The effects of confinement resonances on photoelectron group delay (Wigner time delay) following ionization of an atom encapsulated inside a C60 cage have been studied theoretically using both relativistic and non-relativistic random phase approximations. The results indicate clearly the resonant character of the confinement oscillations in time delay of the 4d shell of Xe@C60 and present a most direct manifestation of Wigner time delay. These oscillations were missed in a previous theoretical investigation of Ar@C60 [PRL 111, 203003 (2013)]. PACS numbers: 32.80.Rm 32.80.Fb 42.50.Hz Unprecedented advances in experimental techniques in measuring time intervals at the attosecond level [1] have engendered the ability to scrutinize the time delay in photoionization of atomic systems in the laboratory [2][3][4], thereby allowing us to probe the fundamental process of photoionization in the time domain. Specifically, using attosecond pulses of electromagnetic radiation, the time difference between the emergence of photoelectrons from two neighboring atomic subshells has been measured both in Ne [3] and Ar [4, 5]. These experimental results have stimulated a host of theoretical calculations to explain and to further explore this phenomenon [6][7][8][9]. This is of great interest, not only as a new way to study a fundamental process of nature, but also as an outstanding, unique opportunity towards a deeper understanding of the most informative parameter of the process, the photoionization amplitude. This is because the time delay is related to the energy derivative of the phase of the amplitude driving the process [10]. Indeed, to date, the only method for getting the maximum experimental information on photoionization lies through a set of measurements of total and differential photoionization cross sections, but allows only the absolute values and relative phases of matrix elements to be deduced; this is known as a complete photoionization experiment [11]. Time delay investigations, however, go beyond the complete experiment strategy and yield the derivative of the phase with respect to the photoelectron energy. Time delay investigations, thus, provide a new avenue to discern the characteristics of the basic physical quantity -the photoionization amplitude -and, thus, of the photoionization phenomenon itself. It is the ultimate aim of this paper to promote the expansion of time delay studies towards situations where they have not yet been exploited and where novel effects might occur -to atoms under confinement.The theory of time delay in physics was developed some time ago [12] and was originally envisioned as a way to study resonances -the temporary trapping of one (or more) electrons in a quasi-bound state or a potential well. Indeed, the Breit-Wigner formula of resonant scattering τ = 2/Γ equates the time delay τ with the resonant width Γ at half maximum of the cross-section [13]. Resonances are ubiquitous in photoionization of atoms, and these resonances can be of different natures: inner-shell excitations, tw...
Angular dependence of photoemission time delay for the valence np 3/2 and np 1/2 subshells of Ar, Kr and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold.
Time delay of photoemission from valence ns, np 3/2 , and np 1/2 subshells of noble-gas atoms is theoretically scrutinized within the framework of the dipole relativistic random phase approximation. The focus is on the variation of time delay in the vicinity of the Cooper minima in photoionization of the outer subshells of neon, argon, krypton, and xenon, where the corresponding dipole matrix element changes its sign while passing through a node. It is revealed that the presence of the Cooper minimum in one photoionization channel has a strong effect on time delay in other channels. This is shown to be due to interchannel coupling.
The angular dependence of photoemission time delay for the inner nd 3/2 and nd 5/2 subshells of free and confined Xe is studied in the dipole relativistic random phase approximation. A finite spherical annular well potential is used to model the confinement due to fullerene C60 cage. Nearcancellations in various of the dipole amplitudes, Cooper-like minima, are found. The effects of confinement on the angular dependence, primarily confinement resonances, are demonstrated and detailed.
We predict an observable Wigner time delay in outer atomic shell photoionization near inner shell thresholds. The near-threshold increase of time delay is caused by inter-shell correlation and serves as a sensitive probe of this effect. The time delay increase is present even when the inner and outer shell thresholds are hundreds of electron volts apart. We illustrate this observation by several prototypical examples in noble gas atoms from Ne to Kr. In our study, We employ the random phase approximation with exchange (RPAE) and its relativistic generalization RRPA. We also support our findings by a simplified, yet quite insightful, treatment within the lowest order perturbation theory.
We introduce an ultra-thin attosecond optical delay line based on controlled wavefront division of a femtosecond infrared pulse after transmission through a pair of micrometer-thin glass plates with negligible dispersion effects. The time delay between the two pulses is controlled by rotating one of the glass plates from absolute zero to several optical cycles, with 2.5 as to tens of attosecond resolution with 2 as stability, as determined by interferometric self-calibration. The performance of the delay line is validated by observing attosecond-resolved oscillations in the yield of high harmonics induced by time delayed infrared pulses, in agreement with a numerical simulation for a simple model atom. This approach can be extended in the future for performing XUV-IR attosecond pump–probe experiments.
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