DRIVEN HARMONIC OSCILLATOR
BY TRAIN OF CHIRPED GAUSSIAN PULSES
S.S. Hassan1,2, R.A. Alharbey3,
T. Jarad2, S. Almaatooq1
1 University of Bahrain
College of Sci., Dept. of Mathematics
P.O. Box 32038, Kingdom of BAHRAIN
2Dept. of Computing and Mathematics
Manchester Metropolitan University
Manchester M1 5GD, UK
3King Abdulzziz University
Fac. of Sci., Mathematics Dept.
P.O. Box 42696, Jeddah 21551
Kingdom of SAUDI ARABIA

Abstract

Exact analytical operator solutions of the interacting model of a single quantized (non-dissipative) harmonic oscillator (HO) with a train of $n$-chirped Gaussian pulses are derived in terms of the error function of complex argument. Explicit expressions are then calculated and examined computationally for the average photon number of the HO and the emitted spectrum. The chirp parameter $(c)$ induces non-sinusoidal oscillations that lead to: (i) 'step-like plateau' in the dynamics of the average photon number with both $n,\tau_R$ (repetition time) large, and, (ii) a 'hole burning' profile and asymmetrical ringing in the spectrum, depends on the initial state of the HO.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 1
Year: 2020

DOI: 10.12732/ijam.v33i1.6

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References

  1. [1] J.C. Garrison and R.Y. Chiao, Quantum Optics, Oxford University Press, New York (2008).
  2. [2] G.S. Agarwal, Quantum Optics, Cambridge University Press, Cambridge (2013).
  3. [3] M.O. Scully, and M.S. Zubairy, Quantum Optics, Cambridge University Press, Cambridge, UK (1997).
  4. [4] D. Felinto, C.A.C. Bosco, L.H. Acioli, S.S Vianna, Coherent accumulation in two-level atoms excited by a train of ultrashort pulses, Optics Communications, 215 (2003), 69-73.
  5. [5] Y.B. Band, Light and Matter, J. Wiley, UK (2006).
  6. [6] Y.A. Sharaby A. Joshi and S.S. Hassan, Coherent population transfer in Vtype atomic system, Journal of Nonlinear Optical Physics and Materials, 22 (2013), 1450044-1450059.
  7. [7] W.H. Steeb and Y. Hardy, Problems and Solutions in Quantum Computing and Quantum Information, 2nd Ed., World Sci. Publ., Singapore (2006).
  8. [8] V. Vedral, Introduction to Quantum Information Science, Oxford Univ.Press, Oxford (2008).
  9. [9] S.S. Hassan, G.P. Hildred, R.R. Puri and R.K. Bullough, Incoherently driven Dicke model, S, J. Phys. B, 15 (1982), 2635-2655.
  10. [10] R.K. Bullough, R.R. Puri and S.S. Hassan, Some remarks on the organisation of living matter and its thermal disorganisation, In: Molecular and Biological Physics of Living Systems (Ed. R.K. Mishra), Kluwer Acad. Publ, Netherlands (1990), 1-18.
  11. [11] M.R. Wahiddin, S.S. Hassan, and R.K. Bullough, Cooperative atomic behaviour and oscillator formation in a squeezed vacuum, Journal of Modern Optics, 42 (1995), 171-189.
  12. [12] H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Yi Chang and H. Yamaguchi, Coherent phonon manipulation in coupled mechanical resonators, Nature Physics, 9 (2013), 480-484.
  13. [13] P. Snyder, A. Joshi, J.D. Serna, Modeling a nanocantilever-based biosensor using a stochastically perturbed harmonic oscillator, International Journal of Nanoscience, 13 (2014), 145001-145009.
  14. [14] A. Joshi and S.S. Hassan, Resonance fluorescence spectra of a two-level atom and of a harmonic oscillator with multimode rectangular laser pulses, J. Phys. B: At. Mol. Opt. Phys., 35 (2002), 1985-2003.
  15. [15] S.S. Hassan, R.A. Alharbey and H. Al-Zaki, Transient spectrum of sin2 pulsed driven harmonic oscillator, J. Nonlinear Optical Phys. and Materials, 23 (2014), 1450052-1450066.
  16. [16] S.S. Hassan, R.A. Alharbey and G. Matar, Haar wavelet Spectrum of sin2 pulsed driven harmonic oscillator, Nonlinear Optics and Quantum Optics, 48 (2016), 29-39.
  17. [17] S.S. Hassan, R.A. Alharbey and T. Jarad, Transient spectrum of pulseddriven harmonic oscillator: damping and pulse shape effects, Nonlinear Optics, Quantum Optics: Concepts in Modern Optics, 48 (2018), 277-288.
  18. [18] P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford Univ. Press, Oxford, 4th Ed. (1981).
  19. [19] H. Tang, T. Nakajima, Effects of the pulse area and pulse number on the population dynamics of atoms interacting with a train of ultrashort pulses, Optics Communications, 281 (2008), 4671-4675.
  20. [20] N.N. Lebedev, Special Functions and Their Application, Dover, New York (1972).
  21. [21] S.S. Hassan, A. Joshi, O.M. Frege and W. Emam, Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation, Annals of Phys., 322 (2007), 2007-2020.
  22. [22] T. Jarad, M.R. Qader and S.S. Hassan, Harmonic oscillator with Offresonant squeezed reservoir, International Journal of Applied Mathematics, 23 (2010), 1061-1067.
  23. [23] S.S. Hassan and R.A. Alharbey, Fourier and Haar wavelet spectra of a driven harmonic oscillator without rotating wave approximation, Nonlinear Optics and Quantum Optics, 50 (2019), 315-325.