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arXiv:2105.12128 · Physical Review A

Quantum feedback control in quantum photosynthesis

Sergei Vladimirovich Kozyrev, Alexander Nikolaevich Pechen

Published Sep 22, 2022• 6 citations
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Abstract

A model of charge separation in quantum photosynthesis as a model of quantum feedback control in a system of interacting excitons and vibrons is introduced. In this approach quantum feedback induces a nonlinear evolution equation which describes the Landau-Zener transition with decoherence and can be considered a quantum ratchet. It explains both the irreversibility in the process of charge separation for quantum photosynthesis (for this model direct transitions have probabilities close to 1, and reverse transitions have probabilities close to zero) and coincidence of the energy of the vibron paired to the transition and the Bohr frequency of the transition.

DOI
10.1103/physreva.106.032218

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•Jan 1, 2018•9 citations
A model of charge separation in quantum photosynthesis as a model of quantum feedback control in a system of interacting excitons and vibrons is introduced. In this approach quantum feedback induces a nonlinear evolution equation which describes the Landau-Zener transition with decoherence and can be considered a quantum ratchet. It explains both the irreversibility in the process of charge separation for quantum photosynthesis (for this model direct transitions have probabilities close to 1, and reverse transitions have probabilities close to zero) and coincidence of the energy of the vibron paired to the transition and the Bohr frequency of the transition.
Abstract Amplification of quantum transfer and ratchet–type processes are important for quantum technologies. We also expect that quantum ratchet works in quantum photosynthesis, where possible role of quantum effects is now widely discussed but the underlying dynamical processes are still not clearly known. In this work, we study a model of amplification of quantum transfer and making it directed, which we call the quantum ratchet model. The model is based on a special quantum control master equation with dynamics induced by a feedback-type process. The ratchet effect is achieved in the quantum control model with dissipation and sink, where the Hamiltonian depends on vibrations in the energy difference synchronized with transitions between energy levels. A similarity between this model and the model of coherent transport in quantum photosynthesis, where the time dependence of the Hamiltonian arises due to vibrons, is studied. Amplitude and frequency of the oscillating vibron together with the dephasing rate are the parameters of the quantum ratchet which determine its efficiency. We study with which parameters the quantum ratchet minimizes the exction recombination time and show that the experimentally known values of the parameters of the photosynthetic reaction center correspond to values of the parameters of the quantum ratchet which realize a local minimum of the exciton recombination time. We also find other values of the parameters of the quantum ratchet minimizing the exciton recombination time, which correspond to a twice smaller frequency of the vibron compared to that observed in experiments.
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.
Introduction In the preceding chapter we introduced quantum trajectories: the evolution of the state of a quantum system conditioned on monitoring its outputs. As discussed in the preface, one of the chief motivations for modelling such evolution is for quantum feedback control. Quantum feedback control can be broadly defined as follows. Consider a detector continuously producing an output, which we will call a current. Feedback is any process whereby a physical mechanism makes the statistics of the present current at a later time depend upon the current at earlier times. Feedback control is feedback that has been engineered for a particular purpose, typically to improve the operation of some device. Quantum feedback control is feedback control that requires some knowledge of quantum mechanics to model. That is, there is some part of the feedback loop that must be treated (at some level of sophistication) as a quantum system. There is no implication that the whole apparatus must be treated quantum mechanically. The structure of this chapter is as follows. The first quantum feedback experiments (or at least the first experiments specifically identified as such) were done in the mid 1980s by two groups [WJ85a, MY86]. They showed that the photon statistics of a beam of light could be altered by feedback. In Section 5.2 we review such phenomena and give a theoretical description using linearized operator equations. Section 5.3 considers the changes that arise when one allows the measurement to involve nonlinear optical processes.
An innovative microscopic model with a minimal number of parameters: tunneling splitting gap, external field sweeping velocity, and decoherence rate is used to describe dynamics of the dissipative Landau-Zener transition in the presence of the decoherence. In limiting cases, the derived equation of motion gives rise to the well-known Landau-Zener and Kayanuma formula. In a general case, the description demonstrates a non-monotonic flipping probability with respect to the sweeping velocity, which is also found in some other models. This non-monotony can be explained by considering the competition and timescale of the quantum tunneling, crossing period, and decoherence process. The simplicity and robustness of the theory offer a practical and novel description of the Landau-Zener transition. In addition, it promises an alternative method to the electron paramagnetic resonance in measuring the effective decoherence rate of relevant quantum systems.
We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the \npossibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a \nframework of three-level model. We compute Landau–Zener probabilities for a linear sweep of the gate charge \nand investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau–Zener probabilities reveal two different patterns: “step”- and “beats”-like \nbehaviors associated with the quantum interference effects. Control on these two regimes is provided by change \nof the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and finetuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between pair of levels \nis forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. \nThis effect can be observed by measuring a population difference slowly varying in time between the states of \nthe Cooper-pair box characterized by the same parity