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Driven Quantized Harmonic Oscillator by Chirped Gaussian Pulse

Hasnaa Saeed Gasim

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

The interacting model of a single quantised harmonic oscillator (HO) with a chirped Gaussian (laser) pulse is studied analytically and computationally. Specifically, exact formulae for the averaged photon number (related to the HO energy) and the transient scattered radiation spectrum are derived. The chirp and detuning parameters together with the initial state of the HO have essential roles for the oscillatory behaviour of the average photon number and for the asymmetry and additional oscillatory peaks in the scattered spectrum.

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The interacting model of a single quantised harmonic oscillator (HO) with a chirped Gaussian (laser) pulse is studied analytically and computationally. Specifically, exact formulae for the averaged photon number (related to the HO energy) and the transient scattered radiation spectrum are derived. The chirp and detuning parameters together with the initial state of the HO have essential roles for the oscillatory behaviour of the average photon number and for the asymmetry and additional oscillatory peaks in the scattered spectrum.
Exact analytical operator solutions of the interacting model of a single quantized (non-dissipative) harmonic oscillator (HO) with a train of n-chirped Gaussian pulses are derived in terms of the error function of complex argument.Explicit expressions are then calculated and examined computationally for the average photon number of the HO and the emitted spectrum.The chirp parameter (c) induces non-sinusoidal oscillations that lead to: (i) 'step-like plateau' in the dynamics of the average photon number with both n, τ R (repetition time) large, and, (ii) a 'hole burning' profile and asymmetrical ringing in the spectrum, depends on the initial state of the HO.
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).
Abstract We investigate the transient and stationary physical spectra of scattered radiation from a single quantized harmonic oscillator (HO) of frequency ω o , which is resonantly driven by an intense driving field of real (amplitude) strength Ω ∼ ω o and damped in a Markovian broadband radiation reservoir. The influence of such an intense field combined with manipulative spectral reservoir parameters results in field strength enhancement and a phase shift gain: Ω → Ω 1 + γ ′ 2 ( ω o ) e i γ ′ ( ω o ) , where γ ′ ( ω o ) = ( d γ ( ω ) / d ω ) ω = ω o is the spectral rate of variation of the damping constant at resonance. This in turn leads to induced coherence in the average amplitude of the HO. Two cases of spectral distribution of the radiation reservoir are considered: the Ohmic power law and the Lorentz-Drude law. The spectral components of the scattered radiation in the transient and stationary regimes are identified analytically and computationally, and comparison is made with the non-intense driving field case (Ω ≪ ω o ). The stationary spectrum is a symmetric Lorentzian of weight dependent on the reservoir spectral parameters and of enhanced value compared with the non-intense field case. The transient spectrum is composed of different lineshapes (Lorentzian, narrowed-Lorentzian, and dispersive) of oscillatory decaying weights. Interference of these transient-spectral components is initiated and caused by both types of non-zero coherence, namely the initial coherence of the HO and the induced coherence in the intense field case, and induces asymmetric side oscillations of amplitude dependent on the reservoir spectral parameters. The present results for the fluorescent spectra of intensely-driven HO and its dependence on the environmental radiation reservoir spectral structure are adequately fitted for intensely driven collective Rydberg atomic systems, as a ‘single site’ atomic sample, O(μm), and behaves as a single quantized HO.
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.
We present a theoretical study of the excitation of a charged quantum linear oscillator by chirped laser pulse with the use of probability of the process throughout the pulse action. We focus on the case of the excitation of the oscillator from the ground state without relaxation. Calculations were made for an arbitrary value of the electric field strength by utilizing the exact expression for the excitation probability. The dependence of the excitation probability on the pulse parameters was analyzed both numerically and by using analytical formulas.
Abstract The dependence of energy transferred to a damped harmonic oscillator by a pulse of periodic force on pulse duration, carrier frequency, and shape of the pulse envelope is investugated. The cases of pulses with an exponential and Gaussian shape of the envelope are analyzed. Analytical expressions describing the process are obtained. It is established that the dependence of energy transferred to the oscillator on pulse duration in the case of an exponential pulse can have an inflection point, while extrema appear in the discussed dependence at sufficiently large offset of the pulse carrier frequency from the oscillator natural frequency in the case of a Gaussian pulse. It is demonstrated that the number of quanta and the amplitude of the average value of the coordinate operator upon excitation of a quantum oscillator are determined by the same dependences on the driving-pulse parameters as in the case of the classical oscillator.