Robust design principles for quantum enhanced excitation transport

Summary form only given. Under which general conditions can fundamental principles of quantum mechanics be exploited to enhance transport in complex systems? Common wisdom suggests that quantum interference can enhance transport across perfectly periodic potentials [1], while it tends to suppress transport in disordered systems [2]. In general, multi-path quantum interference leads to erratic, large scale fluctuations of transmission probabilities when boundary conditions or other system parameters are slightly changed [3]. These fluctuations are often indicative of the strong, non-linear coupling of few degrees of freedom. Can we identify structural properties of the underlying Hamiltonians in those specific instances when they generate quantum-enhanced transport? Are these design-principles statistically robust, in the sense that they are “implementable” by controlling only few coarsegrained parameters, without claiming full control of the detailed structure of a possibly large, composite quantum system with some intrinsic randomness?The answer to this question is affirmative. We show that for a disordered finite quantum system, which can be effectively modelled as a network of sites, it is possible to enhance transport from an initial (uin>) to a final site (lout>) by exploiting the quantum nature of the system. In order to achieve this goal, we need two crucial structural ingredients: The centro-symmetry [3] of the underlying Hamiltonian and the existence of a dominant doublet [4] . The centro-symmetry justifies a block diagonal representation for the Hamiltonian, whereas the dominant doublet guarantees that the coupling to random/chaotic states can efficiently assist the transport in a robust way.Inspired by the mechanism of chaos assisted tunneling [5], we manage to obtain an analytic distribution of the transport timescales as plotted in Fig. 1 . This distribution is fully determined by three coarse-grained parameters: the average coupling of the input and output sites to the intermediate site, the density of states of the intermediate sites, and the total number of sites. We address the potential that this model has to offer for biological systems, by studying its applicability to light harvesting complexes. We present indications that the two main structural properties needed for our model, centro-symmetry and a dominant doublet, could indeed be present in these systems. In our here developed perspective, robust and efficient transport across complex quantum networks is achieved by hardwiring not one single, optimal network conformation, but rather a suitable statistical distribution. We argue that robust optimization and control of the properties of truly complex quantum systems is only achievable by optimal design of probability distributions, combined with redundancy, a recipe also found to stabilize biological functionality.