there. Measurements of the oscillation frequencies as in recent experiments with modulated traps would yield very detailed information on this system.

A hydrodynamical version of the time-dependent Gross-Pitaevskii equation has been formulated and applied to the description of a Bose-Einstein condensate (BEC) of ${}^{87}$Rb atoms in the JILA time-averaged orbiting potential (TOP) trap. The response of the BEC to time-dependent modulations of the trap potential is computed and the characteristic frequencies of a BEC oscillation agree well with those observed in recent experiments. For the axially symmetric $m=0\mathrm{}$ mode of the TOP trap, we find a weak dependence of the oscillatory frequency on the strength of the driving amplitude under conditions comparable to those of current experiments. The free ringing of the BEC that is induced by a transient change in the potential is found to be periodic, in agreement with the predictions of Thomas-Fermi theory. We analyze the harmonic content of the spectral response and consider possibilities for high-harmonic generation in the context of nonlinear atom optics.

We study the buildup of quantum coherence between two Bose-Einstein condensates that are initially in mixed states. We consider in detail the two cases where each condensate is initially in a thermal or a Poisson distribution of atom number. Although initially there is no relative phase between the condensates, a sequence of spatial atom detections produces an interference pattern with arbitrary but fixed relative phase. The visibility of this interference pattern is close to one for the Poisson distribution of two condensates with equal counting rates but it becomes a stochastic variable in the thermal case, where the visibility will vary from run to run around an average visibility of $\pi /4.\mathrm{}$ In both cases, the variance of the phase distribution is inversely proportional to the number of atom detections in the regime where this number is large compared to one but small compared with the total mean number of atoms in the condensates.

We present a quantum theory of low-lying excitations in a trapped Bose condensate with finite particle numbers. We find that even at zero temperature condensate number fluctuations and/or fluctuations of the excitation frequency due to quantum uncertainties of the mode occupation lead to a collapse of the collective modes due to dephasing. Coherent revivals of the collective excitations are predicted on a much longer time scale. Depletion of collective modes due to second-harmonic generation is discussed.

We consider two dilute gas Bose-Einstein condensates with opposite velocities from which a monochromatic light field detuned far from the resonance of the optical transition is coherently scattered. In the thermodynamic limit, when the relative fluctuations of the atom number difference between the two condensates vanish, the relative phase between the Bose-Einstein condensates may be established in a superposition state by detections of spontaneously scattered photons, even though the condensates have initially well-defined atom numbers. For a finite system, stochastic simulations show that the measurements of the scattered photons lead to a randomly drifting relative phase and drive the condensates into entangled superpositions of number states. This is because according to Bose-Einstein statistics the scattering to an already occupied state is enhanced.

We study the normal modes of a cylindrical Bose condensate at $T=0\mathrm{}$ using the linearized time-dependent Gross-Pitaevskii equation in the Thomas-Fermi limit. These modes are relevant to the recent observation of pulse propagation in long, cigar-shaped traps. We find that pulses generated in a cylindrical condensate propagate with little spread at a speed $c=\sqrt{g\mathrm{n̄}/m},$ where $\mathrm{n̄}$ is the average density of the condensate over its cross-sectional area.

We present a detailed theoretical analysis of the properties and formation of single solitons and higher-order bound dipole pairs in media with anisotropic nonlocal photorefractive material response. The single solitons are elliptical beams, whereas the dipole pairs are formed by a pair of displaced elliptical beams with a π phase shift between their fields. The theory predicts convergence of Gaussian beams to the solitary states within a certain basin of attraction. Experimental observation of these solitons has been presented elsewhere. The experimental portion of the present paper concentrates on the region further away in parameter space, where complex spatial oscillations, including asymmetric filamentation into several beamlets, occurs.

We present a semiclassical and quantum analysis of a nonlinear optical interaction in a cavity in which an externally driven fundamental mode at frequency ω transforms into the second-harmonic mode 2ω and then into the fourth-harmonic mode 4ω via cascaded frequency-doubling processes $\omega +\overrightarrow{\omega }2\omega$ and $2\omega +2\mathrm{}\overrightarrow{\omega }4\omega .$ In the adiabatic limit of the strongly damped fourth-harmonic mode the nonlinear system is equivalent to the process of intracavity second-harmonic generation combined with nonlinear two-photon absorption from the second-harmonic mode. Semiclassical steady states and linear stability analysis show that possible operation regimes are substantially different from those for the pure second-harmonic-generation process. It is shown in particular that the system is characterized by two critical points: Starting from a certain critical value of the driving field intensity, one observes self-pulsing instability; however, at higher intensities, beyond a second critical point, the system turns back to the stable generation regime. Moreover, under appropriate values of the control parameters, one may arrive at a complete quenching of self-pulsing behavior and at stabilization of the steady states in the entire domain of the driving field intensity. These stabilization properties become important when turning to the analysis of the quantum fluctuations and quadrature squeezing effect in the fundamental and second-harmonic modes within the ranges of linearized treatment of fluctuations. Due to the emergence of stability in the behavior of the system at high level of coherent excitation, the system becomes capable of generation of bright light with enhanced squeezing properties.

