Haar wavelet spectrum of sin2-pulsed driven qubit

Abstract

The transient scattered spectrum with Haar wavelet window function is calculated analytically for a resonant pulsed driven qubit (taken as spin-12 2-level atom). The pulse shape is taken as the sequential laser sin2-pulse. Effect of the window function dilation and shift parameters are associated with the pulse strength and the initial atomic state. In particular, for strong pulse strength and increasing shift parameter: (i) the 3-peak structure turns into a central broader peak with ‘hole burning’ at its centre, only, for the case of initial ground state, and not with the initial excited state, (ii) for the case of initial atomic coherent state, the 3-peak structure has an oscillatory envelope due to the non-zero initial coherent dipole field.