Exact solution of a realistic model for two-photon ionization

Beers, B. L.; Armstrong, Lloyd

doi:10.1103/physreva.12.2447

Cited by 151 publications

(41 citation statements)

References 17 publications

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“…We have chosen He as a target atom for the following reasons: first, its single-electron excitation energies, e.g., 21.218 eV for 1s2p 1 P and 23.087 eV for 1s3p 1 P [20], coincide with the 13th and 15th harmonic photon energies of a Ti:Sapphire laser, respectively, and also with the typical wavelength range of EUV FELs such as the Spring-8 Compact SASE Source (SCSS) [21], the Freeelectron LASer at Hamburg (FLASH) [22], and FERMI [23]. Second, its simple electronic structure allows for exact time-dependent numerical analysis [24][25][26][27][28], in great contrast to alkali atoms.In the case of resonance-enhanced TPI, the resonant ionization path via resonant levels and the nonresonant path via nonresonant intermediate levels coexist [2]. Our results show that in the few fs regime, the competition between the two paths can be controlled by changing the pulse width when the pulse is resonant with a single excited level.…”

mentioning

confidence: 78%

Competition of Resonant and Nonresonant Paths in Resonance-Enhanced Two-Photon Single Ionization of He by an Ultrashort Extreme-Ultraviolet Pulse

Ishikawa

Ueda

2012

Phys. Rev. Lett.

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We theoretically study the pulse-width dependence of the photoelectron angular distribution (PAD) from the resonance-enhanced two-photon single ionization of He by femtosecond ( 20 fs) extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schrödinger equation. In particular, we focus on the competition between resonant and nonresonant ionization paths, which leads to the relative phase δ between the S and D wave packets distinct from the corresponding scattering phase shift difference. When the spectrally broadened pulse is resonant with an excited level, the competition varies with pulse width, and, therefore, δ and the PAD also change with it. On the other hand, when the Rydberg manifold is excited, δ and the PAD do not much vary with the pulse width, except for the very short-pulse regime.PACS numbers: 32.80. Rm, 32.80.Fb, 41.60.Cr, 42.65.Ky Multiphoton ionization of atoms has consistently been receiving a great deal of attention for decades (see e.g. [1][2][3][4][5][6][7][8][9][10][11]). The advent of intense extreme-ultraviolet (EUV) sources such as high-harmonic generation (HHG) and free-electron lasers (FEL) has enabled two-photon ionization (TPI) of species with a deep ionization potential such as He [12][13][14][15][16] and N 2 [17]. Upon photoionization, the continuum electron wave packet is emitted, which is a superposition of different partial waves, each with its own orbital angular momentum, intensity, and phase. Photoelectron angular distribution (PAD), nowadays extensively studied by the velocity map imaging technique (see e.g. [18,19]), contains information on the interference of these different partial waves.In this Letter, we theoretically study the pulse-widthdependence of the PAD from two-photon single ionization of He by femtosecond (fs) EUV pulses. Especially, we focus on situations where the pulse is closely resonant with an excited level, i.e., resonance-enhanced TPI. We have chosen He as a target atom for the following reasons: first, its single-electron excitation energies, e.g., 21.218 eV for 1s2p 1 P and 23.087 eV for 1s3p 1 P [20], coincide with the 13th and 15th harmonic photon energies of a Ti:Sapphire laser, respectively, and also with the typical wavelength range of EUV FELs such as the Spring-8 Compact SASE Source (SCSS) [21], the Freeelectron LASer at Hamburg (FLASH) [22], and FERMI [23]. Second, its simple electronic structure allows for exact time-dependent numerical analysis [24][25][26][27][28], in great contrast to alkali atoms.In the case of resonance-enhanced TPI, the resonant ionization path via resonant levels and the nonresonant path via nonresonant intermediate levels coexist [2]. Our results show that in the few fs regime, the competition between the two paths can be controlled by changing the pulse width when the pulse is resonant with a single excited level. The relative phase δ between the different partial waves (S and D for He) would be just the scattering phase shift difference for nonreson...

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mentioning

confidence: 78%

Competition of Resonant and Nonresonant Paths in Resonance-Enhanced Two-Photon Single Ionization of He by an Ultrashort Extreme-Ultraviolet Pulse

Ishikawa

Ueda

2012

Phys. Rev. Lett.