The interaction of an atomic two-level system and a squeezed vacuum leads to interesting effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of-phase components of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a $4\pi$ squeezed vacuum. In this paper we show how to “engineer” a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two-level atom is represented by the two ground levels of an atom with an angular momentum $J=1/\overrightarrow{2}J=1/2\mathrm{}$ transition (a four-level system), which is driven by (weak) laser fields and coupled to the vacuum reservoir of radiation modes. Interference between the spontaneous emission channels in optical pumping leads to a squeezed-bath-type coupling and thus to symmetry breaking of decay on the Bloch sphere. With this system it should be possible to observe the effects predicted in the context of squeezed-bath–atom interactions. The laser parameters allow one to choose properties of the squeezed-bath interaction, such as the (effective) photon-number expectation number $N$ and the squeezing phase $\phi$. We present results of a detailed analytical and numerical study.

The transient statistics of a gain-switched coherently pumped class-C laser displays a linear correlation between the first passage time and subsequent peak intensity. Measurements are reported showing a positive or negative sign of this linear correlation, controlled through the switching time and the laser detuning. Further measurements of the small-signal laser gain combined with calculations involving a three-level laser model indicate that this sign fundamentally depends upon the way the laser inversion varies during the gain switching, despite the added dynamics of the laser polarization in the class-C laser.

We report a two-photon interference experiment in which a single-photon wave-packet concept fails to give a correct prediction, but the two-photon wave-packet, or biphoton, concept is helpful. Based on our experiment, we argue that single-photon wave-packet information available from two-photon measurement is limited.

We discuss the threshold characteristics and intensity noise of a laser with excess quantum noise as occurs, e.g., in an unstable-cavity laser. We give a theoretical description of the intensity aspects of excess noise based on laser rate equations, including bad-cavity effects. Experimentally, we have measured spectra of intensity noise and phase noise of small HeXe gas lasers. We operate the laser on either a stable or an unstable cavity, in order to change from a situation of no excess noise to large excess noise. By comparing the measured spectra with the theory, we deduce the excess-noise factor $K$ and the spontaneous-emission factor β.

Spatiotemporal dynamics of patterns of the light beam emitted by a photorefractive oscillator has been investigated in the case of very large transverse dimensions. Time and space averagings show that the transition to turbulence as transverse dimensions are increased is a two-step process. Symmetry properties of the average patterns reveal that after the first transition from a boundary- to a bulk-dominated behavior already observed at Fresnel numbers ${\mathcal{N}}_F\simeq 20$ there is a second transition around ${\mathcal{N}}_F\simeq 100$. The regime corresponds to a complete loss of symmetry and appears here as soon as the correlation length of the patterns becomes of the same size as the period of the optical grating in the gain medium.

It has been suggested that phased atomic decay in a squeezed vacuum could be detected in the fluorescence spectrum emitted from a driven two-level atom in a cavity. Recently, the existence of other very distinctive features in the fluorescence spectra arising from the nonclassical features of the squeezed vacuum has been reported. In this paper, we investigate the possibility of experimental observation of these spectra. The main obstacle to the experimentalist is ensuring an effective squeezed-vacuum-atom coupling. To overcome this problem we propose the use of a Fabry-Pérot microcavity. The analysis involves a consideration of the three-dimensional nature of the electromagnetic field, and the possibility of a mismatch between the squeezed and cavity modes. The problem of squeezing bandwidths is also addressed. We show that under experimentally realistic circumstances many of the spectral anomalies predicted in free space also occur in this environment. In addition, we report large population inversions in the dressed states of the two-level atom.

The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in $\alpha Z$ is formulated. The nuclear recoil corrections for atoms with one and two electrons over closed shells are considered in detail. The problem of the composite nuclear structure in the theory of the nuclear recoil effect is discussed.

We investigate spatial solitons in a resonator with a narrow-band gain element and a saturable absorber placed in Fourier-conjugated resonator planes. Solitons are stationary or move at discrete velocities depending on the resonator tuning. The modulus of the velocity of moving solitons is fixed, but the direction of their motion is arbitrary. Solitons compete in velocity space. The experiments are conducted on a photorefractive oscillator with bacteriorhodopsin saturable absorber. Observations agree well with solutions of a general order parameter equation for such resonators.

The possibilities of observing disentanglement of atomic and field states during their interaction are discussed in the framework of one-atom micromaser action. We find that, in certain cases, the atom can be in a pure state and the cavity field may be in an approximate number state.

Techniques for producing, measuring, and applying ever shorter electromagnetic pulses are being developed for incorporation in a variety of modern high-speed systems. In many cases these pulses are at most a few cycles in length, and so-called half-cycle electromagnetic pulses are also widely employed. The interaction of such pulses with two-level media is considered here in detail, and these media are basic to many of the absorbing and amplifying configurations of optics and laser studies. Significant delays and distortion of the resulting polarization and population pulses can occur, and nonlinear optical effects are also revealed. The limitations of the parity, rate-equation, and rotating-wave approximations for the characterization of such few-cycle interactions are also explored.