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Cosine-Type Absorbing Optical Potential for the Modeling of Quantum Dynamics with the Fourier Grid and Optimizer Packages

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Abstract

In order to model the spectroscopic and scattering properties of a quantum system, we propose and explore a new absorbing complex-type optical potential based on a combination of cosine functions. This function provides a high degree of smoothness to joint with a physical real-type potential. The capabilities of this function are investigated in terms of its effect on otherwise freely evolving quantum dynamics. We use our open-source programs to implement the Fourier Grid method with the Optimizer package (in Matlab), freely available at https://sourceforge.net/projects/optimizer-sovkov/.

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REFERENCES

  1. L. D. Landau, E. M. Lifshitz, Quantum Mechanics. NonRelativistic Theory (Pergamon, Oxford-New York-Toronto- Sydney-Paris-Frankfurt, 1977). https://doi.org/10.1016/C2013-0-02793-4

    Book  Google Scholar 

  2. X. Wang, W. Liu, Y. Li, J. Wu, V.B. Sovkov, J. Ma, S. Onishchenko, P. Li, Y. Fu, D. Li, Q. Fan, L. Xiao, S. Jia, Physical Chemistry Chemical Physics, 22, 3809 (2020). https://doi.org/10.1039/C9CP05870B

    Article  Google Scholar 

  3. J. Wu, W. Liu, X. Wang, J. Ma, D. Li, V. B. Sovkov, L. Xiao, S. Jia, Journal of Chemical Physics, 148, 174304 (2018). https://doi.org/10.1063/1.5023330

  4. N. Zheng, W. Liu, V. B. Sovkov, J. Xu, G. Ge, Y. Li, P. Li, Y. Fu, J. Wu, J. Ma, L. Xiao, S. Jia, Optics Express, 29(21), 32892 (2021). https://doi.org/10.1364/OE.437881

    Article  ADS  Google Scholar 

  5. M. Guo, B. Zhu, B. Lu, X. Ye, F. Wang, R. Vexiau, N. Bouloufa-Maafa, G. Quemener, O. Dulieu, D. Wang, Physical Review Letters, 116, 205303 (2016). https://doi.org/10.1103/PhysRevLett.116.205303

  6. X. Ye, M. Guo, M.L. Gonzalez-Martinez, G. Quemener, D. Wang, Science Advances, 4, eaaq0083 (2018). https://doi.org/10.1126/sciadv.aaq0083

  7. N. Y. Yao, M. P. Zaletel, D. M. Stamper-Kurn, A. Vishwanath, Nature Physics, 14, 405 (2018). https://doi.org/10.1038/s41567-017-0030-7

    Article  ADS  Google Scholar 

  8. N. Goldman, J.C. Budich, P. Zoller. Nature Physics, 12, 639 (2016). https://doi.org/10.1038/nphys3803

    Article  ADS  Google Scholar 

  9. N. R. Cooper, G. V. Shlyapnikov, Physical Review Letters, 103, 155302 (2009). https://doi.org/10.1103/PhysRevLett.103.155302

  10. J. L. Bohn, A. M. Rey, J. Ye, Science, 357, 1002 (2017). https://doi.org/10.1126/science.aam6299

  11. I. Kozyryev, N. R. Hutzler, Physical Review Letters, 119, 133002 (2017). https://doi.org/10.1103/PhysRevLett.119.133002

  12. W. B. Cairncross, D. N. Gresh, M. Grau, K. C. Cossel, T. S. Roussy, Y. Ni, Y. Zhou, J. Ye, E. A. Cornell, Physical Review Letters, 119, 153001 (2017). https://doi.org/10.1103/PhysRevLett.119.153001

  13. J. Kobayashi, A. Ogino, S. Inouye, Nature Communications, 10, 3771 (2019). https://doi.org/10.1038/s41467-019-11761-1

