Quantum entanglement in photosynthetic light-harvesting complexes

Journal name:
Nature Physics
Volume:
6,
Pages:
462–467
Year published:
DOI:
doi:10.1038/nphys1652
Received
Accepted
Published online

Abstract

Light-harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long timescales, despite the decohering effects of their environments. Here, we analyse entanglement in multichromophoric light-harvesting complexes, and establish methods for quantification of entanglement by describing necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna–Matthews–Olson protein to extract the initial state and temperature dependencies of entanglement. We show that, although the Fenna–Matthews–Olson protein in natural conditions largely contains bipartite entanglement between dimerized chromophores, a small amount of long-range and multipartite entanglement should exist even at physiological temperatures. This constitutes the first rigorous quantification of entanglement in a biological system. Finally, we discuss the practical use of entanglement in densely packed molecular aggregates such as light-harvesting complexes.

At a glance

Figures

  1. The light-harvesting apparatus of green sulphur bacteria and the FMO protein.
    Figure 1: The light-harvesting apparatus of green sulphur bacteria and the FMO protein.

    The schematic on the left illustrates the absorption of light by the chlorosome antenna and transport of the resulting excitation to the reaction centre through the FMO protein. On the right is an image of a monomer of the FMO protein, showing also its orientation relative to the antenna and the reaction centre22, 24. The multiring units are BChla molecules and the surrounding β sheets and α helices form the protein environment in which the BChla molecules are embedded. The numbers label individual BChla molecules, also referred to as ‘sites’ in the main text.

  2. Global entanglement in the FMO protein.
    Figure 2: Global entanglement in the FMO protein.

    Time evolution of the global entanglement measure given in equation (1) for the two initial states |1right fence and |6right fence, at low (T=77K) and high (T=300K) temperatures. The inset shows the long-time evolution of the same quantities, together with the trace of the single-excitation density matrix as dashed curves (identical colour coding, and the same units on the axes as in the main figure).

  3. Bipartite entanglement in the FMO protein when the initial state is an excitation localized on site 1.
    Figure 3: Bipartite entanglement in the FMO protein when the initial state is an excitation localized on site 1.

    a,b, Time evolution of the concurrence measure of bipartite site entanglement, Cij=2|ρij|, at 77K (a) and 300K (b). Only curves for the most entangled chromophores are shown. The insets show the long-time behaviour (identical colour coding, and the same units on the axes as in the main figures).

  4. Bipartite entanglement in the FMO protein when the initial state is an excitation localized on site 6.
    Figure 4: Bipartite entanglement in the FMO protein when the initial state is an excitation localized on site 6.

    a,b, Time evolution of the concurrence measure of bipartite site entanglement, Cij=2|ρij|, at 77K (a) and 300K (b). Only curves for the most entangled chromophores are shown. The insets show the long-time behaviour (identical colour coding, and the same units on the axes as in the main figures).

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Affiliations

  1. Berkeley Center for Quantum Information and Computation, Berkeley, California 94720, USA

    • Mohan Sarovar &
    • K. Birgitta Whaley
  2. Department of Chemistry, University of California, Berkeley, California 94720, USA

    • Mohan Sarovar,
    • Akihito Ishizaki,
    • Graham R. Fleming &
    • K. Birgitta Whaley
  3. Physical Bioscience Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Akihito Ishizaki &
    • Graham R. Fleming

Contributions

Calculations were carried out by M.S. and A.I. All authors contributed extensively to the planning, discussion and writing up of this work.

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The authors declare no competing financial interests.

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