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Dynamics of Particle in a Box in Time Varying Potential Due to Chirped Laser Pulse
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Journal of Modern Physics·Volume 01 (2010)·Pages 372–378·Published 29 December 2010·DOI10.4236/jmp.2010.16053
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Abstract
We describe a computational method for simulating the time dependent quantum mechanical system inter-acting with external field. In this method the Schrödinger equation is solved by expanding the wave function in the basis set of unperturbed Hamiltonian. The expansion yields a set of coupled first order differential equation. For expansion coefficients, the coupled channel method is applied to a particle in a box interacting with external field in the form of chirped laser pulse. The pulse shape is taken as Gaussian. We study the ef-fect of different pulse parameters i.e. chirp rate, intensity, center frequency, box length and laser duration on the dynamics of the particle. Many interesting results are obtained and explained.
KeywordsTransition ProbabilityChirp RateBox Length
- D. Bouwmeester, A. K. Ekert and A. Zeilinger, “The Physics of Quantum Information,” Springer Berlin, NY, 2000.
- D. J. Griffiths, “Introduction to Quantum Mechanics,” 2nd Edition, Pearson Prentice Hall, Upper Saddle River, New Jersey, 2005.
- J. Wang and J. D. Champagne, “Simulation of Quantum Systems with Coupled Channel Method,” American Jour-nal of Physics, Vol. 76, No. 4-5, 2008, pp. 493-497.
- W. Koechner, “Solid State Laser Engineering,” 6th Edi-tion, Springer, New York, 2006.
- H. Kawashima, M. M. Wefers and K. A. Nelson, “Fem-tosecond Pulse Shaping, Multiple-Pulse Spectroscopy and Optical Control,” Annual Review of Physical Chem-istry, Vol. 46, October 1995, pp. 627-656.
- P. Krehlik, “Characterization of Semiconductor Laser Frequency Chirp Based on Signal Distortion in Disper-sive Optical Fiber,” Opto-Electronics Review, Vol. 14, No. 2, June 2006, pp. 119-124.
- S. Ruhman and R. Kosloff, “Application of Chirped Ul-trashort Pulses for Generating Large-Amplitude Ground- State Vibrational Coherence: A Computer Simulation,” Journal of the Optical Society of America B, Vol. 7, No. 8, August 1990, pp. 1748-1751.
- J. S. Cao, C. J. Bardeen and K. R. Wilson, “Molecular _ pulses: Population Inversion with Positively Chirped Short Pulses,” Journal of Chemical Physics, Vol. 113, No. 5, August 2000, pp. 1898-1909.
- I. F. Barna and P. Dombi, “Coherent Control for the Spherical Symmetric Box Potential in Short and Intensive XUV Laser Fields,” Central European Journal of Physics, Vol. 6, No. 2, June 2008, pp. 205-210.
- J. P. Hansen and K. Taulbjerg, “Coupled-Channel Calcu-lations of Partial Capture Cross Sections in Multiply Charged Ion Collisions with Hydrogen,” Physical Review A, Vol. 40, No. 7, October 1989, pp. 4082-4084.
- A. P. Hickman, “Coupled-Channel Calculations of Ex-cited-Atom Collisions,” International Reviews in Physi-cal Chemistry, Vol. 16, No. 2, 1997, pp. 177-199.
- M.H. Mitleman “Introduction to the Theory of Laser Atom Interaction,” Plenum Press, New York, 1982.