    Article  ADS  Google Scholar 

  14. S. A. Moses, J. P. Covey, M. T. Miecnikowski, D. S. Jin, J. Ye, Nature Physics, 13(1), 13 (2017). https://doi.org/10.1038/nphys3985

    Article  ADS  Google Scholar 

  15. D. DeMille, Physical Review Letters, 88, 067901 (2002). https://doi.org/10.1103/PhysRevLett.88.067901

  16. N. V. Vitanov, A. A. Rangelov, B. W. Shore, K. Bergmann, Reviews of Modern Physics, 89, 015006 (2017). https://doi.org/10.1103/RevModPhys.89.015006

  17. K. Bergmann, H. Theuer, B.W. Shore, Reviews of Modern Physics, 70, 1003 (1998). https://doi.org/10.1103/RevModPhys.70.1003

    Article  ADS  Google Scholar 

  18. G. Feng, Y. Li, X. Wang, J. Wu, V. B. Sovkov, J. Ma, L. Xiao, S. Jia, Scientific Reports, 7, 13677 (2017). https://doi.org/10.1038/s41598-017-13534-6

    Article  ADS  Google Scholar 

  19. Y. Li, X. Wang, J. Wu, G. Feng, W. Liu, V. B. Sovkov, J. Ma, B. Deb, L. Xiao, S. Jia, Physical Chemistry Chemical Physics, 23(1), 641 (2021). https://doi.org/10.1039/D0CP04840B

    Article  Google Scholar 

  20. J. G. Muga, J. P. Palao, B. Navarro, I. L. Egusquiza, Physics Reports, 395, 357 (2004). https://doi.org/10.1016/j.physrep.2004.03.002

    Article  ADS  MathSciNet  Google Scholar 

  21. V. B. Sovkov. Optimizer:source codes and manuals & collection of applications, 2019-2022. https://sourceforge.net/projects/optimizer-sovkov/

  22. I. Schaefer, R. Kosloff, Physical Review A: Atomic, Molecular, and Optical Physics, 101, 023407 (2020). https://doi.org/10.1103/Phys-RevA.101.023407

  23. B. Schmidt, U. Lorenz, Computer Physics Communications, 213, 223 (2017). https://doi.org/10.1016/j.cpc.2016.12.007

    Article  ADS  Google Scholar 

  24. B. Schmidt, C. Hartmann, Computer Physics Communications, 228, 229 (2018). https://doi.org/10.1016/j.cpc.2018.02.022

    Article  ADS  MathSciNet  Google Scholar 

  25. B. Schmidt, R. Klein, L. C. Araujo, Journal of Computational Chemistry, 40, 2677 (2019). https://doi.org/10.1002/jcc.26045

    Article  Google Scholar 

  26. D. Kosloff, R. Kosloff, Journal of Computational Physics, 52, 35 (1983). https://doi.org/10.1016/0021-9991(83)90015-3

    Article  ADS  Google Scholar 

  27. J. C. Light, I. P. Hamilton, J. V. Lill, Journal of Chemical Physics, 82, 1400 (1985). https://doi.org/10.1063/1.448462

    Article  ADS  Google Scholar 

  28. C. C. Martson, G. G. Balint-Kurti, Journal of Chemical Physics, 91, 3571 (1989). https://doi.org/10.1063/1.456888

    Article  ADS  MathSciNet  Google Scholar 

  29. D. Neuhasuer, M. Baer, Journal of Chemical Physics, 90, 4351 (1989). https://doi.org/10.1063/1.456646

    Article  ADS  Google Scholar 

  30. V. Kokoouline, O. Dulieu, R. Kosloff, F. Masnou-Seeuws, Journal of Chemical Physics, 110, 9865 (1999). https://doi.org/10.1063/1.478860

    Article  ADS  Google Scholar 

  31. D. Lemoine, Chemical Physics Letters, 320, 492 (2000). https://doi.org/10.1016/S0009-2614(00)00269-4

    Article  ADS  Google Scholar 

  32. K. Willner, O. Dulieu, F. Masnou-Seeuws, Journal of Chemical Physics, 120, 548 (2004). https://doi.org/10.1063/1.1630031

