arXiv subjects

L. G. Suttorp

Publications and source records attributed to L. G. Suttorp.

At least 19 recordsLinked to original sources

arXiv2024

Eigenmode analysis of the damped Jaynes-Cummings model

The generating functions for density matrix elements of the Jaynes-Cummings model with cavity damping are analysed in terms of their eigenmodes, which are characterised by a specific temporal behaviour. These eigenmodes are shown to be proportional to particular generalised hypergeometric functions. The relative weights of these eigenmodes in the generating functions are determined by the initial conditions of the model. These weights are found by deriving orthogonality relations involving adjoint modes. In an example it is shown how the time-dependent density matrix elements and the related factorial moments can be extracted from the eigenmode decompositions of the generating functions.

quant-ph↗

arXiv2018

Exact density matrix of a discrete quantum system immersed in a thermal reservoir

quant-ph↗

arXiv2018

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes-Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

quant-ph↗

arXiv2015

Modified atomic decay rate near absorptive scatterers at finite temperature

The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantummechanical model. The medium is a collection of randomly distributed thermally-excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum.

quant-ph↗

arXiv2011

Quantized Media with Absorptive Scatterers and Modified Atomic Emission Rates

Modifications in the spontaneous emission rate of an excited atom that are caused by extinction effects in a nearby dielectric medium are analyzed in a quantummechanical model, in which the medium consists of spherical scatterers with absorptive properties. Use of the dyadic Green function of the electromagnetic field near a a dielectric sphere leads to an expression for the change in the emission rate as a series of multipole contributions for which analytical formulas are obtained. The results for the modified emission rate as a function of the distance between the excited atom and the dielectric medium show the influence of both absorption and scattering processes.

quant-ph↗

arXiv2010

Atomic decay near a quantized medium of absorbing scatterers

The decay of an excited atom in the presence of a medium that both scatters and absorbs radiation is studied with the help of a quantum-electrodynamical model. The medium is represented by a half space filled with a randomly distributed set of non-overlapping spheres, which consist of a linear absorptive dielectric material. The absorption effects are described by means of a quantized damped-polariton theory. It is found that the effective susceptibility of the bulk does not fully account for the medium-induced change in the atomic decay rate. In fact, surface effects contribute to the modification of the decay properties as well. The interplay of scattering and absorption in the total decay rate is discussed.

quant-ph↗

arXiv2008

Sum rules for correlation functions of ionic mixtures in arbitrary dimension $d\geq 2$

The correlations in classical multi-component ionic mixtures with spatial dimension $d\geq 2$ are studied by using a restricted grand-canonical ensemble and the associated hierarchy equations for the correlation functions. Sum rules for the first few moments of the two-particle correlation function are derived and their dependence on $d$ is established. By varying $d$ continuously near $d=2$ it is shown how the sum rules for the two-dimensional mixture are related to those for mixtures at higher $d$.

cond-mat.stat-mech↗

arXiv2007

Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion

A quantum damped-polariton model is constructed for an inhomogeneous anisotropic linear dielectric with arbitrary dispersion in space and time. The model Hamiltonian is completely diagonalized by determining the creation and annihilation operators for the fundamental polariton modes as specific linear combinations of the basic dynamical variables. Explicit expressions are derived for the time-dependent operators describing the electromagnetic field, the dielectric polarization and the noise term in the latter. It is shown how to identify bath variables that generate the dissipative dynamics of the medium.

quant-ph↗

arXiv2006

Damping and dispersion of oscillating modes of a multicomponent ionic mixture in a magnetic field

The collective-mode spectrum of a multicomponent magnetized ionic mixture for small wave number k is studied with the use of magnetohydrodynamics and formal kinetic theory. Apart from the usual thermal and diffusive modes, the spectrum contains a set of four oscillating modes. By evaluating the k^2 contributions to the eigenfrequencies, the damping and the dispersion of these oscillating modes are determined. The long-range nature of the Coulomb interactions is shown to imply that Burnett terms with higher-order gradients in the linear phenomenological laws have to be taken into account in order to obtain a full description of all damping and dispersion effects.

