Table of contents

The fundamentals of Fan's method of integration within ordered products are investigated and it is shown that it is a reliable calculation method in quantum optics. Differentiation within ordered products is included into the considerations. The integrations are, in applications to single boson modes, mostly one-dimensional or two-dimensional integrations over phase-space variables. We examine some examples of integration within ordered products and compare them with calculations of results by other methods such as Lie group methods. A new representation of the main class of quasiprobabilities including the Wigner and the Husimi-Kano quasiprobability is derived by the method. Different representations of squeezing operators are related by the method and discussed. As a further new result, the position and momentum representation of the general unitary squeezing operators are derived and specialized to cases with squeezing in the direction of the coordinate axes which were earlier dealt with by the method under consideration.

We examine the entanglement arising from the bilinear coupling of two nearly single-mode optical beams. We consider both the case of active and passive linear devices. The two modes are initially prepared in a pair of uncorrelated pure Gaussian states, and the degree of entanglement is analytically evaluated in terms of the excess information entropy at the output. A general formula is obtained and relevant cases are analysed in some detail.

We consider the quadratic nonlinear radiation of a plane sheet of oscillating dipoles within a 1D truncated periodic structure. It is shown that in such a microcavity-like structure, not only the amplitude field distribution, but also the phase difference between the dipole oscillation and the field plays a determining role in the process of energy transfer that defines the radiative properties of the dipoles within such a structure. This energy transfer mechanism is found to be very different from the one in free space and strongly dependent on the position of the dipoles within the structure, as well as on their orientation with respect to the same structure. We have also seen that one can distinguish two types of radiation inhibition: one where there is no transfer of energy to either of the counterpropagating components of the field, and another one where one of the components loses the energy that is transferred to the other counterpropagating component.

We discuss phase-difference measurements of two bosonic modes and propose an experimental realization of the phase-difference operator by Luis and Sánchez-Soto (1993 Phys. Rev. A 48 4702). We show that a measurement of a two-mode state will collapse any state into a phase-difference eigenstate. We also show that the phase-difference number-difference commutator can be expressed in the phase-difference distribution. Finally, we discuss the associated minimum uncertainty states.

We analyse the stability of a pair of Fabry-Perot lasers coupled by an intensity-dependent loss mechanism. A self-pulsing instability of the steady state solutions is found. We show analytically that equally pumped lasers become unstable for much smaller values of the loss cross-coupling than unequally pumped lasers.

The emission line profile of an atom in a dissipative medium is investigated theoretically by Langevin formulation. A general formula for the line profile is presented. Among others, there appears an additional broadening originating from the energy width of the photon. The line profile also deviates somewhat from the Lorentzian shape.

Using conditional measurement on a beam splitter, we study the transformation of the quantum state of the signal mode within the concept of two-port non-unitary transformation. Allowing for arbitrary quantum states of both the input reference mode and the output reference mode on which the measurement is performed, we show that the non-unitary transformation operator can be given in a closed form by an s-ordered operator product, where the value of s is entirely determined by the absolute value of the beam splitter reflectance (or transmittance). The formalism generalizes previously obtained results which can be recovered by simple specification of the non-unitary transformation operator. As an application, we consider the generation of Schrödinger-cat-like states. An extension to mixed states and imperfect detection is outlined.

We propose a scheme to generate cat states for trapped ions using a standing wave in both the strong excitation regime and the Lamb-Dicke limit. A single strong standing-wave laser, exciting the ion for a short time, will leave the ion in an entangled state. After a measurement of the internal state, the external state will collapse to an odd or even coherent state.

Using the Pegg-Barnett formalism we study phase properties of nonlinear coherent states. We compute the Pegg-Barnett phase probability distribution of nonlinear coherent states and compare it with phase distributions associated with the Q function and the Wigner function. Squeezing properties of nonlinear coherent states with respect to the number and the phase operator are also studied.

A nonlocal `interaction-free' experiment is discussed. It is shown that the absence of detection of a photon of a polarization-entangled pair can `force' the other photon of the pair into a well-defined polarization state. Its consequences for a possible ontological interpretation of quantum mechanical formalism are examined.

We study the influence of accompanying frequency sweeping on the response of a loss-modulated CO₂ laser when cavity detuning is accounted for. The accompanying phase modulation usually manifests itself in an asymmetry of the amplitude-detuning characteristics, i.e., the laser intensity and dynamical regimes depend on the sign of the detuning.