    Article  ADS  Google Scholar 

  33. A. Vibók, G. G. Balint-Kurti, Journal of Physical Chemistry, 96, 8712 (1992). https://doi.org/10.1021/j100201a012

    Article  Google Scholar 

  34. A. Vibók, G. G. Balint-Kurti, Journal of Chemical Physics, 96, 7616 (1992). https://doi.org/10.1063/1.462414

    Article  ADS  Google Scholar 

  35. U. V. Riss, H.-D. Meyer, Journal of Chemical Physics, 105, 1409 (1996). https://doi.org/10.1063/1.472003

    Article  ADS  Google Scholar 

  36. J.-Yuan Ge, J.Z.H. Zhang, Journal of Chemical Physics, 108, 1429 (1998). https://doi.org/10.1063/1.475514

    Article  ADS  Google Scholar 

  37. J. G. Muga, B. Navarro, Chemical Physics Letters, 390, 454 (2004). https://doi.org/10.1016/j.cplett.2004.04.059

    Article  ADS  Google Scholar 

  38. G. J. Halasz, A. Vibók, Chemical Physics Letters, 323, 287 (2000). https://doi.org/10.1016/S0009-2614(00)00487-5

    Article  ADS  Google Scholar 

  39. A. Vibók, G. J. Halasz, Physical Chemistry Chemical Physics, 3, 3048 (2001). https://doi.org/10.1039/B101900G

    Article  Google Scholar 

  40. S. Kallush, R. Kosloff, Chemical Physics Letters, 433, 221 (2006). https://doi.org/10.1016/j.cplett.2006.11.040

    Article  ADS  Google Scholar 

  41. R. E. Wyatt, B. A. Rowland, Journal of Chemical Theory and Computation, 5, 443 (2009). https://doi.org/10.1021/ct800248w

    Article  Google Scholar 

  42. Y.-C. Han, K.-J. Yuan, W.-H. Hu, S.-L. Cong, Journal of Chemical Physics, 130, 044308 (2009). https://doi.org/10.1063/1.3067921

  43. Y.-C. Han, International Journal of Quantum Chemistry, 119, e25858 (2019). https://doi.org/10.1002/qua.25858

  44. E. W. F. Smeets, G. Fuchsel, G.-J. Kroes, Journal of Physical Chemistry C, 123, 23049 (2019). https://doi.org/10.1021/acs.jpcc.9b06539

    Article  Google Scholar 

  45. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, A. Schadle, Communications in Computational Physics, 4(4), 729 (2008). URL: http://global-sci.org/intro/articlejdetaiPcicp/7814.html

    MathSciNet  Google Scholar 

  46. A. Scrinzi, Physical Review A, 81, 053845 (2010). https://doi.org/10.1103/PhysRevA.81.053845

  47. M. Weinmuller, M. Weinmuller, J. Rohland, A. Scrinzi, Journal of Computational Physics, 333, 199 (2017). https://doi.org/10.1016/j.jcp.2016.12.029

    Article  ADS  MathSciNet  Google Scholar 

  48. J. Kaye, L. Greengard, Transparent boundary conditions for the time-dependent Schrodinger equation with a vector potential, 2019. https://arxiv.org/abs/1812.04200

  49. E. Fattal, R. Baer, R. Kosloff, Physical Review E, 53, 1217 (1996). https://doi.org/10.1103/PhysRevE.53.1217

    Article  ADS  Google Scholar 

  50. V. B. Sovkov, J. Ma, In: Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling, ed. by A. Dadvand, K.V. Nagaraja, M. Mirzazadeh. Advances in Computer Science Research (Atlantis Press, Beijing, China, 2016), vol. 41, p. 369 (No. 083). https://doi.org/10.2991/amsm-16.2016.83

