We calculate the quantum corrections of the thermodynamic quantities of a system of confined bosons at finite temperature. Systematically quantum corrections are written in a series of $ħ,$ which is convergent when $\mathrm{kT}$ is much larger than the spacing between energy levels of the system. We apply this method to the different physical systems. First we calculate the thermodynamic potential of spin-1 bosons confined in a general power-law potential, and calculate the paramagnetic susceptibility of the gas including the quantum corrections. Local-density approximation for charged bosons in the weak magnetic field is improved by the semiclassical expansion. Diamagnetic susceptibility of a system of confined charged bosons is calculated using this method. Finally we apply this method to calculate analytically the thermodynamic potential of a weakly interacting Bose-gas confined in at three-dimensional harmonic-oscillator potential. For a large number of particles, quantum corrections become small, and contribute to the finite-size corrections to scaling.

A hydrodynamic description is used to study the normal modes of a vortex in a zero-temperature Bose-Einstein condensate. In the Thomas-Fermi limit, the circulating superfluid velocity far from the vortex core provides a small perturbation that splits the originally degenerate normal modes of a vortex-free condensate. The relative frequency shifts are small in all cases considered (they vanish for the lowest dipole mode with $|m|=1\mathrm{}$), suggesting that the vortex is stable. The Bogoliubov equations serve to verify the existence of helical waves, similar to those of a vortex line in an unbounded weakly interacting Bose gas. In the large-condensate (small-core) limit, the condensate wave function reduces to that of a straight vortex in an unbounded condensate; the corresponding Bogoliubov equations have no bound-state solutions that are uniform along the symmetry axis and that decay exponentially far from the vortex core.

The momentum distribution function of a parabolically confined gas of bosons with harmonic interparticle interactions is derived. In the Bose-Einstein condensation region, this momentum distribution substantially deviates from a Maxwell-Boltzmann distribution. It is argued that the determination of the temperature of the boson gas from the Bose-Einstein momentum distribution function is more appropriate than the currently used fitting to the high-momentum tail of the Maxwell-Boltzmann distribution.

Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the Bogoliubov approximation, the various contributions to the ground-state condensate energy all have terms of order $R^{-4}\ln R$ and $R^{-4},$ where R is the number-dependent dimensionless condensate radius in units of the oscillator length $\sqrt{ħ/m{\omega }_0}.$ The zero-order hydrodynamic density-fluctuation amplitudes are extended beyond the Thomas-Fermi radius through the boundary layer to provide a uniform description throughout all space. The first-order correction to the excitation frequencies is shown to be of order $R^{-4}.$

An analytical formulation is presented for the derivation of exact differential equations describing the evolution of the complex cavity fields in laser resonators. The starting point is an integral equation, for example, of Fox-Li type, from which a differential equation is derived following a rigorous procedure that guarantees preservation of the resonator modal structure. The form of such evolution equations for given resonator and field definitions is not unique, but all expressions derived by this method are equivalent in the sense that they carry the same dynamical information as the original integral equation. The example of two longitudinally coupled Fabry-Pérot lasers separated by a gap is studied in detail. Agreement with previous heuristic models is found in the weak interaction limit, but in the case of semiconductor lasers, which have comparatively transmissive facets, the corrections are significant. In a second application, the evolution equation of a distributed feedback laser is derived.

We show that two-atom correlation measurements of the type involved in a recent experimental study of the evolution of a mesoscopic superposition state prepared in a definite mode of a high-$Q$ cavity can be used to determine the eigenvalues of the reduced density matrix of the field, provided the assumed dynamical conditions are actually fulfilled to experimental accuracy. These conditions involve (i) a purely dispersive coupling of the field to the Rydberg atoms used to manipulate and to monitor the cavity field, and (ii) the effective absence of correlations in the ground state of the system consisting of the cavity coupled to the “reservoir” which accounts for the decoherence and damping processes. A microscopic calculation at zero temperature is performed and compared to master equation results.

