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

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

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.Comment: 24 page

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.Comment: 20 pages, 1 figur

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.Comment: 24 pages, 1 figur

Bespoke Biomolecular Wires for Transmembrane Electron Transfer: Spontaneous Assembly of a Functionalized Multiheme Electron Conduit.

Shewanella oneidensis exchanges electrons between cellular metabolism and external redox partners in a process that attracts much attention for production of green electricity (microbial fuel cells) and chemicals (microbial electrosynthesis). A critical component of this pathway is the outer membrane spanning MTR complex, a biomolecular wire formed of the MtrA, MtrB, and MtrC proteins. MtrA and MtrC are decaheme cytochromes that form a chain of close-packed hemes to define an electron transfer pathway of 185 Å. MtrA is wrapped inside MtrB for solubility across the outer membrane lipid bilayer; MtrC sits outside the cell for electron exchange with external redox partners. Here, we demonstrate tight and spontaneous in vitro association of MtrAB with separately purified MtrC. The resulting complex is comparable with the MTR complex naturally assembled by Shewanella in terms of both its structure and rates of electron transfer across a lipid bilayer. Our findings reveal the potential for building bespoke electron conduits where MtrAB combines with chemically modified MtrC, in this case, labeled with a Ru-dye that enables light-triggered electron injection into the MtrC heme chain

Which Multi-Heme Protein Complex Transfers Electrons More Efficiently? Comparing MtrCAB from Shewanella with OmcS from Geobacter

Microbial nanowires are fascinating biological structures that allow bacteria to transport electrons over micrometers for reduction of extracellular substrates. It was recently established that the nanowires of both Shewanella and Geobacter are made of multi-heme proteins; but, while Shewanella employs the 20-heme protein complex MtrCAB, Geobacter uses a redox polymer made of the hexa-heme protein OmcS, begging the question as to which protein architecture is more efficient in terms of long-range electron transfer. Using a multiscale computational approach we find that OmcS supports electron flows about an order of magnitude higher than MtrCAB due to larger heme–heme electronic couplings and better insulation of hemes from the solvent. We show that heme side chains are an essential structural element in both protein complexes, accelerating rate-limiting electron tunnelling steps up to 1000-fold. Our results imply that the alternating stacked/T-shaped heme arrangement present in both protein complexes may be an evolutionarily convergent design principle permitting efficient electron transfer over very long distances

Ultrafast Light-Driven Electron Transfer in a Ru(II)tris(bipyridine)-Labelled Multiheme Cytochrome

Multiheme cytochromes attract much attention for their electron transport properties. These proteins conduct electrons across bacterial cell walls, along extracellular filaments, and when purified can serve as bionanoelectronic junctions. Thus, it is important and necessary to identify and understand the factors governing electron transfer in this family of proteins. To this end we have used ultra-fast transient absorbance spectroscopy, to define heme-heme electron transfer dynamics in the representative multiheme cytochrome STC from Shewanella oneidensis in aqueous solution. STC was photo-sensitized by site-selective labelling with a Ru(II)(bipyridine)3 dye and the dynamics of light-driven electron transfer described by a kinetic model corroborated by molecular dynamics simulation and density functional theory calculations. With the dye attached adjacent to STC Heme IV, a rate constant of 87 x 106 s-1 was resolved for Heme IV → Heme III electron transfer. With the dye attached adjacent to STC Heme I, at the opposite terminus of the tetraheme chain, a rate constant of 125 x 106 s-1 was defined for Heme I → Heme II electron transfer. These rates are an order of magnitude faster than previously computed values for unlabeled STC. The Heme III/IV and I/II pairs exemplify the T-shaped heme packing arrangement, prevalent in multiheme cytochromes, whereby the adjacent porphyrin rings lie at 90o with edge-edge (Fe-Fe) distances of ≈6 (11) Å. The results are significant in demonstrating the opportunities for pump-probe spectroscopies to resolve inter-heme electron transfer in Ru-labeled multiheme cytochromes