Photon generation in resonator with time dependent boundary conditions
https://doi.org/10.17586/2220-8054-2021-12-1-73-80
Abstract
We present a simulation of Casimir field generation in the 1D cavity with moving walls and arbitrary variation of boundary conditions. We design a numerical scheme based on the finite element method and compare photon generation due to variation of the geometry of the cavity and due to perturbation of the boundary conditions.
About the Authors
I. S. LobanovRussian Federation
Kronverkskiy, 49, St. Petersburg, 197101; St. Petersburg, 198504
A. I. Trifanov
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
E. S. Trifanova
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
I. Y. Popov
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
E. Fedorov
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
K. V. Pravdin
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
M. A. Moskalenko
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
References
1. Nation P.D., Johansson J.R., Blencowe M.P. Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits. Rev. Mod. Phys., 2012, 84, P. 1–24.
2. Crocce M. Resonant photon creation in a three-dimensional oscillating cavity. Phys. Rev. A, 2001, 64 (1), 013808.
3. Law C. Effective hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium. Physical Review A, 1994, 49 (1), P. 433–437.
4. Law C. Interaction between a moving mirror and radiation pressure: A hamiltonian formulation. Physical Review A, 1995, 51 (3), P. 2537– 2541.
5. Sassaroli E., Srivastava Y., Widom A. Photon production by the dynamical casimir effect. Phys. Rev. A, 1994, 50 (2).
6. Dodonov V. Generation and detection of photons in a cavity with a resonantly oscillating boundary. Phys. Rev. A, 1996, 53 (4).
7. Moore G. Quantum theory of the electromagnetic field in a variable length one dimensional cavity. Journal of Mathematical Physics, 1970, 11, P 2679.
8. Wilson C., Johansson G. Observation of the dynamical Casimir effect in a superconduction circuit. Nature, 2011, 479, P. 376–379.
9. Dodonov V. Current status of the dynamical Casimir effect. Physica Scripta, 2010, 82, 038105.
10. Dodonov V.V. Fifty years of the dynamical Casimir effect. Physics, 2020, 2 (3), P. 67–104.
11. Lähteenmäki P., Paraoanu G.S., Hassel J., Hakonen P.J. Dynamical Casimir effect in a Josephson metamaterial. Proceedings of the National Academy of Sciences, 2013, 110 (11), P. 4234–4238.
12. Svensson I.-M., Pierre M., et al. Microwave photon generation in a doubly tunable superconducting resonator. Journal of Physics: Conference Series, 2018, 969, 012146.
13. Good M.R.R., Linder E.V. Slicing the vacuum: New accelerating mirror solutions of the dynamical Casimir effect. Phys. Rev. D, 2017, 96, 125010.
14. Li L., Li B.-Z. Numerical solutions of the generalized Moore’s equations for a one-dimensional cavity with two moving mirrors. Physics Letters A, 2002, 300 (1), P. 27–32.
15. Alves D.T., Granhen E.R. A computer algebra package for calculation of the energy density produced via the dynamical casimir effect in one-dimensional cavities. Computer Physics Communications, 2014, 185 (7), P. 2101–2114.
16. Popov I.Y. Asymptotic series for the spectrum of the Schrödinger operator for layers coupled through small windows. Theor. Math. Phys., 2002, 131 (3), P. 407–418.
17. Popov I.Y. Asymptotics of bound states and bands for laterally coupled waveguides and layers. J. Math. Phys., 2002, 43 (1), P. 215–234.
18. Popov I., Trifanov A.I., Trifanova E.S. Coupled dielectric waveguides with photonic crystal properties. Zh. Vychisl. Mat. Mat. Fiz., 2010, 50, P. 1931–1937.
19. Nekrashevych V., Teplyaev A. Groups and analysis on fractals, analysis on graphs and its applications. Amer. Math. Soc., 2009, 77, P. 143–180.
20. Korotyaev E. Schrodinger operator with a junction of two 1-dimensional periodic potentials. Asymptotic Analysis, 2005, 45, P. 73–97.
21. Matrasulov D.U., Yusupov J.R., Sabirov K.K., Sobirov Z.A. Time-dependent quantum graph. Nanosystems: Phisycs, Chemistry, Mahematics, 2015, 6 (2), P. 173–181.
22. Lobanov I.S., Nikiforov D.S., et al. Model of time-dependent geometric graph for dynamical Casimir effect. Indian Journal of Physics, 2020, DOI 10.1007/s12648-020-01866-5.
23. Popov I.Yu., Trifanov A.I., Trifanova E.S. Dielectric waveguides with photonic crystal properties. Comp. Math. Math. Phys., 2010, 50 (11), P. 1830–1836.
24. Melikhova A.S., Popov I.Y. Spectral problem for solvable model of bent nanopeapod. Applicable Analysis, 2017, 96 (2), P. 215–224.
25. Vorobiev A.M., Bagmutov A.S., Popov A.I. On formal asymptotic expansion of resonance for quantum waveguide with perforated semitrans-parent barrier. Nanosystems: Phys. Chem. Math., 2019, 10 (4), P. 415–419.
26. Exner P., Kostenko A., Malamud M., Neidhardt H. Spectral theory of infinite quantum graphs. Ann. H. Poincare, 2018, 19, P. 3457–3510.
27. Berkolaiko G., Kuchment P. Introduction to Quantum Graphs. AMS, Providence, 2012.
28. Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y. Wave dynamics on time-depending graph with Aharonov-Bohm ring. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9 (4), P. 457–463.
29. Barseghyan D., Exner P., Khrabustovskyi A., Tater M. Spectral analysis of a class of Schrödinger operators exhibiting a parameter-dependent spectral transition. J. Phys. A, 2016, 49, 165302.
30. Fedorov E.G., Popov A.I., Popov I.Y. Metric graph version of the FitzHugh-Nagumo model. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10 (6), P. 623–626.
Review
For citations:
Lobanov I.S., Trifanov A.I., Trifanova E.S., Popov I.Y., Fedorov E., Pravdin K.V., Moskalenko M.A. Photon generation in resonator with time dependent boundary conditions. Nanosystems: Physics, Chemistry, Mathematics. 2021;12(1):73-80. https://doi.org/10.17586/2220-8054-2021-12-1-73-80