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arXiv:1506.00581 · Laser Physics Letters

Coherent delocalization: views of entanglement in different scenarios

R de J León-Montiel, A Vallés, H M Moya-Cessa, J P Torres

Published Jul 21, 2015• 10 citations
arXivHTMLPDF

Abstract

The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar correlations can be observed when considering different degrees of freedom of a single system, even a classical one. Surprisingly, it has also been suggested that entanglement might be playing a relevant role in certain biological processes, such as the functioning of pigment-proteins that constitute light-harvesting complexes of photosynthetic bacteria. The aim of this work is to show that the presence of entanglement in all of these different scenarios should not be unexpected, once it is realized that the very same mathematical structure can describe all of them. We show this by considering three different, realistic cases in which the only condition for entanglement to exist is that a single excitation is coherently delocalized between the different subsystems that compose the system of interest.

DOI
10.1088/1612-2011/12/8/085204

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The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar correlations can be observed when considering different degrees of freedom of a single system, even a classical one. Surprisingly, it has also been suggested that entanglement might be playing a relevant role in certain biological processes, such as the functioning of pigment-proteins that constitute light-harvesting complexes of photosynthetic bacteria. The aim of this work is to show that the presence of entanglement in all of these different scenarios should not be unexpected, once it is realized that the very same mathematical structure can describe all of them. We show this by considering three different, realistic cases in which the only condition for entanglement to exist is that a single excitation is coherently delocalized between the different subsystems that compose the system of interest.
We explore quantum entanglement among the chlorophyll molecules in light-harvesting complex II, which is the most abundant photosynthetic antenna complex in plants containing over 50% of the world's chlorophyll molecules. Our results demonstrate that there exists robust quantum entanglement under physiological conditions for the case of a single elementary excitation. However, this nonvanishing entanglement is not unexpected because entanglement in the single-excitation manifold is conceptually the same as quantum delocalized states, which are the spectroscopically detectable energy eigenstates of the system. We discuss the impact of the surrounding environments and correlated fluctuations in electronic energies of different pigments upon quantum delocalization and quantum entanglement. It is demonstrated that investigations with tools quantifying the entanglement can provide us with more detailed information on the nature of quantum delocalization, in particular the so-called dynamic localization, which is difficult for a traditional treatment to capture.
We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the electronic entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical" and "quantum" can be made for systems composed of many particles when the properties of the ensemble are determined by the correlations between the constituents. The issue of grasping the nature of entanglement (i.e. quantum correlations) lies in its formal, discriminative definition: "if state is not classical then it is entangled". A possible remedy would be to approach the problem from the utilitarian point of view. The idea is that certain tasks can be performed better when entangled states are used instead of states that are only classically correlated. An example of such task is an entanglement-enhanced interferometer utilizing ensembles of ultra-cold atoms. This line of reasoning leads to the concept of classification of entanglement by the degree of usefulness and allows to relate it to certain well-defined physical properties of the state. The aim of this work is to formalize this abstraction and build upon it an intuitive picture which can help us understand what the entanglement is.
When two or more systems exhibit correlations that are stronger than those that can be explained traditionally, notwithstanding their spatial separation, this phenomenon is known as quantum entanglement. It is regarded as a key component of upcoming quantum technologies and one of the distinctive qualities of quantum physics. The transverse spatial degree of freedom in photonic experiments gives enormous opportunity to investigate different fascinating properties of light. This thesis has therefore focused on the photonic entanglement of transverse spatial formations in order to better explore the nature of quantum entanglement. The orbital angular momentum of photons is an intriguing characteristic caused by their spatial mode structure. Surprisingly, the maximum number of orbital angular momentum quanta that a single photon may carry is unbounded theoretically. As a result, it seems like a good candidate for evaluating photonic entanglement of macroscopic values. It may also add to discussions on macroscopicity and a potential breakdown of quantum mechanics beyond a certain point. Quantum entanglement is a fascinating phenomenon that lies at the heart of quantum mechanics, challenging our traditional understanding of the physical world. This paper aims to provide an overview of quantum entanglement, its experimental verification, and the implications it has on our comprehension of reality. By delving into its theoretical underpinnings and discussing the ongoing debates, we seek to answer the question: Does quantum entanglement make sense?
Introduction In this chapter, we will focus on the phenomenon of quantum entanglement . Entanglement is a special property that some states of two or more quantum particles may possess. When particles are in an entangled state they are correlated. But entanglement is far more than mere correlation . Entanglement is a type of correlation that macroscopic objects cannot have, even in principle; it is what we call a ‘non-local’ correlation. Entanglement, and the non-locality that derives from it, is by now considered to be, arguably, the most important aspect of quantum mechanics. Philosophically it leads to many puzzles and to a complete change in our view of nature. At the same time, the practical implications of this type of correlation are very significant. In particular, they can lead to the dramatically enhanced information processing capabilities that quantum systems possess. The whole field of quantum information processing (Steane, 1998; Bennett and DiVincenzo, 2000; Zoller et al. , 2005) has entanglement at its core. Given the above, it is natural to ask whether biological systems make use and take advantage of the enhanced possibilities that entanglement offers. It seems natural to expect this, especially at biological molecular level, where the laws of quantum mechanics apply. Entanglement between two isolated particles is easy to obtain: almost every time two particles interact they get entangled. But entanglement is very fragile. When two entangled quantum systems interact with a third, they easily become entangled in a tri-partite way; however, any entanglement between any two of them is reduced or disappears altogether.
Ultrafast spectroscopy experiments show that photosynthetic systems can preserve quantum beats in the process of electronic energy transfer between pigments, even at room temperature. But what does this discovery imply for biology - and for quantum mechanics? This dissertation examines photosynthesis through the tools of quantum information science. We evaluate to what extent photosynthesis can be thought of as a type of quantum technology, and consider how we can apply experimental tools widely used for quantum technologies (state tomography and coherent control) to photosynthesis. Throughout, we use the Fenna-Matthews-Olson (FMO) complex of greens sulfur bacteria as a model photosynthetic pigment-protein complex.In Part I, we evaluate two mechanisms for the possible biological relevance of quantum coherent motion. First, we consider the extent to which dynamics in light-harvesting systems exhibit the quantum speedups characteristic of quantum algorithms and quantum walks. Second, we demonstrate a ratchet effect in electronic energy transfer enabled by partially coherent dynamics. To do so, we build a new model of energy transfer between weakly coupled light-harvesting complexes to understand how electronic coherence arises under natural conditions.In Part II, we present proposals for experimental probes of light harvesting dynamics with ultrafast spectroscopy. We show how the signal from pump-probe spectroscopy can be formally inverted to determine the excited state electronic density matrix. Finally, we examine the feasiblity of coherent control experiments on light-harvesting systems, and provide two realistic targets feasible with present-day technology.