The two-component Bose-Einstein condensate exhibits oscillations in the individual particle number when the two species are coupled by a Josephson coupling. We present the results of numerical calculations based on coupled Gross-Pitaevskii equations, and compare the results with an approximate analytic theory. The small amplitude limit reproduces the conventional results, but the large signal regime offers some features characteristic of the trapped systems.

We present an exact quantum-mechanical analysis of collinear four-wave mixing in a multicomponent Bose-Einstein condensate consisting of sodium atoms in the $F=1\mathrm{}$ ground state. Technically, this is achieved by taking advantage of the conservation laws of the system to cast its Hamiltonian in terms of angular momentum operators. We discuss explicitly the build-up of matter-wave side modes from quantum fluctuations, as well as the correlations between these modes. We show the appearance of a strong quantum entanglement between hyperfine states. We also demonstrate that for finite atomic numbers, the system exhibits periodic collapses and revivals in the exchange of atoms between different spin states.

We investigate the collective excitations of a single-species Bose gas at $T=0\mathrm{}$ in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider one-dimensional potentials consisting of two harmonic wells separated by a distance ${2z}_0$, since they essentially contain all the barrier effects that one may visualize in the three-dimensional situation. We find, within a hydrodynamic approximation, that regardless of the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighboring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results obtained from exactly solving the time-dependent Gross-Pitaevskii equation. We also analyze the characteristics of the spatial pattern of excitations of three-dimensional boson systems according to the amount of splitting of the condensate.

A semiclassical model of a unidirectional anisotropic ring cavity dye laser has been investigated analytically and numerically. In spite of the axial symmetry of the inversion angular distribution and the isotropy of the cavity, polarized initial fluctuations cause spontaneous light-polarization symmetry breaking in the form of alternative circularly polarized waves. Polarization symmetry is restored by increasing the orientational relaxation and pumping rates or the anisotropy of the cavity.

We present the time evolution of a two-level atom interacting dispersively with an electromagnetic field in a dissipative cavity. We investigate the influence of dissipation on the entanglement of the two subsystems $(\mathrm{atom}+\mathrm{field}).\mathrm{}$ Simple but realistic, the model displays several nontrivial quantum features, which emerge when an environment is taken into account: the cavity is shown to have practically no influence in the coherence properties of the field from the qualitative point of view. On the other hand, although the atom is not directly coupled to the cavity modes, its coherent properties are strongly influenced by dissipation both qualitatively as well as quantitatively.

Recent theoretical analysis of infrared-visible pumped sum-frequency spectroscopy on adsorbed molecules exhibits a dip structure on the frequency dependence of the sum-frequency signal intensity. To get more physical insight into this dip, which has not yet been observed experimentally, we present a unified description capable of handling, on the same footing, steady-state and pulsed experiments. Contrary to previous treatments, this description is valid for any duration of the dephasing times. Therefore, it enables a detailed discussion about the origin of the dip, as well as a determination of the conditions of its observability. These conditions are, in fact, very sensitive to the pure vibrational dephasing processes. In the nonresonant conditions, usually adopted in these experiments for the visible probe beam, the pure electronic dephasing does not affect the dip structure and the underlying dynamics. However, if the visible probe beam becomes resonant with the electronic transition, the pure electronic dephasing introduces a strong asymmetry of the dip.

The dynamical behavior of two mutually coupled semiconductor lasers is studied experimentally, numerically, and analytically for weak coupling. The lasers have dissimilar relaxation oscillation frequencies and intensities, and their mutual coupling strength may be asymmetric. We find experimentally that the lasers preferentially entrain to the relaxation oscillation frequency of either one of the lasers. But quasiperiodic synchronization, where both relaxation oscillation frequencies appear, is possible. We show that there exist two distinct mechanisms leading to these regimes corresponding to either a bifurcation to a mixed-mode solution or a bifurcation induced by the delay of the mutually injected signal. However, only the second transition can be observed experimentally if the injection strength is continuously increased from zero.

