Physical Review A

Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution

T. K. Fang, T. N. Chang

Published Jun 1, 1998• 26 citations

Abstract

A deconvolution procedure is proposed to determine the resonant width $\ensuremath{\Gamma}$, the asymmetry parameter $q$, and the background cross section ${\ensuremath{\sigma}}_{b}$ of a Fano-type resonance in the absence of an ultrahigh-energy resolution. This procedure enables a direct extrapolation to infinite energy resolution using a set of explicit analytical relations in terms of the ratio between the width $\ensuremath{\Gamma}$ and the experimental energy resolution $\ensuremath{\Omega}$ in the limit of $\ensuremath{\Gamma}/\ensuremath{\Omega}\ensuremath{\ll}1$.

DOI: 10.1103/physreva.57.4407

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Line-profile considerations of resonant multiphoton ionization

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It is shown that the interpretation of the line profile of resonant multiphoton ionization in terms of a Fano profile with a constant background can lead to difficulties. These difficulties are related to the fact that the nonresonant background may exhibit considerable structure as a function of photon frequency.

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The quantum and classical Fano parameter q

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Effects of ultrashort laser-pulse durations on Fano resonances in atomic spectra

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Physical Review AOct 31, 201426 citations

Physical Review A

Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution

T. K. Fang, T. N. Chang

Published Jun 1, 1998• 26 citations

Publisher

Abstract

A deconvolution procedure is proposed to determine the resonant width

\ensuremath{\Gamma}

, the asymmetry parameter

q

, and the background cross section

{\ensuremath{\sigma}}_{b}

of a Fano-type resonance in the absence of an ultrahigh-energy resolution. This procedure enables a direct extrapolation to infinite energy resolution using a set of explicit analytical relations in terms of the ratio between the width

\ensuremath{\Gamma}

and the experimental energy resolution

\ensuremath{\Omega}

in the limit of

\ensuremath{\Gamma}/\ensuremath{\Omega}\ensuremath{\ll}1

DOI: 10.1103/physreva.57.4407

Related papers

Line-profile considerations of resonant multiphoton ionization

S. N. Dixit, P. Lambropoulos

Physical Review AApr 1, 19798 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.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:1810.00627Physica ScriptaFeb 11, 202122 citations

Fano resonances in the overlapping regime

Alexandr I. Magunov, I. Rotter, С. И. Страхова

The line shape of resonances in the overlapping regime is studied by using the eigenvalues and eigenfunctions of the effective Hamiltonian of an open quantum system. A generalized expression ${q}_{k}(E)$ for the Fano parameter of the resonance state k is derived that contains the interaction of the state k with neighbored states $l\ensuremath{\ne}k$ via the continuum. It is energy dependent since the coupling coefficients between the state k and the continuum show a resonancelike behavior at the energies of the neighbored states $l\ensuremath{\ne}k.$ Under certain conditions, the energy dependent ${q}_{k}(E)$ are equivalent to the generalized complex energy independent Fano parameters that are introduced by Kobayashi et al. in analyzing experimental data. Long-lived states appear mostly isolated from one another in the cross section, also when they are overlapped by short-lived resonance states. The ${q}_{k}(E)$ of narrow resonances allow therefore to study the complicated interplay between different time scales in the regime of overlapping resonance states by controlling them as a function of an external parameter.The line shape of resonances in the overlapping regime is studied by using the eigenvalues and eigenfunctions of the effective Hamiltonian of an open quantum system. A generalized expression ${q}_{k}(E)$ for the Fano parameter of the resonance state k is derived that contains the interaction of the state k with neighbored states $l\ensuremath{\ne}k$ via the continuum. It is energy dependent since the coupling coefficients between the state k and the continuum show a resonancelike behavior at the energies of the neighbored states $l\ensuremath{\ne}k.$ Under certain conditions, the energy dependent ${q}_{k}(E)$ are equivalent to the generalized complex energy independent Fano parameters that are introduced by Kobayashi et al. in analyzing experimental data. Long-lived states appear mostly isolated from one another in the cross section, also when they are overlapped by short-lived resonance states. The ${q}_{k}(E)$ of narrow resonances allow therefore to study the complicated interplay between different time scales in the regime of overlapping resonance states by controlling them as a function of an external parameter.