  51. K. Levenberg, Quarterly of Applied Mathematics, 2, 164 (1944).

    Article  MathSciNet  Google Scholar 

  52. D. W. Marquard, Journal of the Society for Industrial and Applied Mathematics, 11, 431 (1963). https://doi.org/10.1137/0111030

    Article  MathSciNet  Google Scholar 

  53. G. H. Golub, C. F. van Loan, Matrix Computations (The John Hopkins University Press, Baltimore and London, 1996). https://jhupbooks.press.jhu.edu/content/matrix-computations

  54. C. Lanczos, Journal of Research of the National Bureau of Standards, 45, 255 (1950). https://doi.org/10.6028/jres.045.026

    Article  Google Scholar 

  55. R. B. Lehoucq, G. G. Gray, D.-H. Zhang, J.-C. Light, Computer Physics Communications, 109, 15 (1998).https://doi.org/10.1016/S0010-4655(98)00002-2

  56. V. B. Sovkov, F. Xie, D. Li, S.S. Lukashov, V. V. Baturo, J. Ma, L. Li, AIP Advances, 8, 125322 (2018). https://doi.org/10.1063/1.5055675

  57. S. S. Onishchenko, V. B. Sovkov, F. Xie, D. Li, S. S. Lukashov, V. V. Baturo, J. Wu, J. Ma, L. Li, Journal of Quantitative Spectroscopy and Radiative Transfer, 250, 107037 (2020).https://doi.org/10.1016/j.jqsrt.2020.107037

  58. A. N. Drozdova, A. V. Stolyarov, M. Tamanis, R. Ferber, P. Crozet, A. J. Ross, Physical Review A: Atomic, Molecular, and Optical Physics, 88(2), 022504 (2013). https://doi.org/10.1103/PhysRevA.88.022504

  59. X. Wang, W. Liu, J. Wu, V. B. Sovkov, J. Ma, P. Li, L. Xiao, S. Jia, Journal of Quantitative Spectroscopy and Radiative Transfer, 240, 106678 (2020). https://doi.org/10.1016/j.jqsrt.2019.106678

  60. P. T. Arndt, V. B. Sovkov, J. Ma, X. Pan, D. S. Beecher, J. Y. Tsai, Y. Guan, A. M. Lyyra, E. H. Ahmed, Physical Review A: Atomic, Molecular, and Optical Physics, 99, 052511 (2019). https://doi.org/10.1103/PhysRevA.99.052511

  61. P. T Arndt, V. B. Sovkov, J. Ma, X. Pan, D. S. Beecher, J. Y. Tsai, Y. Guan, A. M. Lyyra, E. H. Ahmed, Journal of Chemical Physics, 149, 224303 (2018). https://doi.org/10.1063/1.5058282

  62. G. Feng, F. Xie, V. B. Sovkov, J. Ma, L. Xiao, S. Jia, Journal of the Physical Society of Japan, 87, 024303 (2018). https://doi.org/10.7566/JPSJ.87.024303

  63. V. B. Sovkov, F. Xie, A. M. Lyyra, E. H. Ahmed, J. Ma, S. Jia, Journal of Chemical Physics, 147, 104301 (2017). https://doi.org/10.1063/1.5001481

  64. V. B. Sovkov, F. Xie, A. M. Lyyra, E. H. Ahmed, J. Ma, S. Jia. Journal of Chemical Physics, 149, 239901 (2018). https://doi.org/10.1063/1.5083024

  65. W. Liu, J. Wu, J. Ma, P. Li, V. B. Sovkov, L. Xiao, S. Jia, Physical Review A: Atomic, Molecular, and Optical Physics, 94, 032518 (2016). https://doi.org/10.1103/PhysRevA.94.032518

