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Fourier and Haar Wavelet Spectra of a Driven Harmonic Oscillator without RotatingWave Approximation
S. S. Hassan and R. A. Alharbey

Both Fourier transform (FT) and Haar wavelet (WT) spectra of the fluorescent radiation due to coupling of a dissipative single quantised harmonic oscillator (HO) with a rectangular laser pulse are calculated exactly outside the rotating wave approximation (RWA). Comparison of both spectra, within and outside RWA, shows that at exact resonance (Δ’ = 0) and irrespective of the initial HO state, the FT spectrum is a single Lorentzian while the Haar WT spectrum has a symmetric dip structure. In the off-resonance case (Δ’ ≠ 0), within the RWA, the FT spectrum has additional peak of location depends on the initial state of HO, while the Haar WT spectrum becomes asymmetric. Outside RWA, both spectrum have additional asymmetric peak at the normalised detector’s off-set frequency D’ = Δ’ − ω1 where ω1 = 2ωL/Γ, is essentially the ratio of the laser frequency to the detector’s width.

Keywords: Quantised harmonic oscillator, rotating wave approximation, Fourier and wavelet spectra.

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