Captivity decides the electron race

Ultrafast light flashes with the right energy can be blasted onto an atom enclosed in a fullerene cage to kick out electrons from various quantum states. Recently it has been theoretically demonstrated that due to this imprisonment of the atom, there is a spectacular preference: One electron escapes from the cage faster than the other. For free atoms, the delayed response of various exiting electrons to the incident light is known. But is this behavior correct even if the atom is trapped inside a fullerene? An attempt has recently been made to answer this question for an argon atom introduced in C60.

When light strikes a material with enough energy, energy is transferred from the light to the material, whereupon electrons from different quantum states are kicked out of the material. Until recently, however, it was not possible to determine the time of light absorption of the light from the material, i. whether the reaction time to the light absorption is finite, which would lead to a delay time in the photoemission, or whether the ejection of the photoelectron takes place instantaneously. With tremendous technological advances in the generation of ultrashort light flashes in the attosecond range (1as = 10-18s), it is possible to study various long-standing fundamental questions about the dynamic aspects of photoemission in real time. In experiments, a finite delay time of the photoemission was measured from different quantum states in free atoms. The measured delay time varies with the energy of the incident flashes of light and could be tens of attoseconds. The ubiquitous understanding of these measurements is the dominant influence of electron correlation on the delay time of the ejected electrons. Thus, the complex interaction between the electrons is attributed to the finite delay time. The modeling of such complex electronic interactions and thus the estimation of the finite delay time during the photoemission is very demanding. Thus, a series of provocative experiments as well as theoretical work have focused on the question of the finite delay time in the photoemission.

In an article published in Physical Review Letters [111, 203003 (2013)], an international team of theoreticians from Qatar, the US and the Max Planck Society Born-Institut, Berlin, attempts to resolve this controversial discussion on the finite delays of photoemission in the free argon atom (see Figure 1). In the work led by Gopal Dixit, time-dependent density functional theory was used to estimate the delay time between the 3s and 3p quantum states in the argon atom. The estimated delay time is related to the derivation of the quantum phase of the complex photoionization amplitude after energy. Having shown the importance of electron correlation for the estimation of the delay time in a free atom, it is of spontaneous interest to extend these investigations to atoms confined in a particular environment. An excellent natural laboratory for such investigations is an atom endothermically trapped in a fullerene cage (see Figure 2). There are two valid reasons for this choice: (i) such materials are very stable, can be inexpensively stored at room temperature, and the synthesis of such materials is steadily improved; and (ii) it is expected that the correlation of the central atrium with the electrons of the surrounding cage has a spectacular influence on the photoionization of the atomic valence electrons.
The local and energetic proximity of the outer electron of the argon atom to a C60 electron leads to the formation of two Ar-C60 hybrid electrons. Significant ground-state hybridization of Ar 3p with the C60 3p orbital was found, leading to the formation of a symmetric and anti-symmetric wave function. These overlaps are crucial because the structure of a symmetric wavefunction is opposite to that of an anti-symmetric wavefunction across the region of the C60 shell, where both have a large overlap with a multitude of C60 wavefunctions, and thus can build correlations. These opposite forms of overlap from one hybrid to the other reverses the phases of change direction between two hybrid 3p emissions around the corresponding Cooper minimum. As a result, the highest antisymmetric electron delay is approximately twice the maximum advantage (negative delay) of the symmetric electron. Due to the correlations with the electrons of the fullerene one hybrid escapes faster than the other, namely by about 100 attoseconds after the interaction with the ultrashort light flashes (see Figure 3). The source of such amazing behavior is the preservation of the quantum phase. An analogy is the conservation of momentum in the collision of two particles, but in the time domain. The research presented here seeks to combine two seemingly different areas of current attosecond science and nanotechnology and to motivate the development and construction of ultrafast light sensors, where the reaction time of nanomaterials to light is in the attosecond range.

Fig. 1 Relative delay time between the 3s and 3p quantum states of the free argon atom and the comparison with experimental data at three experimental energies. Since all ejected photoelectrons are collected at the detector, the net 3p delay must be a statistical combination, i. the sum of the delays, which are weighted by the branching ratios of the cross sections of the respective photo channels. The inclusion of 3p → ks together with 3p → kd (purple curve) in this way leads to a remarkable change in the shape of the relative delay near the 3p Cooper minimum.

Fig. 2 Schematic representation of an endohedral C60 trapped argon atom. The influence of this imprisonment and of the electron correlations on the relative delay time between the atomic photoemission from the quantum states 3s and 3 is calculated.

Fig. 3 Relative delay between the 3s and the hybrid 3p quantum state (symmetric, black curve, and anti-symmetric, red curve) including the s-wave contribution and its comparison with the relative delay in the free argon atom (violet curve).

Original publication

Time delay in the recoiling valence-photoemission of Ar endohedrally confined in C60

G. Dixit, H. S. Chakraborty, M. E. Madjet

Physical Review Letters 111 (2013) 203003/1-5