Table of contents

Analytical expressions for the time development operators for Wigner functions of harmonic oscillators with quadratic Hamiltonians are developed by the use of group theoretical methods.

I propose a quantum-trajectories approach to parametric identification of the effective Hamiltonian for a Markovian open quantum system, and discuss an application motivated by recent experiments in cavity quantum electrodynamics. This example illustrates a strategy for quantum parameter estimation that efficiently utilizes the information carried by correlations between measurements distributed in time.

We analyse theoretically the stability of the Brillouin fibre ring laser. This study not only allows us to draw the portrait of the unstable domains for a large range of the system parameters, but it also gives valuable information on the dynamical regimes encountered in these domains. We then describe experiments and numerical simulations performed in the particular conditions of a short-length cavity. The effect of cavity detuning on the stability of the laser is investigated. We also report and characterize the dynamics of a Brillouin laser emitting two Stokes components.

Previous papers in recent literature for particle trapping by oscillating fields employ a model by Glauber and a time-dependent canonical transformation to investigate the occurrence of squeezing and instabilities in this system. Here we extend this study to a more realistic case including the presence of dissipation. This influence upon the squeezing effect is investigated, the previous results in the absence of dissipation becoming a particular case of the present work.

A new method for characterization of the long-time dynamics of generation of second and higher harmonics and subharmonics is presented. This method is based on calculation of the spectra of moments of photon numbers and enables us to predict the global behaviour of the process. This is demonstrated by numerical results, which are discussed and related to the time-domain dynamics and to short-time analytical results.

We propose and investigate a scheme describing the interaction of two field modes in a nonlinear structure including second- and third-order nonlinearities. With the help of exact solutions for both Heisenberg equations of motion and the Schrödinger equation we find three different dynamical regimes of the described scheme. In one of the regimes the generation of different macroscopically distinguishable states is possible. We show that the resulting two-mode wavefunction can contain an infinite set of different Schrödinger-cat states.

The emergence of local chaotic antiphase states and self-induced switching among the ruins of local chaotic antiphase attractors (i.e. chaotic itinerancy) leading to fully developed global chaos have been demonstrated by numerical simulations in a model of intracavity second-harmonic generation in multimode lasers. Dynamical characterization of chaotic itinerancy has been carried out using circulation analysis.

Two-photon bistability in a system of three-level atoms driven by a single-frequency field shows nearly ideal squeezing close to a dynamic instability threshold, occurring in the lower branch of the steady-state bistability curve. The squeezing is maximized and becomes very broad band in the bad cavity limit. Such results which were previously predicted on the basis of an effective two-level model, are demonstrated here and analysed by a full three-level treatment of the atoms. In addition, important restrictions and new features are found.

We consider the influence of an external modulation of the laser gain on the antiphase dynamics of a three-mode solid-state laser with intracavity second harmonic generation. The modulation frequency is close to the self-pulsing frequency of an unstable two-mode solution. We find that orthogonally polarized lasing modes display dynamical nonreciprocal independence: modes in one polarization follow the periodic modulation in a nearly linear way while modes in the orthogonal polarization display a rich set of bifurcations leading to chaos.

This latest volume of proceedings from a Scottish Universities Summer School covers a wide range of topics, many at the forefront of current research in Physics, which the editors enthusiastically refer to as Quantum Toys. Certainly there is a sense of playfulness and relative simplicity in the way many topics are addressed by the distinguished authors of the eleven main chapters. The result is a book covering what is at times fairly advanced material, at a level and with a lucidity that will be particularly attractive to newcomers in the field. Amongst those topics are to be found cavity QED, quantum wells, squeezed light, Bell's theorem and Bose - Einstein condensation. It is good to see more molecular material being reflected in the contents - discovering the relationship between squeezing and Franck - Condon factors was for me a pleasant surprise, surpassed only by the first autostereogram I have ever been able to decode. Personally I do not find the eighteen pages devoted to poster abstracts and participant addresses at all useful - most purchasers would rather have £ 5 off!