Haar Wavelet Spectrum and Statistics of a Pulsed-Driven Harmonic Oscillator

Abstract

In this thesis, the Haar wavelet spectrum and statistics of a pulsed-driven har- monic oscillator (HO) are studied. The Heisenberg model equations of a single HO driven by a laser pulse of arbitrary shape are solved. The mean photon number is calculated for various shapes of laser pulses (rectangular, triangular, symmetric square and anti symmetric square pulses) and for different initial states of the HO in (vacuum, number and coherent states).

Sub-Poissonian photon statistics of the emitted radiation by a laser pulsed driven non-dissipative HO is investigated analytically through Mandel’s QM pa- rameter. Conditions for sub-Poissonian behaviour are derived for different initial states of the HO (namely, the number state, single mode squeezed vacuum state, single mode squeezed coherent state and single mode squeezed thermal state) and for arbitrary pulse shape. Computational results are presented for various pulse shapes (namely, the rectangular, triangular, symmetric square and anti-symmetric square pulses). It is also shown that the driven HO with initial coherent, number and squeezed vacuum states evolves in time to a corresponding state, respectively, but with the HO operators and the vacuum state are displaced depending on the input pulse shape.

The transient scattered spectrum with Haar wavelet window function is de- rived analytically for a single quantized HO interacting with the same laser pulses mentioned above. Effects of the window function parameters (delation and shift parameter) are examined if the HO was initially in vacuum, number and coherent states.