Susana F. Huelga

Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain system for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods.

Exploiting Structured Environments for Efficient Energy Transfer: The Phonon Antenna Mechanism.

A nontrivial interplay between quantum coherence and dissipative environment-driven dynamics is becoming increasingly recognized as the key for efficient energy transport in photosynthetic pigment-protein complexes, and converting these biologically inspired insights into a set of design principles that can be implemented in artificial light-harvesting systems has become an active research field. Here we identify a specific design principle, the phonon antenna, by which interpigment coherence is able to modify and optimize the way that excitations spectrally sample their local environmental fluctuations. We provide numerical simulations that suggest that the Fenna-Matthews-Olson complex of green sulfur bacteria has an excitonic structure that is close to such an optimal operating point, and place the phonon antenna concept into a broader context that leads us to conjecture that this general design principle might well be exploited in other biomolecular systems.

Focus on quantum effects and noise in biomolecules

The role of quantum mechanics in biological organisms has been a fundamental question of twentieth-century biology. It is only now, however, with modern experimental techniques, that it is possible to observe quantum mechanical effects in bio-molecular complexes directly. Indeed, recent experiments have provided evidence that quantum effects such as wave-like motion of excitonic energy flow, delocalization and entanglement can be seen even in complex and noisy biological environments (Engel et al 2007 Nature 446 782; Collini et al 2010 Nature 463 644; Panitchayangkoon et al 2010 Proc. Natl Acad. Sci. USA 107 12766). Motivated by these observations, theoretical work has highlighted the importance of an interplay between environmental noise and quantum coherence in such systems (Mohseni et al 2008 J. Chem. Phys. 129 174106; Plenio and Huelga 2008 New J. Phys. 10 113019; Olaya-Castro et al 2008 Phys. Rev. B 78 085115; Rebentrost et al 2009 New J. Phys. 11 033003; Caruso et al 2009 J. Chem. Phys. 131 105106; Ishizaki and Fleming 2009 J. Chem. Phys. 130 234111). All of this has led to a surge of interest in the exploration of quantum effects in biological systems in order to understand the possible relevance of non-trivial quantum features and to establish a potential link between quantum coherence and biological function. These studies include not only exciton transfer across light harvesting complexes, but also the avian compass (Ritz et al 2000 Biophys. J. 78 707), and the olfactory system (Turin 1996 Chem. Sens. 21 773; Chin et al 2010 New J. Phys. 12 065002).These examples show that the full understanding of the dynamics at bio-molecular length (10xa0A) and timescales (sub picosecond) in noisy biological systems can uncover novel phenomena and concepts and hence present a fertile ground for truly multidisciplinary research.

Mappings of open quantum systems onto chain representations and Markovian embeddings

We study systems coupled linearly to a bath of oscillators. In an iterative process, the bath is transformed into a chain of oscillators with nearest neighbour interactions. A systematic procedure is provided to obtain the spectral density of the residual bath in each step, and it is shown that under general conditions these data converge. That is, the asymptotic part of the chain is universal, translation invariant with semicircular spectral density. The methods are based on orthogonal polynomials, in which we also solve the outstanding so-called “sequence of secondary measures problem” and give them a physical interpretation.

Dephasing-assisted transport in linear triple quantum dots

Environmental noise usually hinders the efficiency of charge transport through coherent quantum systems; an exception is dephasing-assisted transport (DAT). We show that linear triple quantum dots in a transport configuration and subjected to pure dephasing exhibit DAT if the coupling to the drain reservoir exceeds a threshold. DAT occurs for arbitrarily weak dephasing and the enhancement can be directly controlled by the coupling to the drain. Moreover, for specific settings, the enhanced current is accompanied by a reduction of the relative shot noise. We identify the quantum Zeno effect and long-distance tunnelling as underlying dynamic processes involved in dephasing-assisted and -suppressed transport. Our analytical results are obtained by using the density matrix formalism and the characteristic polynomial approach to full counting statistics.

Probing quantum coherence in qubit arrays

We discuss how the observation of population localization effects in periodically driven systems can be used to quantify the presence of quantum coherence in interacting qubit arrays. Essential for our proposal is the fact that these localization effects persist beyond tight-binding Hamiltonian models. This result is of special practical relevance in those situations where direct system probing using tomographic schemes becomes infeasible beyond a very small number of qubits. As a proof of principle, we study analytically a Hamiltonian system consisting of a chain of superconducting flux qubits under the effect of a periodic driving. We provide extensive numerical support of our results in the simple case of a two-qubit chain. For this system we also study the robustness of the scheme against different types of noise and disorder. We show that localization effects underpinned by quantum coherent interactions should be observable within realistic parameter regimes in chains with a larger number of qubits.

Theory of Excitonic Delocalization for Robust Vibronic Dynamics in LH2

Nonlinear spectroscopy has revealed long-lasting oscillations in the optical response of a variety of photosynthetic complexes. Different theoretical models that involve the coherent coupling of electronic (excitonic) or electronic-vibrational (vibronic) degrees of freedom have been put forward to explain these observations. The ensuing debate concerning the relevance of either mechanism may have obscured their complementarity. To illustrate this balance, we quantify how the excitonic delocalization in the LH2 unit of Rhodopseudomonas acidophila purple bacterium leads to correlations of excitonic energy fluctuations, relevant coherent vibronic coupling, and importantly, a decrease in the excitonic dephasing rates. Combining these effects, we identify a feasible origin for the long-lasting oscillations observed in fluorescent traces from time-delayed two-pulse single-molecule experiments performed on this photosynthetic complex and use this approach to discuss the role of this complementarity in other photosynthetic systems.

Microscopic Description: Non-Markovian Case

The microscopic description of non-Markovian dynamics is much more involved than the Markovian one, and developing efficient methods to deal with it is actually an active area of research nowadays.

Quantum Effects in Biology and Their Applications to Light Harvesting and Sensing

Abstract This session introduced the novel area of quantum effects in biological systems: it presented its seminal experimental discoveries and theoretical ideas, namely regarding photosynthetic systems and olfactory recognition, and discussed their potential applications to the development of artificial devices for more efficient light harvesting and finer sensing.

The benefit of doing things slowly: employing dissipation for the robust creation of entanglement between ions in spatially separate cavities

We present protocol that allows the generation of a maximally entangled state between individual atoms held in spatially separate cavities. Under ideal conditions, the scheme is deterministic. In a realistic setting, when the the atom-cavity interaction may be weak, and the detectors are imperfect, we show that the scheme is robust against experimental inefficiencies and yields probabilistic entanglement of very high fidelity.