Fano absorption spectrum with the complex spectral analysis

Fukuta, Taku; Garmon, Savannah; Kanki, Kazuki; Noba, Ken-ichi; Tanaka, Satoshi

doi:10.1103/physreva.96.052511

Cited by 15 publications

(20 citation statements)

References 42 publications

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“…1). Our derivation of the Fano asymmetry parameter is inspired by the recent work of Fukuta et al 18 , which used a non-Hermitian approach to compute the Fano factor, although Ref. 18 introduced an artificial model for the continuum and did not relate the lineshape to the complex transition dipole moment.As an application of our approach, we study the suppression and enhancement of photoionization in the presence of an external driving laser [ Fig.…”

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confidence: 99%

Ab-initio theory of photoionization via resonances

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Kaprálová-Žďánská

Moiseyev

2019

The Journal of Chemical Physics

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We present an ab-initio approach for computing the photoionization spectrum near autoionization resonances in multielectron systems. While traditional (Hermitian) theories typically require computing the continuum states, which are difficult to obtain with high accuracy, our non-Hermitian approach requires only discrete bound and metastable states, which can be accurately computed with available quantum chemistry tools. We derive a simple formula for the absorption lineshape near Fano resonances, which relates the asymmetry of the spectral peaks to the phase of the complex transition dipole moment. Additionally, we present a formula for the ionization spectrum of laser-driven targets and relate the "Autler-Townes" splitting of spectral lines to the existence of exceptional points in the Hamiltonian. We apply our formulas to compute the autoionization spectrum of helium, but our theory is also applicable for non-trivial multi-electron atoms and molecules.We present an ab-initio approach for computing the photoionization spectrum near autoionization (AI) resonances in multi-electron systems. Recent developments in attosecondlaser technology enable probing and controlling photoionization processes, and lead to a renewed interest in ionization and related phenomena, such as high-harmonic generation and strong-field electronic dynamics 1-5 . These experimental capabilities call for ab-initio theories, which can relate the electronic structure of the sampled medium to the measured ionization spectrum. However, most existing theories require the calculation of the continuum states 6,7 (above the ionization threshold), which are difficult to obtain with high accuracy with traditional methods 8,9 . In this work, we use non-Hermitian quantum mechanics (NHQM) 10 in order to avoid the need of computing continuum states. Our theory produces a simple formula for the "Fano asymmetry parameter" [Eq. (8)], which expresses the asymmetry of the peaks in the ionization spectrum near AI resonances 11 , and a formula for the photoionization spectrum of laser-driven systems [Eq. (10)]. We relate the Autler-Townes 12 splitting of ionization spectral peaks to the existence of exceptional points 13 (EPs)-special degenerate resonances where multiple AI states share the same energy and wavefunction. We demonstrate the predictions of our theory for helium using ab-initio electronic-structure data from Ref. 14,15. By using advanced non-Hermitian quantum-chemistry algorithms 16,17 , our theory can also be applied for larger atoms and molecules.In NHQM, the time-independent Schrödinger equation is solved with outgoing boundary conditions and the resulting energy spectrum is discrete, containing real-energy bound states and complex-energy metastable states 10 . This situation is very different from traditional Hermitian quantum mechanics (HQM), where metastable (autoionizing) states are described as real-energy bound states embedded in a continuum of free states 11 . Moreover, in HQM, the transition dipole moment is real, while in NHQM, it is ge...

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confidence: 99%

Ab-initio theory of photoionization via resonances

Pick

Kaprálová-Žďánská

Moiseyev

2019

The Journal of Chemical Physics

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“…As ω 0 increases, we encounter the bifurcation of the resonance instability at ω 0 ≃ ω B − B ≃ −0.9, where the cavity mode becomes resonant with the photonic band, resulting in the bifurcation to resonance and anti-resonance modes as in the other decaying systems [46,49,61,62]. In this figure, a positive Imz ξ indicates a decaying state since Ψ ξ (t)⟩ ∝ exp[−(Imz ξ )t] as shown in (9).…”

Section: Resultsmentioning

confidence: 99%

The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal

Tanaka¹,

Kanki²

2020

Preprint

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We theoretically study the dynamical Casimir effect (DCE), i.e., parametric amplification of a quantum vacuum, in an optomechanical cavity interacting with a photonic crystal, which is considered to be an ideal system to study the microscopic dissipation effect on the DCE. Starting from a total Hamiltonian including the photonic band system as well as the optomechanical cavity, we have derived an effective Floquet-Liouvillian by applying the Floquet method and Brillouin-Wigner-Feshbach projection method. The microscopic dissipation effect is rigorously taken into account in terms of the energy-dependent self-energy. The obtained effective Floquet-Liouvillian exhibits the two competing instabilities, i.e., parametric and resonance instabilities, which determine the stationary mode as a result of the balance between them in the dissipative DCE. Solving the complex eigenvalue problem of the Floquet-Liouvillian, we have determined the stationary mode with vanishing values of the imaginary parts of the eigenvalues. We find a new non-local multimode DCE represented by a multimode Bogoliubov transformation of the cavity mode and the photon band. We show the practical advantage for the observation of DCE in that we can largely reduce the pump frequency when the cavity system is embedded in a narrow band photonic crystal with a bandgap.

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“…To solve the problem of the resonance singularity, we extend the eigenvector subspace to the extended Hilbert space, where the norm of the eigenvector vanishes [41,42,44,[46][47][48]55]. The complex eigenvalue problems ofĤ F read…”

Section: Complex Eigenvalue Problem Of the Floquet Hamiltonianmentioning

confidence: 99%

“…The eigenvalue problem of the Floquet Hamiltonian was solved in terms of the Brillouin-Wigner-Feshbach projection method, as shown in Appendix B [46][47][48]53].…”

Section: Complex Eigenvalue Problem Of the Floquet Hamiltonianmentioning

confidence: 99%

“…In fact, how to interpret the dissipative spontaneous photon emission within the framework of quantum mechanics has been a debate since the early days of the theory [37][38][39][40], as an irreversible decay process contradicts the time-reversible quantum dynamics. As a solution to the problem, a new formalism, i.e., complex spectral analysis, has been explored over the last two decades, so that the Hamiltonian can take complex eigenvalues by expanding the vector space to the extended Hilbert space [41][42][43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

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Ultrafast Dynamics of High-Harmonic Generation in Terms of Complex Floquet Spectral Analysis

et al. 2018

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Abstract:We studied the high-harmonic generation (HHG) of a two-level-system (TLS) driven by an intense monochromatic phase-locked laser based on complex spectral analysis with the Floquet method. In contrast with phenomenological approaches, this analysis deals with the whole process as a coherent quantum process based on microscopic dynamics. We have obtained the time-frequency resolved spectrum of spontaneous HHG single-photon emission from an excited TLS driven by a laser field. Characteristic spectral features of the HHG, such as the plateau and cutoff, are reproduced by the present model. Because the emitted high-harmonic photon is represented as a superposition of different frequencies, the Fano profile appears in the long-time spectrum as a result of the quantum interference of the emitted photon. We reveal that the condition of the quantum interference depends on the initial phase of the driving laser field. We have also clarified that the change in spectral features from the short-time regime to the long-time regime is attributed to the interference between the interference from the Floquet resonance states and the dressed radiation field.

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Fano absorption spectrum with the complex spectral analysis

Cited by 15 publications

References 42 publications

Ab-initio theory of photoionization via resonances

Ab-initio theory of photoionization via resonances

The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal

Ultrafast Dynamics of High-Harmonic Generation in Terms of Complex Floquet Spectral Analysis

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