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Physical Review A

Role of the multiple-excitation manifold in a driven quantum simulator of an antenna complex

Alex W. Chin, Brieuc Le Dé, Étienne Mangaud, Osman Atabek, Michèle Desouter-Lecomte

Published Aug 13, 2020• 3 citations
Publisher

Abstract

Biomolecular light-harvesting antennas operate as nanoscale devices in a regime where the coherent interactions of individual light, matter, and vibrational quanta are nonperturbatively strong. The complex behavior arising from this could, if fully understood, be exploited for myriad energy applications. However, nonperturbative dynamics are computationally challenging to simulate, and experiments on biomaterials explore very limited regions of the nonperturbative parameter space. So-called quantum simulators of light-harvesting models could provide a solution to this problem, and here we employ the hierarchical equations-of-motion technique to investigate the recent superconducting experiments of Poto\ifmmode \check{c}\else \v{c}\fi{}nik et al. [A. Poto\ifmmode \check{c}\else \v{c}\fi{}nik et al., Nat. Commun. 9, 904 (2018)] used to explore excitonic energy capture. By explicitly including the role of optical driving fields, nonperturbative dephasing noise, and the full multiexcitation Hilbert space of a three-qubit quantum circuit, we predict the measurable impact of these factors on transfer efficiency. By analysis of the eigenspectrum of the network, we uncover a structure of energy levels that allows the network to exploit optical ``dark'' states and excited-state absorption for energy transfer. We also confirm that time-resolvable coherent oscillations could be experimentally observed, even under the strong, nonadditive action of the driving and optical fields.

