Quantum coherent biomolecular energy transfer with spatially correlated fluctuations

We show that the quantum coherent transfer of excitations between biomolecular chromophores is strongly influenced by spatial correlations of the environmental fluctuations. The latter are due either to propagating environmental modes or to local fluctuations with a finite localization length. A simple toy model of a single donor-acceptor pair with spatially separated chromophore sites allows to investigate the influence of these spatial correlations on the quantum coherent excitation transfer. The sound velocity of the solvent determines the wave lengths of the environmental modes, which, in turn, has to be compared to the spatial distance of the chromophore sites. When the wave length exceeds the distance between donor and acceptor site, we find strong suppression of decoherence. In addition, we consider two spatially separated donor-acceptor pairs under the influence of propagating environmental modes. Depending on their wave lengths fixed by the sound velocity of the solvent material, the spatial range of correlations may extend over typical interpair distances, which can lead to an increase of the decohering influence of the solvent. Surprisingly, this effect is counteracted by increasing temperature

Ultraslow quantum dynamics in a sub-Ohmic heat bath

We show that the low-frequency modes of a sub-Ohmic bosonic heat bath generate an effective dynamical asymmetry for an intrinsically symmetric quantum spin -1/2. An initially fully polarized spin first decays towards a quasiequilibrium determined by the dynamical asymmetry, thereby showing coherent damped oscillations on the (fast) time scale of the spin splitting. On top of this, the dynamical asymmetry itself decays on an ultraslow time scale and vanishes asymptotically since the global equilibrium phase is symmetric. We quantitatively study the nature of the initial fast decay to the quasiequilibrium and discuss the features of ultraslow dynamics of the quasiequilibrium itself. The dynamical asymmetry is more pronounced for smaller values of the sub-Ohmic exponent and for lower temperatures, which emphasizes the quantum many-body nature of the effect. The symmetry breaking is related to the dynamic crossover between coherent and overdamped relaxation of the spin polarization and is not connected to the localization quantum phase transition. In addition to this delocalized phase, we identify a novel phase which is characterized by damped coherent oscillations in the localized phase. This allows for a sketch of the zero-temperature phase diagram of the sub-Ohmic spin-boson model with four distinct phases.Comment: published version (minor changes), 8 pages, 5 figure

Rotating wave approximation: systematic expansion and application to coupled spin pairs

We propose a new treatment of the dynamics of a periodically time-dependent Liouvillian by mapping it onto a time-independent problem and give a systematic expansion for its effective Liouvillian. In the case of a two-level system, the lowest order contribution is equivalent to the well-known rotating wave approximation. We extend the formalism to a pair of coupled two-level systems. For this pair, we find two Rabi frequencies and we can give parameter regimes where the leading order of the expansion is suppressed and higher orders become important. These results might help to investigate the interaction of tunneling systems in mixed crystals by providing a tool for the analysis of echo experiments.Comment: 15 pages, Latex, submitted to European Physical Journal