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The decrease in efficiency above an optimal noise power is due to dephasing-induced population localization, also referred to as the quantum Zeno effect 8 , 9 , The measured integrated powers and hence the efficiency are in good agreement with results from master equation simulations solid lines in Fig. Therefore for practical light harvesting applications one may choose to maximize output power while compromising on efficiency 14 , This experimentally demonstrates the interplay between quantum coherent effects and classical dephasing enhancing excitation transport.

It has been conjectured that structured environmental noise, such as the one originating from long-lived vibrational modes of chlorophyll molecules in photosynthetic complexes, can further enhance the energy transfer efficiency between the disordered molecular sites of the network in a scenario known as the phonon antenna mechanism 1 , In contrast, no energy transfer is observed when the noise is far detuned. Both observations clearly demonstrate the strong sensitivity of the energy transfer on the spectral properties of the environmental noise, and indicate that the noise-assisted transport is enabled by a narrow part of the noise PSD that matches the energy gap otherwise blocking the energy transfer in the system.

This observation is consistent with stochastically averaged master equation simulations see Supplementary Fig. We note that despite applying classical noise the dynamics induced by Lorentzian environment cannot be simulated with the HSR approach or even its extension for colored noise 43 , 44 , due to its strong non-Markovian character.

Therefore, a full quantum numerical simulation is required at the cost of significant computational effort.

However, we note that the extracted power P 4 is almost twice as large at the same bright state excitation amplitude Fig. This indicates that structured environmental noise matching internal energy differences of the quantum network indeed enhances the efficiency of the energy transfer. Estimating the effective qubit-environment coupling constant K see Fig. This demonstrates that strong coupling between qubit and phononic modes is required to achieve maximal energy transport.

Such a situation has been suggested to enhance the transport in cyanobacterial light-harvesting proteins, allophycocyanin, and C-phycocyanin While this case does not occur in natural light harvesting since the environment cannot be fully coherent, it represents an interesting limiting case.

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In natural light-harvesting systems exposed to incoherent environments, the highest transfer efficiency is realized for structured environmental noise with a narrow spectral density peaked at the frequency of the internal energy mismatch between the sites of the network. These aspects are clearly demonstrated by the presented set of experiments comparing energy transfer with white and Lorentzian noise spectral density. In the final set of experiments we excite the qubit system with incoherent microwave radiation to mimic excitation of biological pigment protein complexes with sunlight.

We engineer 0. The incoherent microwave power integrated over the bright state spectrum was adjusted to be equal to the drive power used for the case of coherent excitation. In this experiment we study the transport of incoherently created excitations as a function of applied white noise power. Since it is not possible to distinguish between the broad incoming incoherent and the re-emitted radiation at port 2, we plot in Fig.

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The observed extracted power is a result of direct excitation of the dark state, due to its finite coupling to the open waveguide. When the dark state is not completely dark, simultaneous incoherent excitation of bright and dark states reduces coherence between Q 1 and Q 2 and therefore increases dephasing of the system. Existence of dark states in photosynthetic complexes can therefore help protect the system against dephasing induced by incoherent excitation.

Comparable efficiencies are consistent with rate equation descriptions, where the efficiency is independent of the spectral and coherence properties of the excitation. This indicates that absorption of the incoherent photons is not as strongly affected by environmental dephasing as for coherent excitation, due to a persistent overlap between broadened bright state spectrum and spectrum of the incoherent irradiation. In a proof of concept experiment we studied models of photosynthetic processes using superconducting quantum circuits.

With a system of three coupled qubits we demonstrated how the interplay of quantum coherence and environmental interactions affects energy transport in a system with excellent control achievable over all relevant parameters. We expect this approach to be extensible to study other relevant aspects of light harvesting, such as time-resolved dynamics of the coherent excitation transfer; the role of quantum environments realizable in electronic circuit models as low frequency quantum harmonic oscillators 14 , 26 ; and scaling to systems with a larger number of coherent sites such as the FMO complex.

Furthermore, we expect similar approaches to be applicable not only to study light-harvesting processes but also other interesting aspects of quantum biology such as the sense of smell in animals, humans, and magnetoreception in birds 1 , 2. It could also be interesting to evaluate the potential of the techniques presented here to model processes in quantum chemistry and search for potential future applications of related methods to support, for example, the design of catalysts, e. The authors declare that the data supporting the findings of this study are available within the article and its Supplementary Information files or from the corresponding authors on reasonable request.

This has been corrected in the PDF version of the Article. Huelga, S. Vibrations, quanta and biology. Lambert, N. Quantum biology.

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mathematical nature of the living world [2004]

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