Desperately seeking quantum coherence

There is a paper in Science

Engineering Coherence Among Excited States in Synthetic Heterodimer Systems

Dugan Hayes, Graham B. Griffin, Gregory S. Engel

Six years ago Engel was first author of a Nature paper claiming that photosynthetic systems used quantum computing to maximise efficiency. The claims of this paper are more modest. The abstract begins:

The design principles that support persistent electronic coherence in biological light-harvesting systems are obscured by the complexity of such systems. Some electronic coherences in these systems survive for hundreds of femtoseconds at physiological temperatures, suggesting that coherent dynamics MAY play a role in photosynthetic energy transfer. Coherent effects MAY increase energy transfer efficiency relative to strictly incoherent transfer mechanisms. 

The key data is in the Figure below. It shows a Fourier transform of the "cross peaks in the two-dimensional spectra". The three boxes correspond to the different heterodimers. 

The vertical dashed lines are all present in monomers and are identified as vibronic features of those monomers.

[n.b. In the past some people mistakenly identified such features with coherences between different chromophores in photosynthetic complexes.]

The solid coloured vertical lines are identified as a quantum beating coherence between the two monomors. [But note smaller versions of these peaks are also present in two of the heterodimers]. The corresponding frequencies correspond to the difference frequency epsilon between the two monomers. This is the main result of the paper, the presence of electronic coherences between two dimers.

The decoherence time of the coherences is estimated to be of the order of tens of femtoseconds.
Although, not stated in the paper, this is just what one expects for typical chromophores in polar solvents. This timescale is much shorter than the timescale [1-100 psec] for many of the exciton transport processes in photosynthetic systems.

In a heterodimer the quantum beat frequency is given by

where Delta* is the coupling energy between the two chromophores and epsilon is the energy difference between the excitons in the individual chromophores. Since the authors observe a beat frequency of close to epsilon this means that Delta* is very small, at most tens of cm-1 which is less than thermal energy scales at room temperature.

It should also be pointed out that in the regime where epsilon is much larger than Delta* that the spectral weight of the quantum coherences becomes very small and they are easily decohered.  This can  be seen in Figure 2 of this PRL by Costi and Kieffer.