cond-mat.stat-mech↗

arXiv2004

Oscillator model for dissipative QED in an inhomogeneous dielectric

The Ullersma model for the damped harmonic oscillator is coupled to the quantised 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 diagonalised by performing a normal-mode expansion. The commutation relations of the diagonalising 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 quantised 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.

quant-ph↗

arXiv2004

A multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics

The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-Schwinger equation for the electric field operator plays a central role. The equation describes atoms as point sources and point scatterers for light. First, single-atom properties are calculated such as position-dependent spontaneous-emission rates as well as differential cross sections for elastic scattering and for resonance fluorescence. Secondly, multi-atom processes are studied. It is shown that the medium modifies both the resonant and the static parts of the dipole-dipole interactions. These interatomic interactions may cause the atoms to scatter and emit light cooperatively. Unlike in free space, differences in position-dependent emission rates and radiative line shifts influence cooperative decay in the dielectric. As a generic example, it is shown that near a partially reflecting plane there is a sharp transition from two-atom superradiance to single-atom emission as the atomic positions are varied.

quant-ph↗

arXiv2004

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 Fano's 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.

quant-ph↗

arXiv2004

Field quantization in inhomogeneous absorptive dielectrics

The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.

quant-ph↗

arXiv2004

Spontaneous-emission rates in finite photonic crystals of plane scatterers

The concept of a plane scatterer that was developed earlier for scalar waves is generalized so that polarization of light is included. Starting from a Lippmann-Schwinger formalism for vector waves, we show that the Green function has to be regularized before T-matrices can be defined in a consistent way. After the regularization, optical modes and Green functions are determined exactly for finite structures built up of an arbitrary number of parallel planes, at arbitrary positions, and where each plane can have different optical properties. The model is applied to the special case of finite crystals consisting of regularly spaced identical planes, where analytical methods can be taken further and only light numerical tasks remain. The formalism is used to calculate position- and orientation-dependent spontaneous-emission rates inside and near the finite photonic crystals. The results show that emission rates and reflection properties can differ strongly for scalar and for vector waves. The finite size of the crystal influences the emission rates. For parallel dipoles close to a plane, emission into guided modes gives rise to a peak in the frequency-dependent emission rate.

physics.optics↗

arXiv2003

Time correlations in a confined magnetized free-electron gas

The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.

cond-mat↗

arXiv2003

Multipole interaction between atoms and their photonic environment

Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are determined and in particular the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielectric a dipole couples to a field that is neither the (transverse) electric nor the macroscopic displacement field. The dielectric function is different from the bulk dielectric function at the position of the dipole, so that local-field effects must be taken into account.

quant-ph↗

arXiv2001

Correlations in a confined magnetized free-electron gas

Equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free-electron gas in the presence of a hard wall that is parallel to the field. With the help of a path-integral technique and a Green function representation the modifications in the correlation function caused by the wall are determined both for a non-degenerate and for a completely degenerate gas. In the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field, is found to change from Gaussian in the bulk to algebraic near the wall.

cond-mat.stat-mech↗

arXiv2001

Transient QED effects in absorbing dielectrics

The spontaneous emission rate of a radiating atom reaches its time-independent equilibrium value after an initial transient regime. In this paper we consider the associated relaxation effects of the spontaneous decay rate of atoms in dispersive and absorbing dielectric media for atomic transition frequencies near material resonances. A quantum mechanical description of such media is furnished by a damped-polariton model, in which absorption is taken into account through coupling to a bath. We show how all field and matter operators in this theory can be expressed in terms of the bath operators at an initial time. The consistency of these solutions for the field and matter operators are found to depend on the validity of certain velocity sum rules. The transient effects in the spontaneous decay rate are studied with the help of several specific models for the dielectric constant, which are shown to follow from the general theory by adopting particular forms of the bath coupling constant.

quant-ph↗