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Processos estocásticos na interação da luz com a matéria

Elizabeth Agudelo Ospina

Published Aug 19, 2009• 1 citation
OpenAlex

Abstract

We study and characterize the dynamics of population inversion in the Jaynes-Cummings model. Initially we analyze the less studied case of stochastic phase fluctuations in the atomfield coupling coefficient where the fluctuations are modelled by a random phase telegraph process. We have obtained an equation for the density operator and for the population inversion averaged over the distribution of fluctuations. We present analytical expressions for non-pertuvative quantum effects such as revivals in the inversion for an initial coherent state of the field that was calculated using the Poisson summation and the steepest descent method. The expression found for each revival allow us to estimate their time of occurrence, the oscillation frequency, the width and the time intervals between two consecutive revivals. The same analysis is performed for an ideal atom-field interacting system and for the dissipative one. In the end, we compare the effects on the population inversion due to different processes. We pay particular attention to how quantum effects disappear with the decrease of time intervals between jumps in the atom-field coupling parameter or the increase of the dissipation rate for the field, and the result seems to be completely classical. We show that the details of obtaining the classical limit can be very different for each different process

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We study and characterize the dynamics of population inversion in the Jaynes-Cummings model. Initially we analyze the less studied case of stochastic phase fluctuations in the atomfield coupling coefficient where the fluctuations are modelled by a random phase telegraph process. We have obtained an equation for the density operator and for the population inversion averaged over the distribution of fluctuations. We present analytical expressions for non-pertuvative quantum effects such as revivals in the inversion for an initial coherent state of the field that was calculated using the Poisson summation and the steepest descent method. The expression found for each revival allow us to estimate their time of occurrence, the oscillation frequency, the width and the time intervals between two consecutive revivals. The same analysis is performed for an ideal atom-field interacting system and for the dissipative one. In the end, we compare the effects on the population inversion due to different processes. We pay particular attention to how quantum effects disappear with the decrease of time intervals between jumps in the atom-field coupling parameter or the increase of the dissipation rate for the field, and the result seems to be completely classical. We show that the details of obtaining the classical limit can be very different for each different process
We study the Jaynes-Cummings model (JCM) which describes the interaction between a two-level atom and a single-mode resonant or quasi-resonant electromagnetic field in the non-dissipative and issipative cases. In particular, we study the atomic population inversion whose behavior presents some aspects of purely quantum origin: collapse and revivals. This observables expectation value can be btained analytically without use of approximations for the non-dissipative case and using first-order perturbation in the dissipative case. We make use of the sum of Poisson and the steepest descents method to obtain analytical formulas for the collapse and for each revival. In this way, we can obtain relevant information like the occurrence time, the maximum amplitude, the approximate frequency, and width. The dissipative JCM models the action of the environment on the quantum system. We show that the characteristic time of the revival diminishes as the interaction with the environment enlarges. We consider the limit in which it becomes experimentally impossible to distinguish the obtained curve from the classical one.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic phase fluctuations in the atom-field coupling coefficient. The fluctuations are modelled by random telegraph process and an equation for the density operator averaged over the distribution of fluctuations has been obtained. The solution of this equation is used to study the resulting decoherence effects in the dynamical behaviour of the atom and the statistical properties of the field.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in the atom-field coupling. The coupling coefficient is assumed to fluctuate either in phase or in frequency. The fluctuations are modeled by binary random telegraph processes. Invoking the Markovian property of the telegraph noise, we derive in these two cases an equation for the density operator averaged over the distribution of fluctuations. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.
The collapse-and-revival phenomenon in the population inversion and the time evolution of the quasiprobability Q function of an atom undergoing a two-photon process are investigated when the cavity is supposed to be filled with a Kerr-like medium. An exact expression for the atomic population inversion has been given for a field initially in the coherent state. The closed form of this expression as well as that of the Q function are obtained under the high-field approximation. Also, the tendency toward inhibited decay of the excited state has been explicitly shown. This study reveals how the simultaneous occurrence of two nonlinear processes affects the atomic dynamics.
The phenomenon of atomic population trapping in the Jaynes-Cummings model is analysed from a dressed-state point of view. A general condition for the occurrence of partial or total trapping from an arbitrary, pure initial atom-field state is obtained in the form of a bound to the variation of the atomic inversion. More generally, it is found that in the presence of initial atomic or atom-field coherence the population dynamics is governed not by the field's initial photon distribution, but by a ‘weighted dressedness’ distribution characterizing the joint atom-field state. In particular, individual revivals in the inversion can be analytically described to good approximation in terms of that distribution, even in the limit of large population trapping. This result is obtained through a generalization of the Poisson Summation Formula method for an analytical description of revivals developed by Fleischhauer and Schleich (1993, Phys. Rev A, 47, 4258).
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in atom-field coupling. The coupling coefficient is assumed to fluctuate in phase and/or in amplitude. The phase fluctuations are described by a Wiener-Levy process and the amplitude fluctuations by a colored Gaussian noise. A secular approximation and the theory of the multiplicative stochastic processes are invoked to derive the master equation for the density operator averaged over both phase and amplitude ensembles. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.