We present a detailed treatment of a laser process that has been predicted for an experiment with a single trapped ${\mathrm{Ca}}^{+}$ ion. It is demonstrated how the complex multilevel system can be understood as a coherently pumped three-level scheme with time-delayed pumping out of the metastable lower laser level. This is described by a pump operator, which simplifies the numerical analysis substantially and allows for a treatment of more complicated systems.

We present exact analytic trajectories for a relativistic electron in the presence of an elliptically polarized superintense laser field and a strong uniform magnetic field. Also derived are expressions for the velocity components of the electron and for its energy as functions of the phase of the laser field as a parameter. The analytic trajectory solutions are illustrated by numerical calculations employing laser-field parameters and magnetic-field strengths currently available for laboratory experiments. The trajectory solutions are useful for (among other things) the study of the related problem of emission of radiation in the combined laser and magnetic fields. An exact expression for the cross section of light scattered by an electron initially moving along the laser propagation direction and in a magnetic field is given. It is found that, for observation along the common direction of laser propagation and the magnetic field, light at two frequencies $\omega ={\omega }_0$ and ${\Omega }_0$ is scattered, where ${\Omega }_0={\gamma }_0(1+{\beta }_0){\omega }_c,$ ${\omega }_c$ is the cyclotron frequency of the electron motion in the magnetic field, ${\beta }_0$ is the initial speed of the electron normalized by the speed of light, ${\gamma }_0=(1\mathrm{}-{\beta }_0^2{)}^{-1/2}$, and ${\omega }_0$ is the laser frequency. Using the analytic solutions, we also study numerically the spectrum of radiation emitted along observation directions parallel to the electric and parallel to the magnetic components of the laser field. In each case, we present and discuss the dependence of the spectra on (a) the increase of the electron initial velocity, (b) the intensity and the frequency of the laser, and (c) the strength of the magnetic field.

Studied within the framework of both classical and quantum-mechanical approaches is the resonance interaction between two atomic dipoles one of which is located inside a dielectric microsphere and the other near its outer surface. The dispersion equation of this system is found. The analysis of this equation in a quasistatic approximation has shown that the behavior of the eigenfrequencies depends in a complex manner on the parameters of the system, and that exact resonance can be achieved, provided the parameters are suitably selected. Based on the solutions of the above equation, relationships are found between the energy-transfer rate and the system parameters. It is demonstrated that as the inside atom approaches the surface of the microsphere, resonance excitation transfer from one atom to the other can take place. Similar results are obtained when using the quantum-mechanical density matrix to define the atomic interaction. The results obtained can be of use in implementing selective microscopy with a nanometer-high spatial resolution.

We formulate a wave-atom-optics theory of the collective atomic recoil laser (CARL) where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray-atom-optics theory, which treats the center-of-mass atomic motion classically, we show that for the case of a far off-resonant pump laser the ray-optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in this temperature regime one can no longer ignore the effects of matter-wave diffraction on the atomic center-of-mass motion.

We present an extension of the projection synthesis technique which allows us, at least in principle, to determine the probability distribution for any physical observable associated with a quantized optical field mode. This probability can be inferred from the photodetection statistics obtained by causing the field mode to be measured to interfere with a second mode prepared in a suitable reference state. We give an explicit expression for the required reference state. Weak-field homodyne detection using photon counting is, perhaps, the simplest system to which projection synthesis can be applied. We find the complete set of synthesized projectors for this system and show that they form a probability operator measure. We apply this set of projectors to study the discrimination between coherent states and to measure a quasiprobability distribution.

We study a generalized notion of two-mode squeezing for the Stokes and anti-Stokes fields in a model of a cavity Raman laser, which leads to a significant reduction in decoherence or quantum noise. The model comprises a lossless cavity with classical pump, unsaturated medium, and arbitrary homogeneous broadening and dispersion. Allowing for arbitrary linear combinations of the two modes in the definition of quadrature variables, we find that there always exists a combination of the two output modes that exhibits quadrature squeezing with noise reduction below the vacuum level. The number of noise photons for this combination mode is proportional to the square root of the number of Stokes noise photons.

