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Haar wavelet spectrum of a pulsed-driven qubit

Saad S. M. Hassan, M A Al-Saegh, Ali Mohamed, Hanan Ali Batarfi

Published Jan 1, 2010• 5 citations
OpenAlex

Abstract

The transient fluorescent spectrum of a non-dissipative single 2-level atom driven by a resonant rectangular pulse is investigated analytically and computationally with the Haar wavelet window function. The shift parameter (k) of the mother wavelet function induces periodic effect. For weak pulse, a central dip structure -characteristic of the window transmission lines- occurs in the spectrum. With initial atomic coherent state and for strong pulse and large (k), interference of the strong Rabi oscillations induces asymmetrical dense ’ringing’ around the two Rabi side bands of the spectrum.

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Journal of Nonlinear Optical Physics & Materials•Dec 1, 2014•2 citations
The transient fluorescent spectrum of a non-dissipative single 2-level atom
driven by a resonant rectangular pulse is investigated analytically and
computationally with the Haar wavelet window function. The shift parameter
(k) of the mother wavelet function induces periodic effect. For weak
pulse, a central dip structure -characteristic of the window transmission
lines- occurs in the spectrum. With initial atomic coherent state and for
strong pulse and large (k), interference of the strong Rabi oscillations
induces asymmetrical dense ’ringing’ around the two Rabi side bands of
the spectrum.
The model of a non-dissipative qubit (taken as a single 2-level atom) coupled to a short resonant laser pulse of sin 2 -shape is investigated through the transient fluorescent spectrum.Exact analytical operator solutions for the model Heisenberg equations are utilised to calculate the spectrum in terms of Bessel functions.Asymmetry and ringing in the 3-peak spectrum with strong Rabi frequency are pronounced with initial atomic coherent state as compared with the ground state case.This is due to interference of the sequential-pulse structure of the sin 2 -pulse with the initial dispersive coherence.For moderate Rabi frequency, ringing disappears with ' hole burning' dip shown in the dominant central Lorentzian peak.
The transient spectrum of scattered radiation from a qubit (represented by a spin-1/2 system or a two-level atom) driven by a resonant rectangular pulse is calculated analytically without adopting the rotating wave approximation (RWA). Operator solutions for the non-autonomous model of Heisenberg equations of motion are obtained within an iterative approach to O (λ) where λ is the system parameter representing the ratio of the Rabi frequency of the driving pulse to its circular frequency. The spectrum in the case of an initial ground-state atom and for increasing pulse area shows asymmetric profiles outside the RWA compared with a symmetric profile within the RWA. For the qubit this asymmetry is much pronounced with splitting of side peaks, which develops to ‘ringing’ for larger pulse area (within and outside the RWA). As shown analytically, this is attributed to the strong Rabi oscillations and interference between various amplitude spectral components initiated by the finite atomic coherent dispersion.
The simplest non-dissipative 2-level atom system, a qubit, excited by a train of resonant n-Gaussian laser pulses is investigated. This concerns examination of the averaged atomic variables, the intensity-intensity correlation function, and the transient fluorescent radiation. Analytical formulas for the above expressions are obtained. Computational results show that the transient spectra with the initial ground and coherent atomic states exhibit asymmetric Mollow structure with dip structure, dense oscillation, and narrowing, and depends on the pulse number (n), the repetition time (τR), and the observed time.
Exact analytical results are derived for the coupled system of nondissipative single mode quantized harmonic oscillator (HO) and arbitrary pulse shape. Specifically, for a sin2-pulse shape, the transient fluorescent spectrum is obtained in the general case of initial coherent state |α〉 of the HO. The dominant central Lorentzian is surrounded by weak oscillations due to the larger number of sequential pulses which get amplified asymmetrically in the nonresonant case as a result of balancing and interference processes between the initial excitation (|α2|) and the strength of the exciting pulse. Further pronounced oscillations is noticed with "hole burning" structure in the central peak due to nonzero phase of the initial amplitude (α).