Attosecond time delay in the photoionization of endohedral atomsA@C60: A probe of confinement resonances

Abstract

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...

Attosecond chronoscopy of photoemission

“….) (6.4) giving rise to a modulation of the photoionization cross section (Rüdel et al, 2002) as well as of the EWS time delay Pazourek et al, 2013;Dixit et al, 2013;Nagele et al, 2014;Deshmukh et al, 2014). These modulations bear close resemblance to the extended xray absorption fine structure (EXAFS; Sayers et al, 1971;Stern and Heald, 1983;Ito et al, 2004) by the local crystallographic environment near an absorption site in condensed matter.…”

Electron elastic scattering offA@C60: The role of atomic polarization under confinement

“…Note, a meager amount of research on e+A@C 60 collision is in contrast to the study of photon-A@C 60 collision, different aspect of which has been intensely scrutinized in a great variety of theoretical works to date (see, e.g., Refs. [7][8][9][10][11][12][13][14] and references therein), including experimental studies [15,16] (and references therein). Such disbalance in favor of the number and quality of studies of A@C 60 photoionization versus research on electron-A@C 60 collision is not accidental.…”

Attosecond structures from the molecular cavity in fullerene photoemission time delay

“…Time-resolved access into the photoemission processes in fullerenes can be singularly attractive due to their eminent symmetry and stability. Recent efforts were * himadri@nwmissouri.edu made to predict the time delay in photoemissions from atoms endohedrally confined in C 60 [13][14][15]. However, these studies did not address the direct response of C 60 electrons, but instead focused on the effects of confinement.…”