Abstract
We investigate the nature of spectral lines of emitted radiation due to of a non-dissipative single-mode quantized harmonic oscillator (HO) with train of n-chirped Gaussian pulses. Specifically, we analyze the transient emitted spectrum through two window wavelet functions of the radiation detector, namely the Haar wavelet and Morlet wavelet. Computational display of the exact analytical results shows how the driving pulse parameters (strength and number of pulses, chirping, repetition time) act as control knobs to shape the detected emitted spectrum as desired.
Highlights
For zero shift k o = 0 and no chirp (C = 0), the bi-polar nature of the Haar wavelet (HW) wavelet function reflects itself in the spectrum as two symmetric peaks around D H = 0 with fading symmetric smaller peaks for one pulse (n = 1)case-Figure 1a
The interplay of the detuning parameter (∆o 6= 0) at large shift parameter k o = 10 is shown in Figure 1b, where for one pulse (n = 1), the spectrum is asymmetric
For non-zero chirp parameter (C 6= 0), ∆o, k o 6= 0, the asymmetry is more pronounced for c ≷ 0, with very dense oscillatory envelopes for the main peak shifted for D H > 0 with C > 0 (Figure 2a) or the main peak around D H ∼ 0 with C < 0 (Figure 2b)
Summary
Time-localized structure of different frequency components in the detected signal can be dealt with through adjustment of the time width of the detecting “mother window function” This is known as WT analysis, in which wavelets of high frequencies are narrower and vice versa [9]. Transient wavelet spectral analysis of the emitted radiation of a single 2-level atom driven by a rectangular pulse has been given in the cases of Morlet and Mexican hat [10] and Haar [11] wavelet window functions. We expand our results in [5] for the model of a single non-dissipative HO driven by a field that has the shape of a train of n-Chirped Gaussian pulses and calculate the wavelet transform spectra with two different wavelet window functions, namely Haar wavelet (HW) and Morlet wavelet (MW) windows.
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