Model of Vibrons in Quantum Photosynthesis as an Analog of a Model of Laser

S. V. Kozyrev

Informatics and Automation, Mathematical physics and applications, Tome 306 (2019), pp. 158-169.

Résumé

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.

Bibliographie

[1] Accardi L., Kozyrev S., “Lectures on quantum interacting particle systems”, Quantum interacting particle systems: Lecture notes of the Volterra–CIRM Int. Sch. (Trento, 2000), QP–PQ: Quantum Probab. White Noise Anal., 14, World Scientific, Hackensack, NJ, 2002, 1–195 | DOI | MR

[2] Accardi L., Lu Y.G., Volovich I., Quantum theory and its stochastic limit, Springer, Berlin, 2002 | MR | Zbl

[3] I. Ya. Aref'eva, I. V. Volovich, and S. V. Kozyrev, “Stochastic limit method and interference in quantum many-particle systems”, Theor. Math. Phys., 183:3 (2015), 782–799 | DOI | DOI | MR | Zbl

[4] Engel G.S., Calhoun T.R., Read E.L., Ahn T.-K., Mančal T., Cheng Y.-C., Blankenship R.E., Fleming G.R., “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems”, Nature, 446 (2007), 782–786 | DOI

[5] Fleischhauer M., Lukin M.D., “Dark-state polaritons in electromagnetically induced transparency”, Phys. Rev. Lett., 84:22 (2000), 5094–5097 ; arXiv: quant-ph/0001094. | DOI

[6] Ferretti M., Hendrikx R., Romero E., Southall J., Cogdell R.J., Novoderezhkin V.I., Scholes G.D., van Grondelle R., “Dark states in the light-harvesting complex 2 revealed by two-dimensional electronic spectroscopy”, Sci. Rep., 6 (2016), 20834 | DOI

[7] Ferretti M., Novoderezhkin V.I., Romero E., Augulis R., Pandit A., Zigmantas D., van Grondelle R., “The nature of coherences in the B820 bacteriochlorophyll dimer revealed by two-dimensional electronic spectroscopy”, Phys. Chem. Chem. Phys., 16:21 (2014), 9930–9939 ; Khaken G., Lazernaya svetodinamika, Mir, M., 1988 | DOI

[8] H. Haken, Light, v. II, Laser Light Dynamics, North-Holland, Amsterdam, 1985

[9] Harris S.E., “Lasers without inversion: Interference of lifetime-broadened resonances”, Phys. Rev. Lett., 62:9 (1989), 1033–1036 | DOI

[10] O. A. Kocharovskaya and Ya. I. Khanin, “Coherent amplification of an ultrashort pulse in a three-level medium without a population inversion”, JETP Lett., 48:11 (1988), 630–634

[11] Kolli A., O'Reilly E.J., Scholes G.D., Olaya-Castro A., “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae”, J. Chem. Phys., 137:17 (2012), 174109 | DOI

[12] S. V. Kozyrev, “Quantum transport in degenerate systems”, Proc. Steklov Inst. Math., 301 (2018), 134–143 | DOI | DOI | MR | Zbl

[13] Kozyrev S.V., Mironov A.A., Teretenkov A.E., Volovich I.V., “Flows in non-equilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021 ; arXiv: 1612.00213 [quant-ph] | DOI | MR | Zbl

[14] Kozyrev S.V., Volovich I.V., “Dark states in quantum photosynthesis”, Trends in biomathematics: Modeling, optimization and computational problems: Sel. works from the BIOMAT Consortium Lect. (Moscow, 2017), ed. by R.P. Mondaini, Springer, Cham, 2018, 13–26 | DOI | MR | Zbl

[15] Mompart J., Corbalán R., “Lasing without inversion”, J. Opt. B: Quantum Semiclass. Opt., 2:3 (2000), R7–R24 | DOI

[16] Novoderezhkin V.I., Romero E., van Grondelle R., “How exciton-vibrational coherences control charge separation in the photosystem II reaction center”, Phys. Chem. Chem. Phys., 17:46 (2015), 30828–30841 | DOI

[17] Ohya M., Volovich I., Mathematical foundations of quantum information and computation and its applications to nano- and bio-systems, Springer, New York, 2011 | MR | Zbl

[18] A. N. Pechen and N. B. Il'in, “Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times”, Proc. Steklov Inst. Math., 289 (2015), 213–220 | DOI | DOI | MR | Zbl

[19] Pechen A., Trushechkin A., “Measurement-assisted Landau–Zener transitions”, Phys. Rev. A, 91:5 (2015), 052316 | DOI

[20] Romero E., Augulis R., Novoderezhkin V.I., Ferretti M., Thieme J., Zigmantas D., van Grondelle R., “Quantum coherence in photosynthesis for efficient solar-energy conversion”, Nature Phys., 10 (2014), 676–682 | DOI

[21] Scholes G.D., Fleming G.R., Olaya-Castro A., van Grondelle R., “Lessons from nature about solar light harvesting”, Nature Chem., 3 (2011), 763–774 | DOI

[22] Scully M.O., Zubairy M.S., Quantum optics, Cambridge Univ. Press, Cambridge, 1997

[23] Trushechkin A.S., Volovich I.V., “Perturbative treatment of inter-site couplings in the local description of open quantum networks”, Europhys. Lett., 113:3 (2016), 30005 | DOI

[24] I. V. Volovich and S. V. Kozyrev, “Manipulation of states of a degenerate quantum system”, Proc. Steklov Inst. Math., 294 (2016), 241–251 | DOI | DOI | MR | Zbl