arXiv:quant-ph/0305064Physical review. B, Condensed matterDec 8, 200345 citations

Fano profiles of Efimov resonances in mass-imbalanced ultracold gases

Panagiotis Giannakeas, Chris H. Greene

The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy-heavy and the heavy-light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric Fano lineshape that originates from the coexistence of Efimov resonances with Stuckelberg interference minima. In particular, a closed form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter $q$ . The profile of Efimov resonances exhibits a $q-$ reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e. $|q|\to \infty$ , we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom-dimer continua, and the corresponding Efimov metastable states behave as bound levels.The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy-heavy and the heavy-light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric Fano lineshape that originates from the coexistence of Efimov resonances with Stuckelberg interference minima. In particular, a closed form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter $q$. The profile of Efimov resonances exhibits a $q-$reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e. $|q|\to \infty$, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom-dimer continua, and the corresponding Efimov metastable states behave as bound levels.

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Fano interference in quantum resonances from angle-resolved elastic scattering

Prerna Paliwal, Alexander Blech, Christiane P. Koch +1 more

Asymmetric spectral line shapes are a hallmark of interference of a quasi-bound state with a continuum of states. Such line shapes are well known for multichannel systems, for example, in photoionization or Feshbach resonances in molecular scattering. On the other hand, in resonant single channel scattering, the signature of such interference may disappear due to the orthogonality of partial waves. Here, we show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles also in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules with detection angle, in excellent agreement with theoretical predictions from full quantum scattering calculations. Using a model description for the partial wave interference, we can disentangle the resonant and background contributions and extract the relative phase responsible for the characteristic Fano-like profiles from our experimental measurements.Asymmetric spectral line shapes are a hallmark of interference of a quasi-bound state with a continuum of states. Such line shapes are well known for multichannel systems, for example, in photoionization or Feshbach resonances in molecular scattering. On the other hand, in resonant single channel scattering, the signature of such interference may disappear due to the orthogonality of partial waves. Here, we show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles also in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules with detection angle, in excellent agreement with theoretical predictions from full quantum scattering calculations. Using a model description for the partial wave interference, we can disentangle the resonant and background contributions and extract the relative phase responsible for the characteristic Fano-like profiles from our experimental measurements.

arXiv:2105.05959Nature CommunicationsDec 13, 202111 citations

Effects of ultrashort laser-pulse durations on Fano resonances in atomic spectra

FRANK B. ROSMEJ, Valery Alexandrovich Astapenko, Valerii S. Lisitsa

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 $q$ , the detuned carrier frequencies, and pulse durations.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 $q$, the detuned carrier frequencies, and pulse durations.

Physical Review AOct 31, 201426 citations

A deconvolution procedure is proposed to determine the resonant width

\ensuremath{\Gamma}

, the asymmetry parameter

q

, and the background cross section

{\ensuremath{\sigma}}_{b}

\ensuremath{\Gamma}

and the experimental energy resolution

\ensuremath{\Omega}

in the limit of

\ensuremath{\Gamma}/\ensuremath{\Omega}\ensuremath{\ll}1

The line shape of resonances in the overlapping regime is studied by using the eigenvalues and eigenfunctions of the effective Hamiltonian of an open quantum system. A generalized expression

{q}_{k}(E)

for the Fano parameter of the resonance state k is derived that contains the interaction of the state k with neighbored states $l\ensuremath{\ne}k$ via the continuum. It is energy dependent since the coupling coefficients between the state k and the continuum show a resonancelike behavior at the energies of the neighbored states $l\ensuremath{\ne}k.$ Under certain conditions, the energy dependent

{q}_{k}(E)

are equivalent to the generalized complex energy independent Fano parameters that are introduced by Kobayashi et al. in analyzing experimental data. Long-lived states appear mostly isolated from one another in the cross section, also when they are overlapped by short-lived resonance states. The

{q}_{k}(E)

of narrow resonances allow therefore to study the complicated interplay between different time scales in the regime of overlapping resonance states by controlling them as a function of an external parameter.

q

. The profile of Efimov resonances exhibits a

q-

reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e.

|q|\to \infty

, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom-dimer continua, and the corresponding Efimov metastable states behave as bound levels.

q

, the detuned carrier frequencies, and pulse durations.