Tobias Kramer

Long-Lived Electronic Coherence in Dissipative Exciton Dynamics of Light-Harvesting Complexes

Recent experiments on light-harvesting complexes at ambient temperatures display oscillatory signals in two-dimensional spectroscopy. They suggest mechanisms supporting coherent exciton transport through molecular networks in noisy environments. We demonstrate a mechanism that relies on the continuum properties of the vibronic spectral density. We employ the spectral density of the Fenna–Matthews–Olson (FMO) complex and perform a nonperturbative calculation of two-dimensional spectra. They display long-lasting electronic coherence up to 0.3 ps at a temperature of 277 K. Two important properties of the spectral density found in the FMO complex emerge; (i) the coupling to higher-frequency vibrations is large, as required for efficient transport toward the reaction center, and (ii) the slope of the spectral density at zero frequency approaches zero. We demonstrate that electronic coherence and fast thermalization depend sensitively on the continuum part of the spectral density but can be simultaneously reali...

High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the possibility of memory effects in this process and require one to consider time nonlocal propagation techniques. The hierarchical equations of motion (HEOM) were proposed by Ishizaki and Fleming to describe the site-dependent reorganization dynamics of protein environments ( J. Chem. Phys. 2009 , 130 , 234111 ), which plays a significant role in photosynthetic electronic energy transfer. HEOM are often used as a reference for other approximate methods but have been implemented only for small systems due to their adverse computational scaling with the system size. Here, we show that HEOM are also solvable for larger systems, since the underlying algorithm is ideally suited for the usage of graphics processing units (GPU). The tremendous reduction in computational time due to the GPU allows us to perform a systematic study of the energy-transfer efficiency in the Fenna-Matthews-Olson (FMO) light-harvesting complex at physiological temperature under full consideration of memory effects. We find that approximative methods differ qualitatively and quantitatively from the HEOM results and discuss the importance of finite temperature to achieving high energy-transfer efficiencies.

Scalable High-Performance Algorithm for the Simulation of Exciton Dynamics. Application to the Light-Harvesting Complex II in the Presence of Resonant Vibrational Modes.

The accurate simulation of excitonic energy transfer in molecular complexes with coupled electronic and vibrational degrees of freedom is essential for comparing excitonic system parameters obtained from ab initio methods with measured time-resolved spectra. Several exact methods for computing the exciton dynamics within a density-matrix formalism are known but are restricted to small systems with less than 10 sites due to their computational complexity. To study the excitonic energy transfer in larger systems, we adapt and extend the exact hierarchical equation of motion (HEOM) method to various high-performance many-core platforms using the Open Compute Language (OpenCL). For the light-harvesting complex II (LHC II) found in spinach, the HEOM results deviate from predictions of approximate theories and clarify the time scale of the transfer process. We investigate the impact of resonantly coupled vibrations on the relaxation and show that the transfer does not rely on a fine-tuning of specific modes.

Imaging magnetic focusing of coherent electron waves

The magnetic focusing of electrons has proven its utility in fundamental studies of electron transport. Here we report the direct imaging of magnetic focusing of electron waves, specifically in a two-dimensional electron gas (2DEG). We see the semicircular trajectories of electrons as they bounce along a boundary in the 2DEG, as well as fringes showing the coherent nature of the electron waves. Imaging flow in open systems is made possible by a cooled scanning probe microscope. Remarkable agreement between experiment and theory demonstrates our ability to see these trajectories and to use this system as an interferometer. We image branched electron flow as well as the interference of electron waves. This technique can visualize the motion of electron waves between two points in an open system, providing a straightforward way to study systems that may be useful for quantum information processing and spintronics.

Disentangling electronic and vibronic coherences in two-dimensional echo spectra

The prevalence of long-lasting oscillatory signals in two-dimensional (2D) echo spectroscopy of light-harvesting complexes has led to a search for possible mechanisms. We investigate how two causes of oscillatory signals are intertwined: (i) electronic coherences supporting delocalized wavelike motion and (ii) narrow bands in the vibronic spectral density. To disentangle the vibronic and electronic contributions, we introduce a time-windowed Fourier transform of the signal amplitude. We find that 2D spectra can be dominated by excitations of pathways which are absent in excitonic energy transport. This leads to an underestimation of the lifetime of electronic coherences by 2D spectra.

Revivals of quantum wave packets in graphene

We investigate the propagation of wave packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time evolution of an initially localized wave packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states. We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac–Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Our effective numerical method is of general interest for the solution of the Dirac equation in the presence of potentials and magnetic fields.

Electron dynamics in parallel electric and magnetic fields

We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric, and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors a rich set of features which find their interpretation in the unusual and interesting properties of the classical motion of the electrons: For instance, the number of interfering trajectories can be adjusted in this system, and the turning surfaces of classical motion contain a complex array of singularities. We perform a comprehensive analysis of the semiclassical approximation and compare it to the quantum solution, and we make predictions that should serve as a guide for future photodetachment experiments.

Self-consistent calculation of electric potentials in Hall devices

Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii) confinement to a finite system. By propagating thousands of interacting electrons over million time-steps we capture the build-up of the self-consistent potential, which resembles results obtained by conformal-mapping methods. As shown by a microscopic model of the current injection, the Hall effect is linked to specific boundary conditions at the particle reservoirs.

ON THE ORIGIN OF INNER COMA STRUCTURES OBSERVED BY ROSETTA DURING A DIURNAL ROTATION OF COMET 67P/CHURYUMOV–GERASIMENKO

The Rosetta probe around comet 67P/Churyumov-Gerasimenko (67P) reveals an anisotropic dust distribution of the inner coma with jet-like structures. The physical processes leading to jet formation are under debate, with most models for cometary activity focusing on localised emission sources, such as cliffs or terraced regions. Here we suggest, by correlating high-resolution simulations of the dust environment around 67P with observations, that the anisotropy and the background dust density of 67P originate from dust released across the entire sunlit surface of the nucleus rather than from few isolated sources. We trace back trajectories from coma regions with high local dust density in space to the non-spherical nucleus and identify two mechanisms of jet formation: areas with local concavity in either two dimensions or only one. Pits and craters are examples of the first case, the neck region of the bilobed nucleus of 67P for the latter one. The conjunction of multiple sources in addition to dust released from all other sunlit areas results in a high correlation coefficient (~0.8) of the predictions with observations during a complete diurnal rotation period of 67P.

PREVAILING DUST-TRANSPORT DIRECTIONS ON COMET 67P/CHURYUMOV–GERASIMENKO

Dust transport and deposition behind larger boulders on the comet 67P/Churyumov-Gerasimenko (67P/C-G) have been observed by the Rosetta mission. We present a mechanism for dust transport vectors based on a homogenous surface activity model incorporating in detail the topography of 67P/C-G. The combination of gravitation, gas drag, and Coriolis force leads to specific dust transfer pathways, which for higher dust velocities fuel the near nucleus coma. By distributing dust sources homogeneously across the whole cometary surface, we derive a global dust-transport map of 67P/C-G. The transport vectors are in agreement with the reported wind-tail directions in the Philae descent area.