Table of contents

We determine the conditions under which the global rate equations lead to an antiphase theorem for a laser oscillating on N modes. The global rate equations are N integro-differential equations for the modal intensities coupled to a single differential equation for the space-dependent population inversion. The antiphase theorem states that the total lasing intensity is characterized by a single relaxation oscillation frequency. It holds in the limit of frequency-independent linear gain and loss of the oscillating modes. Additional constraints apply, depending on the nature of the pumping. A quantitative formulation of these conditions is derived.

Bell's theorem reveals contradictions between the predictions of quantum mechanics and the EPR postulates for a pair of particles only in situations involving imperfect statistical correlations. However, with three or more particles, contradictions emerge even for perfect correlations. We describe an experiment which can be realized in the laboratory, using four-photon entangled states generated by parametric down-conversion, to demonstrate this contradiction at the level of perfect correlations.

The cut-off rate performance of quantum communication channels is considered when the signal quantum states are pure and symmetric. The properties of the quantum cut-off rate which is obtained by the entangled measurement of the received signal are investigated for communication channels in which the symmetric quantum states are both linearly independent and linearly dependent. It is found that the quantum cut-off rate becomes independent of the number of the signal quantum states when they are linearly dependent. Furthermore the properties of the semiclassical cut-off rate which is obtained by the disentangled measurement of the received signal are considered. The necessary and sufficient condition for the positive operator-valued measure of the disentangled measurement to maximize the semiclassical cut-off rate is derived. For binary quantum communication channels with pure signal states, the several parameters, such as the channel capacity and the cut-off rate, which characterize the quantum communication channel are compared.

It is found that displacement and squeezing of arbitrary initial states of the field can be produced in the model of a lossless cavity when a large number of two-level atoms is injected, which are prepared in a superposition state coupled to the single mode via a multi-photon transition under the weak atom-field interaction. The dependence of the field density matrix elements on the number of injected atoms indicates that due to the same initial atomic coherence the emission of individual atoms is a co-operative process.

We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state regime. This provides explicit phase-space images of the resulting state of the cavity mode, and allows us to understand how the quantum interference is built up into it. The photon number probability distribution is calculated and analysed as well. We monitor the transition from the semiclassical to extreme quantum regime of operation, and identify qualitative changes, where the conventional characteristics of the model, such as bistability or turning points, become meaningless.

The quantum field theory for the one-dimensional Schrödinger equation with attractive delta function potentials is used for treating the dynamics of collisions between a small number of photons in a nonlinear Kerr medium. The present theoretical analysis takes into account both bound states and dispersive continuum states and the general theory is applied, especially for the systems of diphotons and three-photons.

A two-level system is driven by two strong fields, one on resonance and one close to resonance. There is a resonance-like response of the coupled atom-field system when the detuning of the second field is an integer fraction of the Rabi frequency of the resonant field. These subharmonic resonances are monitored by a transition to a third level and give a characteristic spectrum dominated by a series of doublets.

Symmetry breaking in a system of laterally coupled chaotic class B lasers in a region of chaotic behaviour is investigated. Dynamical mechanisms that played a role in the purely symmetric model, are seen to persist under certain situations when symmetry is broken and certain types of synchronization may still be observed. In the physically realistic case where all symmetry of the system is broken, an instability in phase locking is discovered as a result of fluctuations in the laser amplitudes. These fluctuations were recently observed experimentally in a system of two coupled Nd:YAG lasers and an analysis of their effect on the system is undertaken.

We propose physical interpretations, also valid for temperatures different from zero, for stochastic methods which have been developed recently to describe the evolution of a quantum system interacting with a reservoir. As opposed to the usual reduced density operator approach, which refers to ensemble averages, these methods deal with the dynamics of single realizations, and involve the solution of stochastic Schrödinger equations. These procedures have been shown to be completely equivalent to the master equation approach when ensemble averages are taken over many realizations. We show that these techniques are not only convenient mathematical tools for dissipative systems, but may actually correspond to concrete physical processes, for any temperature of the reservoir. We consider a mode of the electromagnetic field in a cavity interacting with a beam of two- or three-level atoms, the field mode playing the role of a small system and the atomic beam standing for a reservoir at finite temperature, the interaction between them being given by the Jaynes-Cummings model. We show that the evolution of the field states, under continuous monitoring of the state of the atoms which leave the cavity, can be described in terms of either the Monte Carlo wavefunction (quantum jump) method or a stochastic Schrödinger equation, depending on the system configuration. We also show that the Monte Carlo wavefunction approach leads, for finite temperatures, to localization into jumping Fock states, while the diffusion equation method leads to localization into states with a diffusing average photon number, which for sufficiently small temperatures are close approximations to mildly squeezed states. We prove analytically that, in the quantum jump situation, the system evolves in the mean towards a Fock state, even if an infinite number of photon-number amplitudes is present in the initial state.

The structure of ordered expansions in powers of boson operators and of canonical operators and the dual problem of operator reconstruction from ordered moments is derived and applied to the complete Gaussian class of ordering. In particular, the interpolation lines between normal and antinormal ordering and between standard and antistandard ordering with Weyl symmetrical ordering in their centre are dealt with in detail. The auxiliary operators for expansions in symmetrical ordering are explicitly found in the Fock-state representation and in other different representations. General and specialized formulae are derived for different ordering of powers of linear combinations of boson and of canonical operators which involve Hermite polynomials of operators. The link between symmetrical ordering of powers of boson operators and of canonical operators is expressed by means of Jacobi polynomials. Some basic formulae of operator ordering and operator expansion are collected for convenient use in the appendix.

We report on experimental measurements of transition strengths for spectral components associated with a driven two-level atom. The measurements involve time- and frequency-domain techniques and are performed in nuclear magnetic transitions of a nitrogen-vacancy colour centre in diamond using the optical Raman heterodyne method. The transition strengths are shown to depend on the characteristics of the driving field in a way readily accounted for by the dressed state formalism and the data provide an experimental confirmation of some elementary expressions frequently used for dressed states.

We investigate the dynamics of a vector (weakly anisotropic) class-A laser subjected to the modulation of the resonator anisotropy directions. We report on polarization symmetry breaking and, to our knowledge, this is the first explicit example of chaos affecting amplitude and polarization parameters of the field emitted by a laser in which material dynamics is not essential. The physical mechanism of the chaotic behaviour is discussed.