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“…In the case of resonance-enhanced 2PI, the resonant ionization path via resonant levels and the nonresonant path via nonresonant intermediate levels coexist [2]. We have shown [44] that a feature peculiar to the few fs regime is the competition between the two paths, leading to a relative phase δ between s and d that is distinct from the value expected from the corresponding scattering phase shifts, which is otherwise intrinsic to the target atom or molecule.…”

Section: Introductionmentioning

confidence: 89%

“…Although a rectangular pulse is often assumed in previous work [2] and textbooks, we take, as a more realistic choice, a Gaussian profile f (t) = E 0 e −t 2 /2T 2 , with E 0 and T being the field amplitude and the pulse width, respectively. More precisely, T is related to the full-width-at-half-maximum (FWHM) pulse width T 1/2 as T 1/2 = 2 √ ln 2 T .…”

Section: Time-dependent Perturbation Theorymentioning

confidence: 99%

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Photoelectron Angular Distribution and Phase in Two-Photon Single Ionization of H and He by a Femtosecond and Attosecond Extreme-Ultraviolet Pulse

Ishikawa

Ueda

2013

Applied Sciences

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We theoretically study the photoelectron angular distribution (PAD) from the two-photon single ionization of H and He by femtosecond and attosecond extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schrödinger equation. The PAD is formed by the interference of the s and d continuum wave packets, and, thus, contains the information on the relative phase δ and amplitude ratio between them. We find that, when a spectrally broadened femtosecond pulse is resonant with an excited level, the PAD substantially changes with pulse width, since the competition between resonant and nonresonant ionization paths, leading to δ distinct from the scattering phase shift difference, changes with it. In contrast, when the Rydberg manifold is excited, and for the case of above-threshold two-photon ionization, δ and the PAD do not depend much on pulse width, except for the attosecond region. Thus, the Rydberg manifold and the continuum behave similarly in this respect. For a high-harmonic pulse composed of multiple harmonic orders, while the value of δ is different from that for a single-component pulse, the PAD still rapidly varies with pulse width. The present results illustrate a new way to tailor the continuum wave packet.

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“…Owing to a breakdown of the perturbation theory of transitions due to an electromagnetic field when intermediate resonances with bound states occur, theoretical studies of resonant multiphoton ionisation (RMPI) generally rely on the notion that this phenomenon can be looked upon as the decay of a nonstationary state with a complex quasi-energy, engendered by a non-Hermitian Hamiltonian, which is either phenomenological (Beers and Armstrong 1975;Holt et ale 1983) or constructed more formally (Faisal and Moloney 1981;Maquet et ale 1983). Inherent in these formulations, as well as the resolvent operator formalism (Gontier and Trahin 1979;Faisal 1987), is the assumption that the interaction is turned on at time t = 0 and never switched off.…”

Section: Introductionmentioning

confidence: 99%

Renormalised Perturbation Theory of Resonant Multiphoton Ionisation

Unnikrishnan¹

1995

Aust. J. Phys.

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Perturbation theory of multiphoton ionisation due to a classical electromagnetic field is modified to allow for intermediate resonances with bound states. Complex energies, generally associated with resonances, do not enter into this formalism. For a monochromatic field of frequency u, a constant ionisation rate can then be defined unambiguously and only such continuum states are excited which correspond to the absorption of energy in integral multiples of hu. As an application, differential and total cross sections for the two-photon ionisation of hydrogen, for frequencies below the n = 3 resonance region, are obtained in closed form. Existing data for generalised cross sections, calculated numerically using the complex coordinate method, are in good agreement with the present results. Finally, the mean fractional ionisation resulting from a pulse of finite duration is estimated on the basis of the associated power spectrum. For short pulses, the time dependence of ionisation exhibits a departure from that expected of a time-independent rate.

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Exact solution of a realistic model for two-photon ionization

Cited by 151 publications

References 17 publications

Competition of Resonant and Nonresonant Paths in Resonance-Enhanced Two-Photon Single Ionization of He by an Ultrashort Extreme-Ultraviolet Pulse

Competition of Resonant and Nonresonant Paths in Resonance-Enhanced Two-Photon Single Ionization of He by an Ultrashort Extreme-Ultraviolet Pulse

Photoelectron Angular Distribution and Phase in Two-Photon Single Ionization of H and He by a Femtosecond and Attosecond Extreme-Ultraviolet Pulse

Renormalised Perturbation Theory of Resonant Multiphoton Ionisation

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