Phase dependence of resonant and antiresonant two-photon excitations

Anisotropic dynamics of two-photon ionization: An attosecond movie of photoemission

“…Both the streaking (5) and the Reconstruction of Attosecond Beating By Interference of Two-Photon Transitions (RABBIT) technique (6)(7)(8)(9) were applied to revisit photoemission in the time domain, through the first measurements of attosecond photoemission delays in atoms (10,11), molecules (12,13), nanoparticles (14), liquids (15), and solids (16). Access to higher levels of details was gradually achieved using tunable sources (17)(18)(19)(20)(21) or by increasing the spectral resolution at detection with the Rainbow RABBIT technique (22)(23)(24)(25). However, all the aforementioned studies relied on measurements averaged over the direction of photoemission.…”

Relativistic Two-photon Matrix Elements for Attosecond Delays

“…It is interesting to note that Eqs. (15)(16) imply that the irregular (regular) function can readily be obtained when the regular (irregular) one is at hand. In the former case the irregular solution is found as…”

“…The study of attosecond photoionization dynamics has been made possible by coherent light sources in the extreme ultraviolet (XUV) regime based on high-order harmonic generation (HHG) [1]. Experimental techniques that were originally used for pulse characterization, such as the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) [2] and the attosecond streak-camera [3], have proved useful to gain novel insights into the time it takes for electrons to escape the binding potentials of atoms [4][5][6][7][8][9][10][11][12][13][14][15][16], molecules [17][18][19][20][21] and solid state targets [22][23][24]. The main observables are delay-dependent modulations in the photoelectron spectra that arise due a phase-locked laser probe field in the infrared (IR) regime [25][26][27][28][29][30].…”

“…However, the subject of combined time-frequency non-linear metrology is quite subtle and it has been found that a high-energy resolution of photoelectrons in RABBIT sidebands can be used to reconstruct autoionizing processes in time [11]. In this case of resonant excitation, via bound Rydberg states or autoionizating states, it is useful to consider the RABBIT scheme as a combination of one "structured" (resonant) path and another "unstructured" (reference) path [10,11,13,16,53,54]. In this case, the phase variation of the resonant path is typically much stronger than any continuum-continuum (or other non-resonant) phase shift, and the phenomena can be understood by expanding Fano's model for autoionization to laser-assisted photoionization, within the strong-field approximation [55], or using approximate two-photon two-color matrix elements [56,57].…”

“…In the non-relativistic limit ∆ → ∆ nrel ± π/2, for κ > 0 and κ < 0 respectively, and thus the sin / cos -functions in Eqs. (15)(16) are replaced with ∓ cos / ± sin in the upper components of Eq. (22)(23).…”