Direct observation of Young’s double-slit interferences in vibrationally resolved photoionization of diatomic molecules

Abstract

Vibrationally resolved valence-shell photoionization spectra of H 2 , N 2 and CO have been measured in the photon energy range 20-300 eV using third-generation synchrotron radiation. Young's double-slit interferences lead to oscillations in the corresponding vibrational ratios, showing that the molecules behave as two-center electron-wave emitters and that the associated interferences leave their trace in the angle-integrated photoionization cross section. In contrast to previous work, the oscillations are directly observable in the experiment, thereby removing any possible ambiguity related to the introduction of external parameters or fitting functions. A straightforward extension of an original idea proposed by Cohen and Fano [Cohen HD, Fano U (1966) photoelectron spectroscopy | molecular spectroscopy | molecular ionization | density functional theory | quantum chemistry T he recognition of wave-particle duality, resolving centuries of scientific debate, is nowadays considered as a milestone in the development of Quantum Mechanics. This revolutionary concept has been repeatedly demonstrated in variations of Young's double-slit experiment, where a beam of massive particles, from electrons (1) to fullerenes (2), with momentum p e , passing through two slits separated by a distance comparable to their associated de Broglie wavelength (λ e ¼ h∕p e ) displays temporal and spatial coherence evidenced through interferogram fringes (3). In the 1960's, Cohen and Fano (4) conjectured the possibility to realize the double-slit experiment on the microscopic length scale by photoionizing a diatomic molecule, where the source of free electrons is delocalized over two atomic centers. A sketch of the interference expected from the coherent emission of the two centers is shown in Fig. 1.Coherence is observable when the electron-wave length λ e is of the order of R e , or equivalently, when the photon energy hν is of the order of I p þ h 2 ∕ð2m e R 2 e Þ, where R e is the internuclear distance at equilibrium, m e is the electron mass, and I p is the vertical ionization potential. These energies correspond to incoming photons of a few hundred eV, i.e., to vacuum or extreme ultraviolet radiation. Fingerprints of this coherent emission can be found in the total photoionization cross section, which in the case of a homonuclear diatomic molecule is approximately given by the formulawhere σ 0 is an atomic photoionization cross section (for an effective charge Z eff ) and k e ¼ 2π∕λ e is the electron-wave vector. The oscillatory term within brackets quantifies the interference effect (hereafter called Cohen-Fano, CF, interference). The beauty of such a simple expression is that it is proportional to the very general intensity pattern produced by two dipole antennas separated by a distance R e that radiate coherently (5). Eq. 1 is obtained by assuming that the ionized molecular orbital ψ can be expressed by a linear combination of atomic orbitals (LCAO):where 1s A and 1s B are identical 1s atomic orbitals centered on atoms A and B of...

Vibrational branching ratios in the photoelectron spectra of N2 and CO: interference and diffraction effects

“…Only a few methods described in the previous section have been used to study vibrationally resolved photoionization of CO 13,43,50,52,54,55,58,[65][66][67][68]78 and N 2 13,30,35,58,60,61,63,64,69-71,78 , and almost none in the region of high photon energies 78 . The reason is that one has to evaluate electronic continuum wave functions and potential energy curves in a dense grid of internuclear distances, which makes most methods prohibitively expensive.…”

“…The latter difficulty can be easily overcome by taking the ratios between two related cross sections, the neatest examples being 1σ g /1σ u emission in N 2 or the HOMO/HOMO-1 in C 60 . Alternatively, such oscillations become apparent in angular distribution parameters 95 and in non-dipolar parameters 96 , as well as in the ratios of vibrationally resolved photoelectron spectra 78 . It is this latter observable that we shall explore in the present paper.…”

“…In this paper we present a detailed description of the theoretical methods used in reference 78 and present further evidence of interference effects in N 2 and CO vibrationally resolved photoionization cross sections. We also show that similar conclusions are obtained by using an even more sophisticated theoretical method.…”

“…In particular, results for N 2 and CO obtained from these methods have led to the observation of interesting interference phenomena that are often difficult to identify in total photoelectron spectra, especially at high photon energies 4,11,61,64,69,[74][75][76][77][78] . Two of these phenomena, which lie at the heart of quantum mechanics, have been recently observed in vibrationally resolved photoelectron spectra from valence-shell orbitals 78 : (i) two-center coherent electron emission leading to Young's type double-slit interferences 79 and (ii) electron diffraction by the molecule's atomic centers. These processes are possible because, at high photon energy, the wavelength λ e of the ejected electron is comparable to or smaller than the size of the molecule 80,81 ; consequently, ejected electrons experience the same phenomena as normal wave do.…”

Diffraction using laser-driven broadband electron wave packets

“…3a,b), at high collision energies, electron-atom backscattering DCS is monotonically decaying and structureless. Consequently, the modulation must be attributed to the intramolecular term, which is produced by interfering backscattered waves emanating from each atomic core, analogous to the two-centre effect observed in high harmonic generation 44 , valence/core-shell photoionization spectrum 45,46 and ion impact electron ionization spectrum 47 from a diatomic molecule. Additional experimental confirmations were established at other driving laser wavelengths (see Supplementary Fig.…”