Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B./Physical review. B

Fano resonance in the strong-coupling regime

M. Ahsan Zeb

Published Oct 18, 2022• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.106.155134

Related papers

Transition from Lorentz to Fano Spectral Line Shapes in Nonrelativistic Quantum Electrodynamics

Davis M. Welakuh, Prineha Narang

Spectroscopic signatures associated with symmetric Lorentzian and asymmetric Fano line shapes are ubiquitous. Distinct features of Fano resonances in contrast with conventional symmetric resonances have found several applications in photonics such as optical switching, sensing, lasing, and nonlinear and slow-light devices. It is therefore important to effectively generate and control these resonances. In this work, we show through ab initio simulations of coupled light–matter systems that Fano interference phenomena can be realized in a multimode photonic environment by strong coupling to the electromagnetic continuum. Specifically, we show that by effectively enhancing the light–matter coupling strength to the photon continuum in an experimentally feasible way, we can achieve a transition from Lorentzian to Fano lines shapes for both electronic and polaritonic excitations. An important outcome of switching between these spectral signatures is the possibility to control the Purcell enhancement of spontaneous emission alongside electromagnetically induced transparency, which is a special case of Fano resonances. Switching from Fano back to a Lorentzian profile can be achieved by physically reducing the coupling strength to the continuum of modes. Our results hold potential for realizing tunable Fano resonances of molecules and materials interacting with the electromagnetic continuum within multimode photonic environments.

arXiv:2112.05114•ACS Photonics•Aug 11, 2022•9 citations

Non-linear Fano Interferences in Open Quantum Systems: an Exact Solution

Daniel Finkelstein‐Shapiro, Mónica Calatayud, Osman Atabek +2 more

We obtain an explicit solution for the stationary state populations of a dissipative Fano model, where a discrete excited state is coupled to a continumm set of states; both excited set of states are reachable by photo-excitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values. We show that the continuum states population as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4 × 4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic induced-transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter. The original Fano model was introduced by U. Fano in 1961 [1] to explain the asymmetric profile that was obtained when monitoring the photo-current as a function of the laser frequency used to ionize a gaz of Helium-like atoms. In parallel, Friederichs [2] developed the mathematical formalism to describe the essential feature of the Fano model: a discrete state coupled to a continuum set of states; both sets of states being reachable by photo-excitation from the ground state. The resulting photo-current, which is proportional to the population of the continuum set of states, as a function of the excitation laser frequency ω L is known as the Beutler-Fano or Fano profile: f (q) = (q + 2 /(2 + 1), where q is the ratio of the transition dipole moment of the ground-discrete and ground-continuum transitions, and = (ω L − ω e)/γ where e is the energy of the discrete state relative to the ground state, ω L is te radiation field frequency, and = nπV 2 is the linewidth of the excited state, induced by its coupling (per unit of energy) nV 2 to the continuum set of states, n being the density of states. Two extensions of the original model have been considered: inclusion of incoherent relaxation and dephasing processes and high field intensities. The motivation to include incoherent processes was first to describe the pressure broadening [3] due to elastic collisions, laser phase fluctuations [4] and spontaneous emission [5, 6]. Nowadays , Fano profiles in nanoscale structures are standard [7, 8], for example in plasmonic nanostructures [9–11], quantum dots, decorated nanoparticles [12] and spin filters [13]. The coherent coupling with the incident light induces large Rabi frequencies which in turn compete with the relaxation rates in order to modify the stationary state. The ability to predict the lineshape, and in general to investigate non linear optical phenomena in

•Nov 18, 2015•0 citations

Fano coupling of Wannier-Stark excitons in superlattices

C. P. Holfeld, F. Löser, M. Sūdžius +3 more

Summary form only given.Fano resonances arise due to quantum mechanical coupling of a discrete state to a degenerate continuum. The line shape in optical absorption spectra is characterized by an intrinsic broadening of the line, strong asymmetry, and a reduced absorption at one side of the peak falling well below the pure continuum level. Intensive theoretical investigations predicted Fano resonances as a general feature of a large variety of low-dimensional semiconductors. We present the observation of Fano resonances in semiconductor superlattices (SL). In SL, discrete excitonic states of the Wannier-Stark ladder are in resonance with subband continua of lower ladder states. The coupling between discrete and continuous states is mediated by Coulomb interaction, which is also responsible for the formation of the discrete excitonic states. As a unique feature of Fano resonances in SL, the Fano coupling strength can be continuously changed in the experiment by tuning the applied electric field. We have also performed time-integrated four-wave-mixing experiments to investigate the influence of Fano coupling on the polarization decay of a Wannier-Stark exciton. We have been able to resolve the polarization decay of a Fano resonance in the time-integrated signal and to follow its changes with field.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 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

Coupled-square-well model and Fano-phase correspondence

Bin Yan, Chris H. Greene

This paper investigates the Fano-Feshbach resonance with a two-channel coupled-square-well model in both the frequency and time domains. This system is shown to exhibit Fano line-shape profiles in the energy absorption spectrum. The associated time-dependent transition moment response has a phase shift that has recently been understood to be related to the Fano line-shape asymmetric $q$ parameter by $\ensuremath{\varphi}=2arg(q\ensuremath{-}i)$. The present study demonstrates that the phase-$q$ correspondence is general for any Fano resonance in the weak-coupling regime, independent of the transition mechanism.

