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Infinite Dimensional Analysis Quantum Probability and Related Topics

Entangled and dark stationary states of excitation energy transport models in quantum many-particle systems and photosynthesis

J. C. García, Souhir Gliouez, F. Guerrero-Poblete, Roberto B. Quezada

Published Aug 17, 2018• 7 citations
Publisher

Abstract

We characterize the stationary states of an excitation energy transfer model in quantum many-particle systems [Y. Aref’eva, I. Volovich and S. Kozyrev, Stochastic limit method and interference in quantum many-particles systems, Theor. Math. Phys. 183(3) (2015) 782–799] as well as the stationary states of a quantum photosynthesis model [S. Kozyrev and I. Volovich, Dark states in quantum photosynthesis, arXiv:1603.07182v1 [physics.bio-ph]] in terms of a transport operator. It turns out that, apart from the ground state, all invariant states of the excitation energy transport model are entangled. For the photosynthesis model, any invariant state in the commutant of the system Hamiltonian is a mixed bright–dark state in the sense of [S. Kozyrev and I. Volovich, Dark states in quantum photosynthesis, arXiv:1603.07182v1 [physics.bio-ph]] and it is pure dark if and only if the bright vector belongs to the kernel of this state.

DOI
10.1142/s0219025718500182

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We characterize the stationary states of an excitation energy transfer model in quantum many-particle systems [Y. Aref’eva, I. Volovich and S. Kozyrev, Stochastic limit method and interference in quantum many-particles systems, Theor. Math. Phys. 183(3) (2015) 782–799] as well as the stationary states of a quantum photosynthesis model [S. Kozyrev and I. Volovich, Dark states in quantum photosynthesis, arXiv:1603.07182v1 [physics.bio-ph]] in terms of a transport operator. It turns out that, apart from the ground state, all invariant states of the excitation energy transport model are entangled. For the photosynthesis model, any invariant state in the commutant of the system Hamiltonian is a mixed bright–dark state in the sense of [S. Kozyrev and I. Volovich, Dark states in quantum photosynthesis, arXiv:1603.07182v1 [physics.bio-ph]] and it is pure dark if and only if the bright vector belongs to the kernel of this state.
Transport in nonequilibrium degenerate quantum systems is investigated. The transfer rate depends on the parameters of the system. In this paper we investigate the dependence of the flow (transfer rate) on the angle between “bright” vectors (which define the interaction of the system with the environment). We show that in some approximation for the system under investigation the flow is proportional to the cosine squared of the angle between the “bright” vectors. Earlier the author has shown that in this degenerate quantum system excitation of nondecaying quantum “dark” states is possible; moreover, the effectiveness of this process is proportional to the sine squared of the angle between the “bright” vectors (this phenomenon was discussed as a possible model of excitation of quantum coherence in quantum photosynthesis). Thus quantum transport and excitation of dark states are competing processes; “dark” states can be considered as a result of leakage of quantum states in a quantum thermodynamic machine which performs the quantum transport.
Photosynthesis is an important and complex physical process in nature, whose comprehensive understanding would have many relevant industrial applications, for instance, in the field of energy production. In this paper, we propose a quantum algorithm for the simulation of the excitonic transport of energy, occurring in the first stage of the process of photosynthesis. The algorithm takes in account the quantum and environmental effects (pure dephasing), influencing the quantum transport. We performed quantum simulations of such phenomena, for a proof of concept scenario, in an actual quantum computer, IBM Q, of 5 qubits. We validate the results with the Haken-Ströbl model and discuss the influence of environmental parameters on the efficiency of the energy transport.
We prove that every stationary state in the annihilator of all Kraus operators of a weak coupling limit-type Markov generator consists of two pieces, one of them supported on the interaction-free subspace and the second one on its orthogonal complement. In particular, we apply the previous result to describe in detail the structure of a slightly modified quantum transport model due to Arefeva et al. (modified AKV’s model) studied first in [J. C. García et al., Entangled and dark stationary states of excitation energy transport models in many-particles systems and photosynthesis, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21(3) (2018), Article ID: 1850018, p. 21, doi:10.1142/S0219025718500182], in terms of generalized annihilation and creation operators.
The mechanism of vibronic amplification of transport of excitons has been discussed in connection with quantum photosynthesis. Vibrons (some modes of vibrations of molecules) have been observed experimentally in photosynthetic systems. In the present paper we consider models of vibronic amplification of quantum transfer in which the generation of vibrons as a coherent vibrational mode is described by an analog of the semiclassical laser theory. We study two models: a model of nonequilibrium three-level system with vibronic mode, and a variant of a model of lasing without inversion. We conjecture that the dark states discussed in connection with quantum photosynthesis might be related to the mechanism of vibronic “laser” without inversion, which amplifies the transfer of excitons. We prove that in the presence of a vibronic mode the transfer rate of excitons increases, and compute the dependence of the transfer rate on the parameters of the model.
Photosynthesis is an important and complex physical process in nature, whose comprehensive understanding would have many relevant industrial applications, for instance in the field of energy production. In this paper we propose a quantum algorithm for the simulation of the excitonic transport of energy, occurring in the first stage of the process of photosynthesis. The algorithm takes in account the quantum and environmental effects (pure-dephasing), influencing the quantum transport. We performed quantum simulations of such phenomena, for a proof of concept scenario, in an actual quantum computer the IBM Q, of 5 qubits. We validate the results with the Haken-Str\"obl model and discuss the influence of environmental parameters on the efficiency of the energy transport.
Transport across quantum networks underlies many problems, from state transfer on a spin network to energy transport in photosynthetic complexes. However, networks can contain dark subspaces that block the transportation, and various methods used to enhance transfer on quantum networks can be viewed as equivalently avoiding, modifying, or destroying the dark subspace. Here, we exploit graph theoretical tools to identify the dark subspaces and show that asymptotically almost surely they do not exist for large networks, while for small ones they can be suppressed by properly perturbing the coupling rates between the network nodes. More specifically, we apply these results to describe the recently experimentally observed and robust transport behaviour of the electronic excitation travelling on a genetically-engineered light-harvesting cylinder (M13 virus) structure. We believe that these mainly topological tools may allow us to better infer which network structures and dynamics are more favourable to enhance transfer of energy and information towards novel quantum technologies.