DOI
10.1103/physreva.102.023708

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•Dec 28, 2019•0 citations
Biomolecular light-harvesting antennas operate as nanoscale devices in a regime where the coherent interactions of individual light, matter, and vibrational quanta are nonperturbatively strong. The complex behavior arising from this could, if fully understood, be exploited for myriad energy applications. However, nonperturbative dynamics are computationally challenging to simulate, and experiments on biomaterials explore very limited regions of the nonperturbative parameter space. So-called quantum simulators of light-harvesting models could provide a solution to this problem, and here we employ the hierarchical equations-of-motion technique to investigate the recent superconducting experiments of Poto\ifmmode \check{c}\else \v{c}\fi{}nik et al. [A. Poto\ifmmode \check{c}\else \v{c}\fi{}nik et al., Nat. Commun. 9, 904 (2018)] used to explore excitonic energy capture. By explicitly including the role of optical driving fields, nonperturbative dephasing noise, and the full multiexcitation Hilbert space of a three-qubit quantum circuit, we predict the measurable impact of these factors on transfer efficiency. By analysis of the eigenspectrum of the network, we uncover a structure of energy levels that allows the network to exploit optical ``dark'' states and excited-state absorption for energy transfer. We also confirm that time-resolvable coherent oscillations could be experimentally observed, even under the strong, nonadditive action of the driving and optical fields.
Biomolecular light-harvesting antennas operate as nanoscale devices in a regime where the coherent interactions of individual light, matter and vibrational quanta are non-perturbatively strong. The complex behaviour arising from this could, if fully understood, be exploited for myriad energy applications. However, non-perturbative dynamics are computationally challenging to simulate, and experiments on biomaterials explore very limited regions of the non-perturbative parameter space. So-called `quantum simulators' of light-harvesting models could provide a solution to this problem, and here we employ the hierarchical equations of motion technique to investigate recent superconducting experiments of Poto{č}nik et\it{et}et al.\it{al.}al. (Nat. Com. 9, 904 (2018)) used to explore excitonic energy capture. By explicitly including the role of optical driving fields, non-perturbative dephasing noise and the full multi-excitation Hilbert space of a three-qubit quantum circuit, we predict the measureable impact of these factors on transfer efficiency. By analysis of the eigenspectrum of the network, we uncover a structure of energy levels that allows the network to exploit optical `dark' states and excited state absorption for energy transfer. We also confirm that time-resolvable coherent oscillations could be experimentally observed, even under strong, non-additive action of the driving and optical fields.
Abstract Near-unity energy transfer efficiency has been widely observed in natural photosynthetic complexes. This phenomenon has attracted broad interest from different fields, such as physics, biology, chemistry, and material science, as it may offer valuable insights into efficient solar-energy harvesting. Recently, quantum coherent effects have been discovered in photosynthetic light harvesting, and their potential role on energy transfer has seen the heated debate. Here, we perform an experimental quantum simulation of photosynthetic energy transfer using nuclear magnetic resonance (NMR). We show that an N-chromophore photosynthetic complex, with arbitrary structure and bath spectral density, can be effectively simulated by a system with log2N qubits. The computational cost of simulating such a system with a theoretical tool, like the hierarchical equation of motion, which is exponential in N, can be potentially reduced to requiring a just polynomial number of qubits N using NMR quantum simulation. The benefits of performing such quantum simulation in NMR are even greater when the spectral density is complex, as in natural photosynthetic complexes. These findings may shed light on quantum coherence in energy transfer and help to provide design principles for efficient artificial light harvesting.
Quantum synchronisation has recently been proposed as a mechanism for electronic excitation energy transfer in light-harvesting complexes, yet its robustness in driven-dissipative settings remains under active investigation. Here, we revisit this mechanism in cryptophyte photosynthetic antennae using an exciton--vibrational dimer model. By comparing the full open quantum dynamics with semi-classical rate equations for electronic density-matrix elements and vibrational observables, we demonstrate that quantum correlations between electronic and vibrational degrees of freedom, beyond the semi-classical factorised limit, underpin the emergence of quantum synchronisation. Furthermore, we introduce an environment-assisted transfer mechanism arising as a nonlinear, non-Condon correction to the dipole--dipole interaction. This mechanism enables long-lived quantum coherence and continuous, synchronisation-enhanced energy transfer in a driven-dissipative regime, thereby suggesting new avenues for investigating photosynthetic energy-transfer dynamics.
Light-harvesting in nature is known to work differently than conventional man-made solar cells. Recent studies found electronic excitations, delocalised over several chromophores, and a soft, vibrating structural environment to be key schemes that might protect and direct energy transfer yielding increased harvest efficiencies even under adversary conditions. Unfortunately, testing realistic models of noise assisted transport at the quantum level is challenging due to the intractable size of the environmental wave function. I developed a powerful tree tensor network states (TTNS) method that finds an optimally compressed explicit representation of the combined electronic and vibrational quantum state. With TTNS it is possible to simulate exciton-phonon quantum dynamics from small molecules to larger complexes, modelled as an open quantum system with multiple bosonic environments. After benchmarking the method on the minimal spin-boson model by reproducing ground state properties and dynamics that have been reported using other methods, the vibrational quantum state is harnessed to investigate environmental dynamics and its correlation with the spin system. To enable simulations of realistic non-Born-Oppenheimer molecular quantum dynamics, a clustering algorithm and novel entanglement renormalisation tensors are employed to interface TTNS with ab initio density functional theory (DFT). A thereby generated model of a pentacene dimer containing 252 vibrational normal modes was simulated with TTNS reproducing exciton dynamics in agreement with experimental results. Based on the environmental state, the (potential) energy surfaces, underlying the observed singlet fission dynamics, were calculated yielding unprecedented insight into the super-exchange mediated avoided crossing mechanism that produces ultrafast and high yield singlet fission. This combination of DFT and TTNS is a step towards large scale material exploration that can accurately predict excited states properties and dynamics. Furthermore, application to biomolecular systems, such as photosynthetic complexes, may give valuable insights into novel environmental engineering principles for the design of artificial light-harvesting systems.
A wellknown approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through photosynthetic light harvesting complexes (LHCs). The hierarchical equations of motion (HEOM) was adapted by Ishizaki and Fleming [J. Chem. Phys.130, 234111 (2009)] to simulate open quantum dynamics in the biological regime. We generate a set of time-dependent observables that depict the coherent propagation of electronic excitations through the LHCs by solving the HEOM. The computationally intractable problem here is addressed using classical machine learning (ML). The ML architecture constructed here is of model character and it is used to solve the inverse problem for open quantum systems within the HEOM approach. The objective is to determine whether a trained ML model can perform Hamiltonian tomography by using the time dependence of the observables as inputs. We demonstrate the capability of convolutional neural networks to tackle this research problem. The models developed here can predict Hamiltonian parameters such as excited state energies and inter-site couplings of a system up to 99.28% accuracy.
The study of quantum phenomena in biology has received significant attention in the last decade. One of the problems of most interest is the understanding of quantum effects during the first steps of photosynthesis. Ultrafast two-dimensional electronic spectroscopy has revealed that pigment-protein complexes responsible for light- harvesting and charge separation in photosynthetic organisms can support quantum coherent dynamics in the excited state, for up to few hundreds of femtoseconds. The leading hypothesis on the mechanisms supporting this coherent behaviour is quan- tum interactions between electronic and some specific vibrational motions in the excited state. This hypothesis, however, awaits unambiguous confirmation. Among the most powerful techniques to investigate the quantum behaviour of an emitter is the study of quantum optical properties of the light it emits. This thesis de- velops theoretical studies showing that frequency-filtered and time-resolved photon counting statistics of the light emitted by a prototype photosynthetic unit can give important insight into the quantum coherent nature and the mechanisms underlying excited state dynamics in single photosynthetic complexes. By developing a pertur- bative and efficient approach to the computation of frequency- and time- resolved photon correlation functions, we show that such correlations have the potential to give unambiguous signatures of coherence contributions to the steady state emis- sion. For a light-harvesting unit emitting in free space, the signatures of excited state coherence manifest themselves as non-trivial antibunching. This feature can- not be probed by measuring unfiltered photon correlations. We then consider the situation in which a prototype energy transfer unit is embedded in an optical cavity such that its emission rate is enhanced. In this case we observed a rich behaviour of the frequency-filtered, second-order photon correlations that allows a clear distinc- tion of coherence contributions, and their variation, depending of the electronic and vibrational interactions in the system of interest.