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Quality of Control in the Tavis–Cummings–Hubbard Model

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A Correction to this article was published on 01 July 2021

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In this paper, the Discrete Sources Method has been extended to describe the influence of the geometry asymmetry of a core-shell particle accounting for the effect of spatial dispersion inside the plasmonic metal shell. We found that varying the plasmonic shell thickness has more influence on the near field intensity distribution then on the average enhancement factor. Besides, we demonstrates that the effect of spatial dispersion can decrease the near field intensity up to 60% of its value and it provides a small blue shift.

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References

  1. E. T. Jaynes and F.W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE, 51, No. 1, 89–109 (1963).

    Article  Google Scholar 

  2. M. T. Tavis, A Study of an N Molecule Quantized-Radiation-Field Hamiltonian, Dissertation; https://arxiv.org/abs/1206.0078 (2012).

  3. M. I. Makin, Jared H. Cole, Charles D. Hill, Andrew D. Greentree, and Lloyd C. L. Hollenberg, “Time evolution of the onedimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A, 80 (2009).

  4. Guilherme M. A. Almeida and Andre M. C. Souza, “Quantum transport with coupled cavities on an Apollonian network,” Phys. Rev. A, 87 (2013).

  5. Shifeng Cui, F. Hébert, B. Grémaud, V. G. Rousseau, Wenan Guo, and G. G. Batrouni, “Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: Photon-pair superradiance, Mott insulator, and normal phases,” Phys. Rev. A, 100 (2019).

  6. L. Garbe, I. L. Egusquiza, E. Solano, C. Ciuti, T. Coudreau, P. Milman, and S. Felicetti, “Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model,” Phys. Rev. A, 95 (2017).

  7. R. Gutiérrez-Jáuregui and G. S. Agarwal, “Probing the spectrum of the Jaynes-Cummings-Rabi model by its isomorphism to an atom inside a parametric amplifier cavity,” Phys. Rev. A, 103 (2021).

  8. T. Mohamadian, J. Negro, L. M. Nieto, and H. Panahi, “Tavis–Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians,” Eur. Phys. J. Plus, 134, No. 363 (2019).

  9. E. A. Matweev, S. E. Igoshina, and A. A. Karmanov, “Quantum Phase Transition as a Basis for Practical Realization of the ATF Communication Technology,” Programmnaya Ingeneria, 10, No. 7-8, 305–310 (2019).

  10. A. Ambainis, “Quantum walks and their algorithmic applications,” International Journal of Quantum Information, 1, No. 4, 507–518 (2003).

  11. Luca Razzoli, Matteo G. A. Paris, and Paolo Bordone, “Continuous-time quantum walks on planar lattices and the role of the magnetic field,” Phys. Rev. A, 101 (2020).

  12. C. Zalka, “Simulating quantum systems on a quantum computer,” Proceedings of The Royal Society A, 454(1969), 313–322 (1998).

    Article  Google Scholar 

  13. Richard P. Feynman, “Simulating Physics with Computers,” Int. J. Theoretical Physics, 21, 467–488 (1982).

  14. L. Grover, “A fast quantum mechanical algorithm for database search,” STOC ’96: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing,, 212–219 (1996).

  15. P. Shor, “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer,” SIAM J. Sci. Statist. Comput., 26, No. 5, 1484–1509 (1997).

    MathSciNet  MATH  Google Scholar 

  16. A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A, 52, No. 5 (1995).

  17. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature, 409, 46–52 (2001).

    Article  Google Scholar 

  18. D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature, 402, 390–393 (1999).

    Article  Google Scholar 

  19. Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, andWilliam K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett., 70, No. 13 (1993).

  20. S. Popescu, “Knill-Laflamme-Milburn Quantum Computation with Bosonic Atoms,” Phys. Rev. Lett., 99, No. 13 (2007).

  21. G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett., 58, No. 4, 353–356 (1987).

    Article  Google Scholar 

  22. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett., 75, No. 25, 4714–4717 (1995).

    Article  MathSciNet  Google Scholar 

  23. H. Azuma, “Quantum computation with the Jaynes–Cummings model,” Prog. Theor. Phys., 126, No. 3, 369–385 (2011).

    Article  Google Scholar 

  24. Y. I. Ozhigov, “Quantum gates on asynchronous atomic excitations,” Quantum Electronics, 50, No. 10, 947–950 (2020).

  25. V. Ladunov, Y. Ozhigov, and N. Skovoroda, “Computer simulation of quantum effects in Tavis-Cummings model and its applications,” Proc. SPIE 10224, International Conference on Micro- and Nano-Electronics 2016 (2016).

  26. A. V. Kulagin and Y. I. Ozhigov, “Optical Selection of Dark States of Multilevel Atomic Ensembles,” Computational Mathematics and Modeling, 31, 431–441 (2020).

    Article  MathSciNet  Google Scholar 

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Düll, R., Kulagin, A., Lee, W. et al. Quality of Control in the Tavis–Cummings–Hubbard Model. Comput Math Model 32, 75–85 (2021). https://doi.org/10.1007/s10598-021-09517-y

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