© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Chinese Physics Letters

Three-Channel Interference Interpretation of Fano Profile

Bo 波 Li 李, Tian-Jun Li, Zi-Ru Ma, Xiyuan Wang, Xin‐Chao Huang, Lin-Fan 林繁 Zhu 朱

Published Apr 10, 2024• 1 citation

Abstract

Fano resonance is a ubiquitous phenomenon, and it is commonly interpreted as a two-channel interference of the discrete and continuous channels. The present work investigates the Fano profile from a perspective of the temporal evolution of the wave function. By exciting the atom with a δ pulse and calculating the evolution of the wave function, the Fano formula is deduced. The results clearly show that the Fano resonance is of a three-channel interference, which is different from the traditional understanding. The three channels are revealed as the ground-continuum, ground-discrete-continuum, and a previously unmentioned third channel, i.e., ground-continuum-discrete-continuum. The present three-channel interpretation can be easily generalized to other physical systems, contributing to a deeper understanding of the Fano profile.

DOI: 10.1088/0256-307x/41/5/053201

Related papers

Fano resonance in the strong-coupling regime

M. Ahsan Zeb

Fano resonance is a well-celebrated weak-coupling phenomenon whereby a small interaction between a discrete and a continuum of excited states leads to an interference between the respective two transition amplitudes, resulting in an asymmetric line shape in the excitation spectra. We present the strong-coupling phase of the Fano's model where the interaction is localized in a region $\ensuremath{\xi}$ that is smaller than the collective coupling between the discrete state and the continuum. We explore the behavior of the excitation probability $\ensuremath{\sigma}$ as a function of $\ensuremath{\xi}$, the ratio of the bare transition amplitudes, and the energy of the discrete state. In the strong-coupling phase, the spectral function of the discrete state splits up and produces up to three complete destructive interferences or zeros of $\ensuremath{\sigma}$ along with ultrasharp features. We also find that the discrete state does not have to lie within the continuum to produce the well-known weak-coupling profiles of $\ensuremath{\sigma}$ as long as the collective coupling is strong enough. In addition, we consider a broadened state instead of a continuum and present a method that exactly treats such cases by explicitly including the source of the broadening---a weak coupling to the continuum of environment states---in the model.

Physical review. B./Physical review. B•Oct 18, 2022•9 citations

Perspectives on the Fano Resonance Formula

A. R. P. Rau

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.

Physica Scripta•Dec 22, 2003•80 citations

First Observation of New Flat Line Fano Profile via an X-Ray Planar Cavity

Zi-Ru Ma, Xin‐Chao Huang, Tian-Jun Li +6 more

A new Fano profile of a flat line is achieved experimentally by manipulating the relative amplitude of the continuum path, when q takes the pure imaginary number of -i in the x-ray regime. The underlying mechanism is that the interference term in the scattering will cancel the discrete term exactly. This new Fano profile renders only an observable continuum along with an invisible response to the discrete state of atomic resonance. The results suggest not only a different strategy to invisibility studies which provides a possible tool to identify weaker structures hidden by the strong white line, but also a new scenario to enrich the manipulations of two-path interference and nonlinear Fano resonance.

Physical Review Letters•Nov 16, 2022•12 citations

Effect of Fano Resonance in photovoltaic

Dong Sun

Abstract We have shown that the Fano interference in the decay channels of a three-level system can lead to considerably different absorption and emission profiles. We found that a coherence can be built up in the ground state doublet, with strength depending on a coupling parameter that arises from the Fano interference. The coherence can in principle lead to breaking of the detail balance between the absorption and emission processes in atomic systems.

Coherent Phenomena•Jan 22, 2014•0 citations

The quantum and classical Fano parameter q

Masatomi Iizawa, Satoshi Kosugi, Fumihiro Koike +1 more

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.

arXiv:1810.00627•Physica Scripta•Feb 11, 2021•22 citations

Signatures of Fano resonances in four-wave-mixing experiments

T. Meier, A. Schulze, P. Thomas +2 more

Optical transitions into discrete levels coupled to an optically active continuum lead to asymmetrical Fano lines in the linear absorption spectra, reflecting interference between the excitation channels. We investigate the corresponding four-wave-mixing spectra for the nonlinear optical response within a model of noninteracting electrons. Our results show that four-wave-mixing experiments provide a useful tool to identify Fano resonances.

Physical review. B, Condensed matter•May 15, 1995•23 citations

Fano resonance is a ubiquitous phenomenon, and it is commonly interpreted as a two-channel interference of the discrete and continuous channels. The present work investigates the Fano profile from a perspective of the temporal evolution of the wave function. By exciting the atom with a δ pulse and calculating the evolution of the wave function, the Fano formula is deduced. The results clearly show that the Fano resonance is of a three-channel interference, which is different from the traditional understanding. The three channels are revealed as the ground-continuum, ground-discrete-continuum, and a previously unmentioned third channel, i.e., ground-continuum-discrete-continuum. The present three-channel interpretation can be easily generalized to other physical systems, contributing to a deeper understanding of the Fano profile.

Fano resonance is a well-celebrated weak-coupling phenomenon whereby a small interaction between a discrete and a continuum of excited states leads to an interference between the respective two transition amplitudes, resulting in an asymmetric line shape in the excitation spectra. We present the strong-coupling phase of the Fano's model where the interaction is localized in a region $\ensuremath{\xi}$ that is smaller than the collective coupling between the discrete state and the continuum. We explore the behavior of the excitation probability $\ensuremath{\sigma}$ as a function of $\ensuremath{\xi}$, the ratio of the bare transition amplitudes, and the energy of the discrete state. In the strong-coupling phase, the spectral function of the discrete state splits up and produces up to three complete destructive interferences or zeros of $\ensuremath{\sigma}$ along with ultrasharp features. We also find that the discrete state does not have to lie within the continuum to produce the well-known weak-coupling profiles of $\ensuremath{\sigma}$ as long as the collective coupling is strong enough. In addition, we consider a broadened state instead of a continuum and present a method that exactly treats such cases by explicitly including the source of the broadening---a weak coupling to the continuum of environment states---in the model.

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.

A new Fano profile of a flat line is achieved experimentally by manipulating the relative amplitude of the continuum path, when q takes the pure imaginary number of -i in the x-ray regime. The underlying mechanism is that the interference term in the scattering will cancel the discrete term exactly. This new Fano profile renders only an observable continuum along with an invisible response to the discrete state of atomic resonance. The results suggest not only a different strategy to invisibility studies which provides a possible tool to identify weaker structures hidden by the strong white line, but also a new scenario to enrich the manipulations of two-path interference and nonlinear Fano resonance.

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.