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arXiv:physics/0111004 · Physical Review A

Statistical theory of Fano resonances in atomic and molecular photoabsorption

W. Ihra

Published Aug 30, 2002• 9 citations
arXivHTMLPDF

Abstract

A statistical theory of Fano resonances is presented for highly excited atomic and molecular systems with a classical chaotic limit. The probability distribution of the Fano parameter, which characterizes the asymmetry profile of a single resonance, is derived both for the case when the quantum system obeys time-reversal symmetry and when time-reversal symmetry is broken. Applications of the theory to photodissociation spectra of molecules and autoionization of Rydberg atoms are discussed.

DOI
10.1103/physreva.66.020701

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A statistical theory of Fano resonances is presented for highly excited atomic and molecular systems with a classical chaotic limit. The probability distribution of the Fano parameter, which characterizes the asymmetry profile of a single resonance, is derived both for the case when the quantum system obeys time-reversal symmetry and when time-reversal symmetry is broken. Applications of the theory to photodissociation spectra of molecules and autoionization of Rydberg atoms are discussed.
The general profile of a resonance, as given by Fano in 1961, is well known throughout physics. This Comment provides some of the simplest derivations of this formula, together with a discussion of subtleties in handling continuum states with regard to their normalization, orthogonality, and completeness. Inadequate appreciation of these subtleties has led to misconceptions and errors in analysis. Recent, novel applications of the Fano formula in condensed matter systems include systems with decoherence and lack of time reversal symmetry which make the resonance profile parameter complex.
Abstract The Fano resonance has been a familiar and important feature in atomic and molecular physics for more than half a century. Typically, the combination of a discrete state with one or more continua results in an asymmetric peak in the ionization spectrum. The peak-shape, called the Fano profile, can be expressed by a simple formula derived by Fano in 1935. However, the interpretation of its characteristic parameter q , which represents the asymmetry of the peak in the formula, is not necessarily intuitively transparent. The Fano resonance is not necessarily a quantum effect, but it is a manifestation of a certain physical mechanism in various systems, both quantum and classical. Through the derivation of q from the known classical pictures with the classical coupled oscillator, we interpret the q value with a geometrical view. And further, we introduce a complex valued q parameter for the description of the resonance with a damped oscillator.
The Fano resonance theory is modified to account for photoionization by ultrashort laser pulses where the probability definition due to the nonlinear dependence on time is no longer valid. We employ the exact integrals over the Fourier transform of the photoionization cross section including the Fano resonances and a corrected Gaussian pulse shape that has vanishing electric field for zero frequency. Numerical results are presented for neutral helium that allow us to deduce the spectral distribution of the Fano resonance for different parameters and to identify the cases where the linear regime is invalid. Analytical approximations are given that provide a clear understanding of the linear and nonlinear regime related to the Fano parameter qqq, the detuned carrier frequencies, and pulse durations.
Fano Resonances in the Time Domain - understanding and controlling the absorption and emission of light—Within this work, starting from the well known theory for photoabsorption cross sections by Ugo Fano, a new formalism is developed, which enables measurement and control of phase and amplitude changes in an emitting dipole. This is shown by experimental measurements in singly and doubly excited helium that confirm the formalism. An application in time-domain quantum holography of excited states, allowing to separate laser-induced coupling pathways, is also presented.
In this paper we apply the T matrix formalism of scattering theory to derive general expressions for the absorption cross sections, the cross sections for resonance fluorescence and the emission quantum yields from large molecules in the statistical limit. In the simple case of an isolated molecular resonance both the absorption line shape and the photon scattering cross section exhibit a Lorentzian distribution on the photon energy, the emission quantum yields are distributed among the ground state vibronic levels according to their radiative widths and, most important, the emission quantum yields are independent of the photon energy and of the spectral width of the exciting light. We were able to derive general expressions for the resonance scattering from a pair of overlapping resonances, including radiative corrections to infinite order. The absorption cross section does not vanish in the region of destructive interference but assumes a finite value which depends on the radiative widths. A sharp maximum in the partial and in the total emission quantum yields is exhibited in the destructive interference regions. This general scheme was applied to a pair of zero order discrete states, one of which is optically active, which interact with an optically inactive quasicontinuum. The energy dependent quantum yield depends on the total width of the radiatively impotent state and may exhibit a minimum. We have demonstrated that when interference effects are involved the decay characteristics of this system will differ for coherent and for narrow band excitation. The general formalism was utilized to derive approximate relations for the resonance fluorescence cross sections and for the quantum yield in the case of a Fano absorption line shape which are valid away from the interference region. Finally, we have applied the general theoretical scheme to the case of the direct photodissociation spectrum of molecules. We have demonstrated that a finite energy dependent emission quantum yield will be observed when a molecule is optically pumped into a dissociative continuum.