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

Abstract

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...

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

“…We have recently studied the PAD from two-photon single ionization of He by femtosecond (fs) EUV pulses theoretically [44]. In the case of resonance-enhanced 2PI, the resonant ionization path via resonant levels and the nonresonant path via nonresonant intermediate levels coexist [2].…”

Photoelectron angular distributions for the two-photon ionization of helium by ultrashort extreme ultraviolet free-electron laser pulses

“…In the case of the 24.3 eV excitation, the intense ultrashort EUV pulses used in the present study coherently excite several Rydberg states 1snp 1 P with n = 6 − 9. In such a situation, the Rydberg manifold behaves similarly to the continuum near the threshold and both the relative phase ∆ [33] and the TPI yield [48] would smoothly vary when measured by increasing the photon energy across the ionization threshold. It should be noted that the extra phase shift difference due to free-free transitions plays a significant role in recently observed time delays in photoemission by attosecond EUV pulses [49,50].…”

“…Photon energies 21.3 and 23.0 eV are close to the 1s2p 1 P and 1s3p 1 P (23.087 eV) [37] resonances. According to theoretical predictions [33], we may expect that competition between resonant and nonresonant paths can be seen. A photon energy of 24.3 eV corresponds to excitation to the 1snp 1 P Rydberg manifold (n ∼ 7).…”

“…If a resonant two-photon ionization path is dominant, ∆ is again close to ∆ sc , since c 0 and c 2 are both real. On the other hand, if the contributions from both the resonant via a single or several resonant levels) and non-resonant paths (via all the intermediate levels) are present, then ∆ = ∆ sc in general [33] and an extra phase shift difference ∆ ex ≡ ∆ − ∆ sc = arg c 0 /c 2 occurs that can be viewed as a measure of the competition between them. In the present study, the pulses with ω = 21.3, 23.0, and 24.3 eV induce resonant two-photon ionization via 1s2p 1 P , 1s3p 1 P , and a Rydberg manifold (1snp 1 P with n = 6 − 9), respectively.…”

“…Within the framework of the second-order timedependent perturbation theory [33], c l can be defined in such a way that its real and imaginary parts correspond to the resonant and non-resonant paths, respectively. If the pulse is non-resonant, c 0 and c 2 are pure imaginary, resulting in ∆ = ∆ sc .…”