We present a microscopically based vertical-cavity surface-emitting laser (VCSEL) model that treats plasma and lattice heating self-consistently and includes gain dispersion in a fashion facilitating the incorporation of many-body effects. This model is used to investigate the interplay of thermal effects and transverse mode behavior observed in recent experiments with large-aperture selectively oxidized VCSELs. We confirm that the highly divergent single-mode emission seen experimentally at low ambient temperatures may be caused by a redshift of the cavity resonance frequency relative to the quantum-well gain peak. Moreover, due to the dependence of the gain spectrum on temperature our model qualitatively reproduces the measured increase of the dominant spatial scale of the low-temperature steady-state field patterns with pumping. Finally, we demonstrate that spatial hole burning plays a significant role at larger ambient temperatures and explains the decrease of the spatial wavelength with pumping, in agreement with the experiments.

We show that a system managed by quantum theory bears chaotic behavior induced by unitarity collapse in its time development. Nonunitary time evolution of the Jaynes-Cummings (JC) model, the interacting system consisting of two subsystems (a two-level atom and a quantized photon field), under a continuous quantum-nondemolition (QND) measurement of the photon number is investigated. In the regime of weak coupling between the subsystems, the measured system shows the Rabi oscillation and the decrease of the photon number variance, which mimic the unmeasured JC system and the photon field under the continuous QND photodetection, respectively. In the strong-coupling regime, the quantum system shows a nonintegrable nature, that is, it yields weak chaos characterized by both the broad continuous power spectrum and the decaying correlation function due to the lack of quantum recurrence.

The propagation of intense femtosecond pulses in a nonlinear, dispersive bulk medium is investigated numerically in the regime where the combined effects of diffraction, normal dispersion, and cubic nonlinearity lead to pulse splitting. We present numerical solutions of a modified $\mathrm{}(3+1)\mathrm{}$-dimensional nonlinear Schrödinger equation, accounting for the Raman effect, linear and nonlinear shock terms, third-order dispersion, and initial temporal third-order phase modulation. The calculated results are found to be in good agreement with experimental measurements.

High-harmonic generation in He atoms illuminated by high-intensity femtosecond excitation pulses is studied. It is shown that single attosecond pulses as well as trains of several attosecond pulses, one per half a period, can be generated in the multicycle regime of the driver pulse.

We study the steady states of a solid-state laser containing a birefringent frequency-doubling crystal such as a YAG-KTP laser and assess their stability in a systematic way. We show that as the pump power is increased, different scenarios arise: Hopf bifurcation to antiphased periodic regimes, mode hopping between different cw states, and finally breakup of the multimode states for a single- or two-mode cw regime involving homoclinic points.

The dynamical algebraic structure of a time-dependent $L-S$ coupled system is studied. Based on this algebraic structure, the exact solution of the Schrödinger equation for the $s=\frac{1}{2}$ case is obtained by using the method of algebraic dynamics. For the $s=1\mathrm{}$ case, the SU(3) structure of the time-dependent $L-S$ coupled system is also investigated, and it can be solved by the same method.

This work shows that an orthogonal tetrat basis element made up of two photons can be generated with two optical parametric down-converters and identified with a multiport detection system for coincidences. The transmission gain over the usual coding in bits is $g=2.\mathrm{}$ The information is assigned to each photon pair using a single conjugate beam of the parametric down-conversion. This system also demonstrates a way to get a pair of disentangled polarized photons by handling just one photon of an entangled pair.

The triply excited ${2s}^{2}2p{}^2{P}^o$ state of ${\mathrm{He}}^{-}$ is studied by using the saddle-point complex-rotation method. The energy and Auger width of this resonance are calculated. Relativistic corrections are evaluated with the first-order perturbation theory, and the mass-polarization effect is also included. The partial Auger widths are calculated for the individual open channels. The total width is obtained by coupling the important open channels and summing over the other channels. These results are compared with the theoretical and experimental data in the literature.