We investigate the spontaneous parametric down-conversion for light beams possessing orbital angular momentum. The experimental results indicate that the orbital angular momentum is not conserved within the classical light fields. This is in contrast to second harmonic generation where the conservation of orbital angular momentum leads to a well-defined mode transformation. We attribute this difference in behavior to the loss of spatial coherence within each of the down-converted fields.

A new type of transverse instability in dispersively nonlinear optical cavities, called the optical whistle, is discussed. This instability occurs in the mean-field, soliton-forming limit when the cavity is driven with a finite width Gaussian beam, and gives rise to oscillation, period doubling, and chaos. It is also seen that bistability is strongly affected due to the oscillation within the upper transmission branch. The phenomenon is interpreted as a mode mismatch in the soliton-formation process and is believed to have broad applicability.

This paper develops a method of manipulating the squeezed atom state to generate a few-photon state whose phase or photon-number fluctuations are prescribed at our disposal. The squeezed-atom state is a collective atomic state whose quantum fluctuations in population difference or collective dipole are smaller than those of the coherent atom state. It is shown that the squeezed-atom state can be generated by the interaction of atoms with a coherent state of the electromagnetic field, and that it can be used as a tunable source of squeezed radiation. A variety of squeezed states, including the photon-number squeezed state and the phase squeezed state, can be produced by manipulating the atomic state. This is owing to the fact that quantum-statistical information of the atomic state is faithfully transferred to that of the photon state. Possible experimental situations to implement our theory are discussed.

A hypersound wave grating generated by stimulated-Brillouin-scattering (SBS) is applied in a laser resonator as a nonlinear mirror. This self pumped SBS mirror can be used for a passive Q switching of the laser by operating it inside a starter cavity. The Q-switch energy and pulse duration can be varied with a neutral glass filter. The Q-switch mechanism is explained and the pulse energy is calculated. As a consequence of the Brillouin frequency shift such resonators show a special behavior of the longitudinal modes. The longitudinal modes and the corresponding pulse shape of such a laser are investigated experimentally as a function of the start resonator length and the position of the SBS mirror. The results are explained by a superposition of modes of the SBS resonator taking into account their phases. Finally, the spectrum of the longitudinal modes is shown to be time dependent. These investigations yield in design criteria for efficient application of SBS mirrors as a laser resonator mirror.

An effective two-level Maxwell-Bloch formalism is developed to describe various time-dependent phenomena in a three-level V-type system. The Maxwell-Bloch equations govern the temporal evolution of a probe field while a strong driving field is applied on the adjacent transition. The main assumption adopted throughout the paper is that the spontaneous decay rate on the coherently driven transition exceeds the decay rate on the probe transition as well as inverse time variations of both pulses. It is shown that the probe pulse interacts with such a medium in a manner similar to that in a self-induced transparency. An amplification without inversion of a relatively short probe pulse while propagating through an optically thick atomic medium is analyzed.

We study the generation of an ultranarrow gain spectrum in an atomic transition when the upper transition level is coupled to the lower transition level by one laser and to a metastable state by another laser. It is shown that this spectrum switches abruptly into an ultranarrow absorption line with an increase in the first laser intensity. These results are explained by investigating the electromagnetically induced transparency (EIT) in a system where the upper transition level is coupled to two metastable states by two laser fields (K system). We discuss various features of such a transparency and show how it can be described as a structuring process, similar to the laser-induced continuum structure. Utilizing such a description of EIT, we explain the ultranarrow gain generation as a stimulated Rayleigh scattering process.

We report an experimental observation of coherent population trapping in multilevel dark states prepared in the ground hyperfine states of ${}^{87}\mathrm{Rb}$ atoms confined in a room-temperature vapor cell. The dark states are created by a linearly polarized coupling laser that is tuned to the ${}^{87}\mathrm{Rb}$ $D_1$ $F=2\mathrm{}\leftrightarrow F^{\prime }=1\mathrm{}$ or 2 transition and establishes Λ-type transition chains. The Doppler shift for the Λ-type transition chains is compensated by the left and right circularly polarized components of the coupling laser. The multilevel dark states that consist of three or two magnetic sublevels among the five degenerate magnetic sublevels in the $F=2\mathrm{}$ ground hyperfine state are probed by a weak probe laser scanned across the same $D_1$ transition and their existence is manifested by a strong dependence of the probe excitation on the probe polarization. Our experiment demonstrates the importance of coherent population trapping in a laser coupled degenerate multilevel open atomic system, which may play an important role in diverse physical phenomena such as atom cooling and trapping, optical pumping, and multiple laser excitation and ionization of atoms and molecules.

