A. J. van Wonderen

Time-resolved measurement of the refractive index for photopolymerization processes

A double-interferometer technique is employed to examine the dynamics of a photopolymerization process. The dye molecule is eosine Y. The refractive index and the thickness of the photopolymerizable film are measured as a function of time. During the photopolymerization process, the first quantity increases by 2%, while the second quantity decreases by more than 4%. Therefore, the refractive index cannot be measured by means of single-interferometer techniques. By fitting our experimental curves to a rate equation, the quantum yield and the absorption coefficient of the sample can be determined with good accuracy.

Fano diagonalization of a polariton model for an inhomogeneous absorptive dielectric

The Hamiltonian of a polariton model for an inhomogeneous linear absorptive dielectric is diagonalized by means of Fanos diagonalization method. The creation and annihilation operators for the independent normal modes are explicitly found as linear combinations of the canonical operators. The coefficients in these combinations depend on the tensorial Green function that governs the propagation of electromagnetic waves through the dielectric. The time-dependent electromagnetic fields in the Heisenberg picture are given in terms of the diagonalizing operators. These results justify the phenomenological quantization of the electromagnetic field in an absorptive dielectric.

Equilibrium properties of a multi-component ionic mixture

Equilibrium statistical methods are used to derive sum rules for two- and three-particle correlation functions of a multi-component ionic mixture. Some of these rules are general consequences of the electrostatic character of the interaction, whereas others depend on specific thermodynamic properties of the system. The first group of rules follows from the BBGKY hierarchy and a clustering hypothesis for Ursell functions. The sum rules of the second group are obtained by describing the system with the help of a restricted grand-canonical ensemble in which the particle numbers of the various components in the mixture fluctuate under the condition that the total charge in the system remains constant.

Equilibrium properties of a multi-component ionic mixture II. Fluctuations formulas

The complete set of fluctuation formulae for the partial densities, the pressure and the energy density of a multi-component ionic mixture is derived from equilibrium statistical mechanics. Sum rules for the pair correlation functions are used to write the fluctuation formulae in terms of thermodynamical quantities.

Stability analysis for absorptive optical bistability in a Fabry-Perot cavity

A stability analysis is performed for absorptive optical bistability in a medium of arbitrary absorption coefficient, which is contained in a Fabry-Perot cavity with non-ideal mirrors. In order to describe this system we use a hierarchical set of equations which is obtained from Maxwell-Bloch theory by expanding the polarization and population inversion in slowly varying harmonics. We reduce the stability problem to two pairs of coupled differential equations for the amplitudes and the phases of the space-dependent deviations of the forward and the backward electric field envelopes. The coefficients of these equations depend on the stationary inversion fields for which a representation in terms of Chebyshev polynomials depending on the electric field envelopes is given. The influence of a truncation of the Bloch hierarchy on the instabilities is studied numerically in the uniform-field limit.

Virtues and limitations of markovian master equations with a time-dependent generator

A Markovian master equation with time-dependent generator is constructed that respects basic constraints of quantum mechanics, in particular the von Neumann conditions. For the case of a two-level system, Bloch equations with time-dependent parameters are obtained. Necessary conditions on the latter are formulated. By employing a time-local counterpart of the Nakajima–Zwanzig equation, we establish a relation with unitary dynamics. We also discuss the relation with the weak-coupling limit. On the basis of a uniqueness theorem, a standard form for the generator of time-local master equations is proposed. The Jaynes–Cummings model with atomic damping is solved. The solution explicitly demonstrates that reduced dynamics can be described by time-local master equations only on a finite time interval. This limitation is caused by divergencies in the generator. A limit of maximum entropy is presented that corroborates the foregoing statements. A second limiting case demonstrates that divergencies may even occur for small perturbations of the weak-coupling regime.

Uniform-field theory of phase instabilities in absorptive optical bistability

Starting from the Maxwell-Bloch theory in the uniform-field approximation we investigate the stability of the phase of the output field for absorptive optical bistability in a Fabry-Perot cavity. Our main results are analytical. We show that a truncation of the Maxwell-Bloch hierarchy introduces serious anomalies in the instability spectrum. For the full Maxwell-Bloch hierarchy phase instabilities are found to occur only if the ratio γ11/γ1 of the medium damping coefficients is larger than 1. In that case phase instabilities can be present along the upper branch of the steady-state curve.

The oscillator model for dissipative QED in an inhomogeneous dielectric

The Ullersma model for the damped harmonic oscillator is coupled to the quantized electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalized by performing a normal-mode expansion. The commutation relations of the diagonalizing operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantized electric field is completely determined by the sources of the reservoir. Through a Riemann?Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices.

Reduced dynamics for entangled initial state of the full density operator

Starting from the Schrodinger equation for a system and a reservoir, we construct a quantum dynamical map that describes reduced dynamics. We work with an arbitrary initial state for the system and reservoir, and thus refrain from performing any factorizations. The map is found to be nonlinear, not completely positive, and not unique. To investigate the physical implications, the Bloch equations are constructed. If the freedom the new map offers us is fully exploited, then the classic inequality γ⊥≥γ∥/2 for the damping coefficients must be replaced by a weaker condition.

Dispersive optical bistability in a nonideal Fabry-Perot cavity I. Stability analysis of the Maxwell-Bloch equations

A stability analysis is performed for optical bistability in a Fabry-Pérot cavity with mirrors of arbitrary transmission coefficient. The mixed absorptive and dispersive régime is covered. In order to describe the system we use the Maxwell0Bloch equations formulated in terms of slowly varying envelopes. Standing-wave effects are completely taken into account by refraining from a truncation of the harmonic expansions for the polarization and the inversion density. We represent the solutions of the linearized Bloch hierarchy in terms of Chebyshev polynomials depending on the stationary electric field envelopes. In this way, we reduce the stability problem to a four-dimensional set of linear differential equations. Together with a couple of boundary conditions these equations govern the spatial behaviour of the deviations of the forward and the backward electric field envelopes. Our final stability problem becomes much simpler in the uniform-field limit and in the adiabatic limit. If we choose the stationary backward electric field equal to zero we recover results that were derived earlier for the case of a ring cavity.