We model recent experiments on living sulphur bacteria interacting with quantised light, using the Dicke model. Our analysis shows that the strong coupling between the bacteria and the light, when both are treated quantum-mechanically, indicates that in those experiments there is entanglement between the bacteria (modelled as dipoles) and the quantised light (modelled as a single quantum harmonic oscillator). The existence of lower polariton branch due to the vacuum Rabi splitting, measured in those experiments for a range of different parameters, ensures the negativity of energy (with respect to the lowest energy of separable states), thus acting as an entanglement witness.Witnessing quantum effects in living systems was long considered an impossible task, even by the pioneers of quantum theory, such as Bohr [1]. Recent advances in theoretical and experimental techniques, however, are bringing us closer to accomplishing it. Entanglement has extensively been investigated, and even detected, in various many-body systems [2]. Since living systems are (most probably) special cases of many-body systems, they can (presumably) be analysed with the same methods. In this paper we model recently performed experiments where living sulphur bacteria are entangled with a quantised field of light [3]. This is particularly exciting, since the quantised nature of light was at the heart of the complementarity that Bohr thought would ultimately make it impossible for us to detect quantum effects in a living entity. We also offer an argument that semi-classical models would be insufficient to explain the experiments' results.
Summary of the experimentLet us first summarise the basics of the experiments in [3]. Green sulphur bacteria are found in anaerobic environments rich in sulphur compounds, such as microbial mats and around hot springs [4]. They are photosynthetic and are able to survive in extreme locations where light intensity drops to only a few hundred photons per second per bacteria [5]. The bacteria have evolved antenna complexes called chlorosomes, which are large aggregates of approximately 200,000 self-assembled bacteriochlorophyll (BChl) molecules. When light is absorbed by these antenna complexes, an exciton is created, which then travels to a protein baseplate attached to the chlorosome, and then to the reaction centre, where it is used to power chemical reactions.Each bacterium contains around 200 chlorosomes, where the dense packing of the molecules and their high dipole moments result in high oscillator strengths that make the bacteria (and organic matter in general) good candidates for strong coupling between excitons and photons. Their size, approximately 2 μm×500 nm, means that they can also be inserted into a micron-sized optical microcavities with well-defined photon mode energies. The strong coupling condition is met when the leakage of the light trapped in the microcavity is slow compared to the energy exchange rate between the light and bacteria. This results in a modification of the energy sp...