The center-of-mass motion of two two-level atoms coupled to a single damped mode of an electromagnetic resonator is investigated. For the case of one atom being initially excited and the cavity mode in the vacuum state, it is shown that the atomic time evolution is dominated by the appearance of dark states. These states, in which the initial excitation is stored in the internal atomic degrees of freedom and the atoms become quantum mechanically entangled, are almost immune against photon loss from the cavity. Various properties of the dark states within and beyond the Raman-Nath approximation of atom optics are worked out.

Pattern formation is theoretically investigated in the process of second-harmonic generation in an externally driven plane-plane optical cavity which uses phase matching of type II. It is shown that in this system a symmetry-breaking polarization instability at the fundamental frequency can lead to the spontaneous appearance of self-organized states, which can be periodic or quasiperiodic in space. A weakly nonlinear analysis in the vicinity of the bifurcation point where these patterns emerge is developed by deriving both a complex order parameter equation of the Swift-Hohenberg type close to resonance, and a set of amplitude equations for the neutral modes far from resonance. The amplitude equations reveal the existence of multistability and pattern coexistence, and show that, besides the most common periodic patterns such as rolls, squares, and hexagons, quasipatterns with an arbitrary orientational order can be selected by the nonlinearity in this system. Numerical simulations of the original field equations are presented and the main predictions of the weakly nonlinear analysis are compared with the numerical results.

Phase-matched high-order-harmonic generation of Ti:sapphire laser pulses of $\approx {10}^{14}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ has been demonstrated using a gas-filled hollow fiber. The high-order-harmonic spectrum emitted from the fiber showed an intensity distribution significantly different from that in free space, indicating more than a hundred times enhancement around the 25th harmonic. A simple phase-matching calculation considering positive dispersion due to plasma and negative dispersion due to neutrals indicates that macroscopic phase matching achieved in the fiber is responsible for the strong enhancement.

The effect of pressure and laser power on the high-resolution spectra of commonly available gases is studied with the help of the optically heterodyne Raman-induced Kerr effect (OHD-RIKE). The results show the expected pressure dependence of the spectra, but the effects of saturating laser power are different from previous similar studies employing other four-wave mixing techniques. In OHD-RIKE no observable sign of saturation such as power broadening, saturation dips in the line center, or deviation from a linear dependence of the signal strength with laser intensity was observed for several orders of magnitude greater intensities than previously reported for the saturation intensities in coherent anti-Stokes Raman spectroscopy (CARS). Saturation is therefore not the ultimate limit of sensitivity for OHD-RIKE. This may be an advantage of RIKE in comparison to other coherent Raman techniques.

We calculate the far-field intensity pattern of superradiant emission from an optically thin ensemble of atomic oscillators excited by a spatially nonuniform laser pulse of large Rabi area. As the excitation intensity is increased, the superradiant field develops ring structure and expands due to self-diffraction. This effect is made manifest by a two-pulse photon echo experiment where the second pulse is spatially much broader than the first and has a small Rabi area. As a function of the intensity of the first excitation pulse, we measure the on-axis and off-axis echo intensity and find, in agreement with our calculations, that the two behave differently. We also show that for a random, sufficiently smooth excitation profile, the total power of cooperative emission is proportional to the integral, over the excited volume, of the induced dipole moment squared.

The master equation is derived for describing spatially correlated decoherence, which includes independent decoherence and collective decoherence as its special cases. Spatial correlation in the decoherence is measured by the correlation matrix or by the independence entropy. By applying the conventional quantum error correction schemes correcting for single-qubit errors, we calculate the state fidelity and demonstrate that these schemes are valid for reducing spatially correlated decoherence.