Abstract
We consider the dynamics of an open three-level quantum degenerate system. One of the levels in this system is degenerate. The system interacts with three reservoirs (quantum fields) and a classical external field. We show that nondecaying so-called dark states are generated in this system. Since the interactions of the degenerate level with two different reservoirs are different (correspond to different spaces of dark states), we can describe excitation and manipulations for this kind of states (in particular, observation in spectroscopical experiments). Possible applications of this model in quantum optics, quantum computations, and quantum photosynthesis are discussed.
Similar content being viewed by others
References
L. Accardi and S. Kozyrev, “Lectures on quantum interacting particle systems, ” in Quantum Interacting Particle Systems (World Scientific, Singapore, 2002), QP-PQ: Quantum Probab. White Noise Anal. 14, pp. 1–195.
L. Accardi, S. V. Kozyrev, and A. N. Pechen, “Coherent quantum control of Λ-atoms through the stochastic limit, ” in Quantum Information and Computing, Ed. by L. Accardi, M. Ohya, and N. Watanabe (World Scientific, Hackensack, NJ, 2006), QP-PQ: Quantum Probab. White Noise Anal. 19, pp. 1–17; arXiv: quant-ph/0403100.
L. Accardi, Y. G. Lu, and I. Volovich, QuantumTheory and Its Stochastic Limit (Springer, Berlin, 2002).
I. Ya. Aref’eva, I. V. Volovich, and S. V. Kozyrev, “Stochastic limit method and interference in quantum manyparticle systems, ” Teor. Mat. Fiz. 183 (3), 388–408 (2015) [Theor. Math. Phys. 183, 782–799 (2015)].
H. Dong, D.-Z. Xu, J.-F. Huang, and C.-P. Sun, “Coherent excitation transfer via the dark-state channel in a bionic system, ” Light: Sci. Appl. 1, e2, doi: 10.1038/lsa.2012.2 (2012).
G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Manˇcal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems, ” Nature 446, 782–786 (2007).
M. Ferretti, R. Hendrikx, E. Romero, J. Southall, R. J. Cogdell, V. I. Novoderezhkin, G. D. Scholes, and R. van Grondelle, “Dark states in the light-harvesting complex 2 revealed by two-dimensional electronic spectroscopy, ” Sci. Rep. 6, 20834 (2016).
M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency, ” Phys. Rev. Lett. 84 (22), 5094–5097 (2000); arXiv: quant-ph/0001094.
A. S. Holevo, QuantumSystems, Channels, Information: A Mathematical Introduction (de Gruyter, Berlin, 2012).
A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory, ” Usp. Mat. Nauk 70 (2), 141–180 (2015) [Russ. Math. Surv. 70, 331–367 (2015)].
M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, “Environment-assisted quantum walks in photosynthetic energy transfer, ” J. Chem. Phys. 129 (17), 174106 (2008).
M. Ohya and I. Volovich, MathematicalFoundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems (Springer, New York, 2011).
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, ” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 289, 227–234 (2015) [Proc. Steklov Inst. Math. 289, 213–220 (2015)].
A. Pechen and A. Trushechkin, “Measurement-assisted Landau–Zener transitions, ” Phys. Rev. A 91 (5), 052316 (2015).
G. D. Scholes, G. R. Fleming, A. Olaya-Castro, and R. van Grondelle, “Lessons from nature about solar light harvesting, ” Nature Chem. 3, 763–774 (2011).
M. O. Scully and M. S. Zubairy, QuantumOptics (Cambridge Univ. Press, Cambridge, 1997).
M. E. Shirokov, “On quantum zero-error capacity, ” Usp. Mat. Nauk 70 (1), 187–188 (2015) [Russ. Math. Surv. 70, 176–178 (2015)].
A. S. Trushechkin and I. V. Volovich, “Perturbative treatment of inter-site couplings in the local description of open quantum networks, ” Europhys. Lett. 113 (3), 30005 (2016).
G. Vattay and S. A. Kauffman, “Evolutionary design in biological quantum computing,” arXiv: 1311.4688 [condmat. dis-nn].
I. V. Volovich, “Models of quantum computers and decoherence problem,” arXiv: quant-ph/9902055.
I. V. Volovich, “Cauchy–Schwarz inequality-based criteria for the non-classicality of sub-Poisson and antibunched light, ” Phys. Lett. A 380 (1–2), 56–58 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 294, pp. 256–267.
Rights and permissions
About this article
Cite this article
Volovich, I.V., Kozyrev, S.V. Manipulation of states of a degenerate quantum system. Proc. Steklov Inst. Math. 294, 241–251 (2016). https://doi.org/10.1134/S008154381606016X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S008154381606016X