  66. J. Yang, Y. Guan, W. Zhao, Z. Zhou, X. Han, J. Ma, V. B. Sovkov, V. S. Ivanov, E. H. Ahmed, A. M. Lyyra, X. Dai, Journal of Chemical Physics, 144, 024308 (2016). https://doi.org/10.1063/1.4939524

  67. P. G. Volkov, S. I. Korobeinikov, V. I. Nikolaev, V. B. Sovkov, Journal of Analytical Chemistry, 71(5), 471 (2016). https://doi.org/10.1134/S1061934816030151

    Article  Google Scholar 

  68. W. Liu, R. Xu, J. Wu, J. Yang, S. S. Lukashov, V. B. Sovkov, X. Dai, J. Ma, L. Xiao, S. Jia, Journal of Chemical Physics, 143, 124307 (2015). https://doi.org/10.1063/1.4931646

  69. V. B. Sovkov, V. S. Ivanov, Journal of Chemical Physics, 140, 134307 (2014). https://doi.org/10.1063/1.4869981

  70. V. B. Sovkov, V. S. Ivanov, Vestnik St. Petersburg University. Ser. 4, 1(59), 473 (2014). http://elibrary.ru/item.asp?id=22697447

  71. J. Ma, W. Liu, J. Yang, J. Wu, W. Sun, V. S. Ivanov, A. S. Skublov, V. B. Sovkov, X. Dai, S. Jia, Journal of Chemical Physics, 141, 244310 (2014). https://doi.org/10.1063/1.4904265

  72. V. B. Sovkov, D. Li, V. S. Ivanov, A. S. Skublov, F. Xie, Li Li, S. Magnier, Chemical Physics Letters, 557, 66 (2013). https://doi.org/10.1016/j.cplett.2012.12.030

    Article  ADS  Google Scholar 

  73. V. B. Sovkov, V. S. Ivanov, K. V. Minaev, M. S. Aleksandrov, Optics and Spectroscopy, 114(2), 167 (2013). https://doi.org/10.1134/S0030400X13020288

    Article  ADS  Google Scholar 

  74. Y. Guan, X. Han, J. Yang, Z. Zhou, X. Dai, E. H. Ah-med, A. M. Lyyra, S. Magnier, V. S. Ivanov, A. S. Sku-blov, V. B. Sovkov, Journal of Chemical Physics, 139, 144303 (2013). https://doi.org/10.1063/1.4823496

  75. F. Xie, Li Li, D. Li, V. B. Sovkov, K. V. Minaev, V. S. Ivanov, A. M. Lyyra, S. Magnier, Journal of Chemical Physics, 135, 024303 (2011). https://doi.org/10.1063/1.3606397

  76. F. Xie, K. V. Minaev, V. B. Sovkov, V. S. Ivanov, D. Li, Li Li, Chemical Physics Letters, 493, 238 (2010). https://doi.org/10.1016/j.cplett.2010.05.060

    Article  ADS  Google Scholar 

  77. F. Xie, V. B. Sovkov, A. M. Lyyra, D. Li, S. Ingram, J. Bai, V. S. Ivanov, S. Magnier, Li Li, Journal of Chemical Physics, 130, 051102 (2009). https://doi.org/10.1063/1.3075580

  78. Bediha Beser, V. B. Sovkov, J. Bai, E. H. Ahmed, C. C. Tsai, F. Xie, Li Li, V. S. Ivanov, A. M. Lyyra, Journal of Chemical Physics, 131, 094505 (2009). https://doi.org/10.1063/1.3194290

  79. F. Xie, D. Li, L. Tyree, L. Li, V. B. Sovkov, V. S. Ivanov, S. Magnier, A. M. Lyyra, Journal of Chemical Physics, 128, 204313 (2008). https://doi.org/10.1063/1.2920191

  80. D. Li, F. Xie, Li Li, V. B. Sovkov, V. S. Ivanov, E. Ah-med, A. M. Lyyra, J. Huennekens, S. Magnier, Journal of Chemical Physics, 126, 194314 (2007). https://doi.org/10.1063/1.2730804

