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Transient Spectrum of Pulsed-driven Harmonic Oscillator: Damping and Pulse Shape Effects
S. S. Hassan, R. A. Alharbey and T. Jarad

Exact analytical and computational results are presented for the transient spectrum of the dissipative harmonic oscillator (HO) driven by different shapes of the laser pulses (rectangular, exponential, sin2-pulses). The spectrum function is composed of three terms. One term of Lorentzian shape of width Γ1 (the photon detector’s width) and of weight propotional to the initial value of the HO photon number. The second term is proportional to the pulse strength, which comprises the effect of the HO damping parameter (γ) and the pulse shape parameters. The third term representing the interference between the non-zero average amplitude of the initial state of the HO with the exciting pulse. Main specific features are: (i) The ’hole burning’ structure in the spectrum or asymmetric two-peak structure occurring in absence of damping (γ’ = 0) becomes a dominant single peak for larger γ’ > 1, with additional weak ringing (depending on the pulse shape and the initial state of the HO). (ii) For the sequential pulse shape, sin2(), with large number of pulses (n = 10) the spectrum is of very weak weight with asymmetric side structure and ringing for γ’ = 0, which becomes relatively prominent due to damping effect (γ ≠ 0).

Keywords: Quantised harmonic oscillator, transient spectrum, pulsed fields.

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