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Optics and Spectroscopy

Peculiarities of Excitation of a Harmonic Oscillator for Various Driving-Pulse Parameters

Valery Alexandrovich Astapenko, Yu. A. Krotov, S. V. Sakhno

Published Jan 1, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s0030400x24700322

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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.
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Abstract This article proposes a model that accounts for damping of a quantum oscillator (QO) during pulsed excitation. Our model is based on the Schwinger formula, which calculates oscillator’s excitation probability through the energy of an associated classical damped oscillator. We utilize this model to describe the influence of damping on temporal and spectral dependences of QO excitation, induced by electromagnetic pulses with exponential and double exponential envelopes. The oscillator excitation is analyzed in terms of transition probability between stationary states after pulse termination. Here, we present an analytical description of these dependences, along with numerical results. Specifically, we derive analytical expressions that depict the saturation effect during pulsed excitation, taking into account the damping of a QO. The evolution of the temporal dependence of the excitation probability with a change in the damping constant is numerically traced. We demonstrate that the number of maxima in this dependence is determined by the values of pulse parameters and the damping constant.
Abstract The dynamics of time evolution of quantum oscillator excitation by electromagnetic pulses is investigated theoretically for an arbitrary field amplitude in a pulse. We consider a harmonic oscillator without damping and excitation between stationary states. The general formula for the excitation of quantum states as a function of time is derived in terms of instantaneous energy of an associated classical oscillator in the field of an electromagnetic pulse. The derived expression is used in detailed analysis of the time dependence of the quantum oscillator excitation probability beyond the range of perturbation theory for various pulse parameters including total excitation from the ground state, excitation from excited states, and excitation spectra.
The behaviour of an oscillator may be controlled by the frequency time-dependence. For example, one can kick the oscillator frequency by short pulses and this kicking produces an excitation of the parametric oscillator. The amplitude of the oscillator vibrations and its energy may increase due to the external influence expressed as the frequency time-dependence. Also the statistical properties of the oscillator state may be changed due to the action of external forces. The aim of the talk is to discuss the exact solution of the time-dependent Schrodinger equation for a damped quantum oscillator subject to a periodical frequency delta-kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola-Kanai model [1], [2].
The quantum harmonic oscillator is a model system that is actively used in many applications of quantum and nonlinear physics, molecular chemistry and biophysics. In this paper, a formula is obtained for the probability amplitude of the transition of a quantum harmonic oscillator from an oscillatory state with the numberν\nuνto a state with the numberν+n\nu+nν+n, which is affected by an external force depending on time using a method based on the Magnus and Baker-Campbell-Hausdorff decomposition. A formula is obtained for the special case of interaction of a quantum harmonic oscillator with an ultrashort pulse field. As an example, graphs of the probabilities of the oscillator transition from the first oscillatory state to the second and third, the average energy received and the rms fluctuation of the energy received for different values of the ratio of the carrier frequency of the pulse and the frequency of the oscillator are constructed. Conclusions are drawn about the correctness of using the concept of average energy in relation to this problem.
The paper is devoted to the theoretical investigation of time dependences of quantum oscillator excitation by electromagnetic pulses for arbitrary values of field amplitude in the pulse. We consider the harmonic oscillator without relaxation and excitation between stationary states. The general formula for excitation of quantum states as function of time is derived in terms of instant energy of associated classical oscillator in the field of electromagnetic pulse. Thus, it is established that time dependence of quantum oscillator excitation is completely determined by the energy of the associated classical oscillator at given moment of time. Using derived expression time dependence of quantum oscillator excitation is investigated in details including total excitation from ground state, excitation from excited states, total excitation probability and corresponding excitation spectra.