  81. D. Li, F. Xie, Y. Chu, Li Li, S. Magnier, V. B. Sovkov, V. S. Ivanov, Chemical Physics, 332, 10 (2007). https://doi.org/10.1016/j.chemphys.2006.11.018

    Article  ADS  Google Scholar 

  82. V. B. Sovkov, V. S. Ivanov, D. Li, F. Xie,Li Li, Optics and Spectroscopy, 103(5), 723 (2007). https://doi.org/10.1134/S0030400X07110069

    Article  ADS  Google Scholar 

  83. F. Xie, D. Li, Y. Chu, Li Li, S. Magnier, V. B. Sovkov, V. S. Ivanov, Journal of Physical Chemistry A, 110, 11260 (2006). https://doi.org/10.1021/jp063266m

    Article  ADS  Google Scholar 

  84. V. B. Sovkov, V. S. Ivanov, Li Li, Z. Chen, S. Magnier, Journal of Molecular Spectroscopy, 236, 35 (2006).https://doi.org/10.1016/j.jms.2005.12.005

  85. E. Ahmed, A. M. Lyyra, F. Xie, D. Li, Y. Chu, Li Li, V. S. Ivanov, V. B. Sovkov, S. Magnier, Journal of Molecular Spectroscopy, 234, 41 (2005).https://doi.org/10.1016/j.jms.2005.08.001

  86. E. Ahmed, A. M. Lyyra, Li Li, V. S. Ivanov, V. B. Sov-kov, S. Magnier, Journal of Molecular Spectroscopy, 229, 122 (2005). https://doi.org/10.1016/j.jms.2004.08.021

    Article  ADS  Google Scholar 

  87. P. Yi, X. Dai, J. Li, Y. Liu, Li Li, V. B. Sovkov, V. S. Ivanov, Journal of Molecular Spectroscopy, 225, 33 (2004). https://doi.org/10.1016/j.jms.2004.02.005

    Article  ADS  Google Scholar 

  88. V. S. Ivanov, V. B. Sovkov, Li Li, Journal of Chemical Physics, 118, 8242 (2003). https://doi.org/10.1063/1.1565107

    Article  ADS  Google Scholar 

  89. V. S. Ivanov, V. B. Sovkov, N. Gallice, Li Li, Y. Liu, A.M. Lyyra, S. Magnier, Journal of Molecular Spectroscopy, 209, 116 (2001). https://doi.org/10.1006/jmsp.2001.8413

    Article  ADS  Google Scholar 

  90. V. S. Ivanov, V. B. Sovkov, Li Li, A. M. Lyyra, T.‑J. Whang, S. Magnier, Journal of Chemical Physics, 114, 6077 (2001). https://doi.org/10.1063/1.1355979

    Article  ADS  Google Scholar 

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Funding

This research was funded by National Key R&D Program of China grant number 2017YFA0304203, the National Natural Science Foundation of China grant numbers 61722507, 61675121, 111 project grant number D18001, the Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi (OIT), the Applied Basic Research Project of Shanxi Province grant number 201901D211191, the Shanxi 1331 KSC, and collaborative grant by the Russian Foundation for Basic Research and NSF of China grant number 62011530047 (in NSF) and 20-53-53025 (in RFBR).

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Authors and Affiliations

  1. St. Petersburg State University, 199034, St. Petersburg, Russia

    V. B. Sovkov

  2. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, 030006, Taiyuan, China

    V. B. Sovkov, Jizhou Wu & Jie Ma

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  1. V. B. Sovkov
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  2. Jizhou Wu
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Sovkov, V.B., Wu, J. & Ma, J. Cosine-Type Absorbing Optical Potential for the Modeling of Quantum Dynamics with the Fourier Grid and Optimizer Packages. Opt. Spectrosc. 131, 907–919 (2023). https://doi.org/10.1134/S0030400X23070160

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