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Haar Wavelet Spectrum of an Exponentially Pulsed Driven Qubit
H. A. Batarfi and S. S. Hassan

The transient Haar wavelet spectrum of a non-dissipative qubit (2-level atom) driven by an exponentially decaying resonant pulse is calculated analytically in terms of the incomplete Γ-Function for initially ground state atom. The shift parameter (k) of the Haar mother wavelet function has a pronouncing effect on the spectrum. For k = 0, the dip of the ‘hole burning’ structure in the central part of the spectrum depends on the ratio Γ’ (the pulse time scale to the detector’s lifetime). The small ringing structure in the spectrum is independent of this ratio. For non-zero shift (k ≠ 0) and for increasing pulse strength, the central dip structure washes away where the spectrum exhibits pronounced multiple side peaks. In general, the increase of the central dip structure is a reflection of the bipolar structure of the Haar mother wavelet window function.

Effect of the dilation parameter ( j ) is to deepen the central ‘hole burning’, almost independent of the system parameters Γ’, k and pulse strength.

Keywords: Haar Wavelet, exponential pulse and scattered radiation.

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