arXiv:1701.02640•Physical Review A•Mar 29, 2017•6 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 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 \ensuremathξ\ensuremath{\xi}\ensuremathξ that is smaller than the collective coupling between the discrete state and the continuum. We explore the behavior of the excitation probability \ensuremathσ\ensuremath{\sigma}\ensuremathσ as a function of \ensuremathξ\ensuremath{\xi}\ensuremathξ, 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 \ensuremathσ\ensuremath{\sigma}\ensuremathσ 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 \ensuremathσ\ensuremath{\sigma}\ensuremathσ 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.
Spectroscopic signatures associated with symmetric Lorentzian and asymmetric Fano line shapes are ubiquitous. Distinct features of Fano resonances in contrast with conventional symmetric resonances have found several applications in photonics such as optical switching, sensing, lasing, and nonlinear and slow-light devices. It is therefore important to effectively generate and control these resonances. In this work, we show through ab initio simulations of coupled light–matter systems that Fano interference phenomena can be realized in a multimode photonic environment by strong coupling to the electromagnetic continuum. Specifically, we show that by effectively enhancing the light–matter coupling strength to the photon continuum in an experimentally feasible way, we can achieve a transition from Lorentzian to Fano lines shapes for both electronic and polaritonic excitations. An important outcome of switching between these spectral signatures is the possibility to control the Purcell enhancement of spontaneous emission alongside electromagnetically induced transparency, which is a special case of Fano resonances. Switching from Fano back to a Lorentzian profile can be achieved by physically reducing the coupling strength to the continuum of modes. Our results hold potential for realizing tunable Fano resonances of molecules and materials interacting with the electromagnetic continuum within multimode photonic environments.
We obtain an explicit solution for the stationary state populations of a dissipative Fano model, where a discrete excited state is coupled to a continumm set of states; both excited set of states are reachable by photo-excitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values. We show that the continuum states population as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4 × 4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic induced-transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter. The original Fano model was introduced by U. Fano in 1961 [1] to explain the asymmetric profile that was obtained when monitoring the photo-current as a function of the laser frequency used to ionize a gaz of Helium-like atoms. In parallel, Friederichs [2] developed the mathematical formalism to describe the essential feature of the Fano model: a discrete state coupled to a continuum set of states; both sets of states being reachable by photo-excitation from the ground state. The resulting photo-current, which is proportional to the population of the continuum set of states, as a function of the excitation laser frequency ω L is known as the Beutler-Fano or Fano profile: f (q) = (q + 2 /(2 + 1), where q is the ratio of the transition dipole moment of the ground-discrete and ground-continuum transitions, and = (ω L − ω e)/γ where e is the energy of the discrete state relative to the ground state, ω L is te radiation field frequency, and = nπV 2 is the linewidth of the excited state, induced by its coupling (per unit of energy) nV 2 to the continuum set of states, n being the density of states. Two extensions of the original model have been considered: inclusion of incoherent relaxation and dephasing processes and high field intensities. The motivation to include incoherent processes was first to describe the pressure broadening [3] due to elastic collisions, laser phase fluctuations [4] and spontaneous emission [5, 6]. Nowadays , Fano profiles in nanoscale structures are standard [7, 8], for example in plasmonic nanostructures [9–11], quantum dots, decorated nanoparticles [12] and spin filters [13]. The coherent coupling with the incident light induces large Rabi frequencies which in turn compete with the relaxation rates in order to modify the stationary state. The ability to predict the lineshape, and in general to investigate non linear optical phenomena in
Summary form only given.Fano resonances arise due to quantum mechanical coupling of a discrete state to a degenerate continuum. The line shape in optical absorption spectra is characterized by an intrinsic broadening of the line, strong asymmetry, and a reduced absorption at one side of the peak falling well below the pure continuum level. Intensive theoretical investigations predicted Fano resonances as a general feature of a large variety of low-dimensional semiconductors. We present the observation of Fano resonances in semiconductor superlattices (SL). In SL, discrete excitonic states of the Wannier-Stark ladder are in resonance with subband continua of lower ladder states. The coupling between discrete and continuous states is mediated by Coulomb interaction, which is also responsible for the formation of the discrete excitonic states. As a unique feature of Fano resonances in SL, the Fano coupling strength can be continuously changed in the experiment by tuning the applied electric field. We have also performed time-integrated four-wave-mixing experiments to investigate the influence of Fano coupling on the polarization decay of a Wannier-Stark exciton. We have been able to resolve the polarization decay of a Fano resonance in the time-integrated signal and to follow its changes with field.
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.
This paper investigates the Fano-Feshbach resonance with a two-channel coupled-square-well model in both the frequency and time domains. This system is shown to exhibit Fano line-shape profiles in the energy absorption spectrum. The associated time-dependent transition moment response has a phase shift that has recently been understood to be related to the Fano line-shape asymmetric qqq parameter by $\ensuremath{\varphi}=2arg(q\ensuremath{-}i)$. The present study demonstrates that the phase-qqq correspondence is general for any Fano resonance in the weak-coupling regime, independent of the transition mechanism.