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.

Recent experimental observations of time-dependent beatings in the two-dimensional echo-spectra of light-harvesting complexes at ambient temperatures have opened up the question of whether coherence and wave-like behaviour play a significant role in photosynthesis. We carry out a numerical study of the absorption and echo-spectra of the Fenna-Matthews-Olson (FMO) complex in Chlorobium tepidum and analyse the requirements in the theoretical model needed to reproduce beatings in the calculated spectra. The energy transfer in the FMO pigment-protein complex is theoretically described by an exciton Hamiltonian coupled to a phonon bath which accounts for the pigments' electronic and vibrational excitations, respectively. We use the hierarchical equations of motions method to treat the strong couplings in a non-perturbative way. We show that the oscillations in the two-dimensional echo-spectra persist in the presence of thermal noise and static disorder. 3 different information from the population dynamics and needs to be calculated and analysed separately in detail. In principle, techniques such as quantum state and process tomography made out of a sequence of 2D echo-spectra can be used to map out the complete density matrix [13]. In contrast to energy-transfer efficiency studies where an initial excitation enters the complex at specific sites close to the antenna, in 2D echo-spectra the whole complex is simultaneously excited. Also the two-exciton manifold yields prominent contributions to the signal, resulting in negative regions in the 2D echo-spectra.The non-pertubative calculation of 2D echo-spectra presents a considerable computational challenge owing to the presence of two excitons giving rise to excited state absorption and the requirement to consider ensemble averages over differently orientated complexes with slightly varying energy levels. Previous calculations have used Markovian approximations [14,15] or exclude the double-exciton manifold [16]. In addition, the systematic study of beatings in a series of 2D echo-spectra requires an effective means of calculating a huge number of such spectra. So far, no theoretical method has been able to describe the long-lasting beatings in the time-resolved 2D spectra [14,16,17]. One possible explanation for the persistence of long coherence times has been the sluggish absorption of the reorganization energy by the molecule, which requires theoretical descriptions that go beyond the Markovian approximation and the rotating wave approximation [18]. The hierarchical equations of motions (HEOM), first developed by Tanimura and Kubo [19] and subsequently refined in [20][21][22][23], show oscillations in the dynamics of the exciton populations that persist even at temperature T = 300 K [24,25]. The HEOM include the reorganization process in a transparent way and are directly applicable to computations at physiological temperatures. A calculation at temperature 77 K of the 2D echospectra with the HEOM method has recently been performed by Chen et al [17], which does not di...

We propose a novel way to communicate signals in the form of waves across a d-dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties. This is an example of using wave interference as a resource by controlling localization phenomena effectively. Possible experimental realizations will be discussed.

We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley [1]. We show that there exists a whole class of quantum search algorithms in the symmetry reduced space which perform a search of a marked vertex in time of order √ N where N = 2 n , the number of vertices. In analogy to Grover's algorithm, the spatial search is effectively facilitated through a rotation in a two-level sub-space of the full Hilbert space. In the hypercube, these two-level systems are introduced through avoided crossings. We give estimates on the quantum states forming the 2-level sub-spaces at the avoided crossings and derive improved estimates on the search times. arXiv:0906.3094v1 [quant-ph]

Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions