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Einstein–Bohr recoiling double-slit gedanken experiment performed at the molecular level
Abstract and Figures
Double-slit experiments illustrate the quintessential proof for wave–particle complementarity. If information is missing about which slit the particle has traversed, the particle, behaving as a wave, passes simultaneously through both slits. This wave-like behaviour and corresponding interference is absent if ‘which-slit’ information exists. The essence of Einstein–Bohr's debate about wave–particle duality was whether the momentum transfer between a particle and a recoiling slit could mark the path, thus destroying the interference. To measure the recoil of a slit, the slits should move independently. We showcase a materialization of this recoiling double-slit gedanken experiment by resonant X-ray photoemission from molecular oxygen for geometries near equilibrium (coupled slits) and in a dissociative state far away from equilibrium (decoupled slits). Interference is observed in the former case, while the electron momentum transfer quenches the interference in the latter case owing to Doppler labelling of the counter-propagating atomic slits, in full agreement with Bohr’s complementarity.
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Supplementary resource (1)
... Our article is devoted to a rather frequent situation when the external path-detector is absent. For example, this is the case of the here analyzed RAS experiment with the O 2 molecule where the which-path information is offered by nature itself via the Doppler labeling of the atomic slits [19,20]. The wave-particle duality for the YDSE problem taking into account the external path-detectors was studied in Refs. ...
... Another objective of our article is to apply our and GY's formulations of the complementarity principle between the WPI and the INT to two types of RAS by diatomic molecules where the two core-excited atoms play the role of the double slit. The first one is the RAS experiment with fixed-in-space molecules [19,21] which is the first experimental realization of an analog of the Einstein-Bohr recoiling double-slit gedanken experiment at the molecular level [19,20]. The analysis of the second type of RAS experiment [22] performed with randomly oriented oxygen molecules allows us to shed light on the role of the orientational dephasing on the studied duality relation. ...
... We consider the general case of the scattering of the light or electrons on two slits. It can be the resonant inelastic xray scattering [19,23] or the resonant Auger scattering [19,20] described below. The scattering amplitude is the sum of the scattering amplitudes on the right (R) and left (L) slits, ...
Different types of Young's double-slit experiments contain a significant amount of both particle and wave information running from full-particle to full-wave knowledge depending on the experimental conditions. We study the Young's double-slit interference in resonant Auger scattering from homonuclear diatomic molecules where opposite Doppler shifts for the dissociating atomic slits provide path information. Different quantitative formulation of Bohr's complementarity principle—path information vs interference—is applied to two types of resonant Auger scattering experiments, with fixed-in-space and randomly oriented molecules. Special attention is paid to the orientational dephasing in conventional Auger experiments with randomly oriented molecules. Our quantitative formulation of the complementarity is compared with the formulation made earlier by Greenberger and Yasin [D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988)].
... Similar interference fringes were later observed for electrons [2], atoms, and molecules [3]. Effects akin to YDSE were also manifested in two-center interference in photoionization [4], resonant Auger scattering [5], resonant inelastic x-ray scattering (RIXS) [6][7][8][9][10][11], and infinite-slit interference in RIXS of crystals [10,12]. One of the important fingerprints of the YDSE interference is that it opens parity-forbidden RIXS channels [6,10,13]. ...
... One of the important fingerprints of the YDSE interference is that it opens parity-forbidden RIXS channels [6,10,13]. Another important feature of YDSE, YDSE interference fringe, was observed in resonant Auger scattering [5], hard x-ray RIXS from fixed-in-space molecules [7], and in soft x-ray RIXS from randomly oriented molecules [13]. ...
... The dependence of the two-center term on the complex scattering duration τ c = 1/( − ı ) [19] reflects the dynamical origin of this contribution. Let us single out three important differences between the conventional one-center and the additional two-center terms in Eq. (5). First, the two-center terms, being proportional to , vanish when |τ c | 1. ...
In the description of resonant inelastic x-ray scattering (RIXS) from inversion-symmetric molecules the small core-level splitting is typically neglected. However, the spacing Δ between gerade and ungerade core levels in homonuclear diatomic molecules can be comparable with the lifetime broadening of the intermediate core-excited state Γ. We show that when Δ∼Γ the scattering becomes nonlocal in the sense that x-ray absorption at one atomic site is followed by emission at the other one. This is manifested in an unusual dependence of the RIXS cross section on the sum of the momenta of incoming and outgoing x-ray photons k+k′, contrary to the normal k−k′ dependence in the conventional local RIXS theory. The nonlocality of the scattering influences strongly the scattering angle and excitation energy dependence of the intensity ratio between parity forbidden and allowed RIXS channels. Numerical simulations for N2 show that this effect can readily be measured at present-day x-ray radiation facilities.
... Quasielastic scattering back into the electronic ground state is a particularly powerful probe of vibrational structure, since the quasielastic vibrational progression is usually nicely separated from the electronically inelastic RIXS bands [6,15,17]. A particular effect observed in the presence of vibronic coupling or ultrafast dissociation is core-hole localization, which has been observed in simple diatomics and other symmetric molecules [18][19][20]. It is important to notice that the vibronic coupling of core-excited states and related core-hole localization in symmetric polyatomic molecules can have very strong influence due to intrinsic near-degeneracy of core-hole states. ...
... In addition, we also performed simulations of dynamical RIXS spectra by inclusion of nuclear dynamics in one dimension, again under the assumption of instantaneous core-hole localization. Importantly, we notice that diffraction between scattering against different fluorine atoms is neglected [18][19][20], but the processes of core-hole localization and multicenter scattering will be considered in future studies. Also dynamics in other degrees of freedom is neglected. ...
We report on a computational study of resonant inelastic x-ray scattering (RIXS), at different fluorine K-edge resonances of the SF6 molecule, and corresponding nonresonant x-ray emission. Previously measured polarization dependence in RIXS is reproduced and traced back to the local σ and π symmetry of the molecular orbitals and corresponding states involved in the RIXS process. Also electron-hole coupling energies are calculated and related to experimentally observed spectator shifts. The role of dissociative S-F bond dynamics is explored to model detuning of RIXS spectra at the |F1s−16a1g1〉 resonance, which shows challenges to accurately reproduce the required steepness for core-excited potential energy surface. We show that the RIXS spectra can only be properly described by considering breaking of the global inversion symmetry of the electronic wave function and core-hole localization, induced by vibronic coupling. Due to the core-hole localization we have symmetry forbidden transitions, which lead to additional resonances and changing width of the RIXS profile.
... Multiphoton light-matter interactions invoke a so-called 'Black Box' in which the experimental observations contain the quantum interference between multiple pathways (1)(2)(3). Here, we employ attosecond coincidence metrology (4,5) with a partial wave polarization manipulator to deduce the pathway interference within this quantum 'Black Box' (6) for two-photon ionization of neon and argon. The angle-dependent and attosecond time-resolved photoelectron spectra are measured across a broad energy range. ...
... Pathway interference plays a fundamental role in light-matter interaction (1), most famously in two-center or double slit interference (3,7,8). This paradigm has been used to interpret many phenomena including Cohen-Fano photoelectron emission time delays (9), attosecond photoelectron holography (10), electron localization in a molecule (11,12), quantum trajectory interference in high-order harmonic generation (13,14), and even zeptosecond scale electron birth time (15). ...
Multiphoton light-matter interactions invoke a so-called ‘Black Box’ in which the experimental observations contain the quantum interference between multiple pathways ( 1–3 ). Here, we employ attosecond coincidence metrology ( 4, 5 ) with a partial wave polarization manipulator to deduce the pathway interference within this quantum ‘Black Box’ ( 6 ) for two-photon ionization of neon and argon. The angle-dependent and attosecond time-resolved photoelectron spectra are measured across a broad energy range. Two-photon phase shifts for each partial wave are reconstructed through the comprehensive analysis of these photoelectron spectra. We resolve the quantum interference between the p → d → p and p → s → p ionization pathways, in agreement with our theoretical simulations. Our approach thus provides a microscope to look inside the ‘black box’ of pathway interference in ultrafast dynamics of atoms, molecules, and condensed matter.
... Nondipole effects are being investigated in photoionization (11), and notably, they have also been analyzed in terms of YDSE interference (12,13). In the strong field regime, effects beyond the dipole approximation now attract growing attention (14). ...
Resonant inelastic x-ray scattering (RIXS) is a major method for investigation of electronic structure and dynamics, with applications ranging from basic atomic physics to materials science. In RIXS applied to inversion-symmetric systems, it has generally been accepted that strict parity selectivity applies in the sub–kilo–electron volt region. In contrast, we show that the parity selection rule is violated in the RIXS spectra of the free homonuclear diatomic O 2 molecule. By analyzing the spectral dependence on scattering angle, we demonstrate that the violation is due to the phase difference in coherent scattering at the two atomic sites, in analogy with Young’s double-slit experiment. The result also implies that the interpretation of x-ray absorption spectra for inversion symmetric molecules in this energy range must be revised.
... This gedanken experiment was recently confirmed at the molecular level. 35 An interesting version of Einstein's gedanken double-slit experiment was considered by Bohr, which conceptually is identical to the original Einstein's gedanken experiment. In his gedanken experiment, Bohr considered a two-slit experiment where one of the slits can move if the particle passes through. ...
The notion of wave–particle duality remains one of the most debated subjects in the history of quantum physics. The most famous debate on the subject occurred between Bohr and Einstein. In this work, we revisit the wave–particle duality in the Bohr–Einstein debate from the viewpoint of the recently established duality-entanglement relation. We show that the duality-entanglement relation can provide a valuable framework for quantitative analysis of the Einstein's gedanken double-slit experiment and clarify some of its fundamental aspects.
... than Einstein's big mass light bent angle, possibly Einstein himself had already noticed that, since in the Bohr-Einstein debate, Einstein proposed a recoiling double-slit experiment8 and later Einstein's box. These two designs were quite likely to test why the bent angles after the slit(s) were larger than his gravitational lens. ...
Note: Please see pdf for full abstract with equations.
Inversion energy is parameter-against-gravity-internal-fluctuation, the non-simultaneousness gravitational tension among turnover fluctuations is quantizing time. Modified Newtonian Laws, first: 𝑑 𝑑𝑥 cosx =−𝑠𝑖𝑛𝑥, 𝑑 𝑑𝑥 sinx = 𝑐𝑜𝑠𝑥; second: 𝐹⃗ = 𝑚 ∙ 𝑎⃗ + |𝑚𝑔⃗ ∫ 𝑡𝑔𝜃 ⋅ 𝑑𝜃 ⟩ ↿⇂ third: Wavelength = 2 𝑛 , reeueenc = n𝑓0 . Bio-systems are topological spaces through repetitiveness memories to deliver a degenerated entropy for offspring, the trigonometric flux through the space by environmental surface inversion is bio-inertia. Schrödinger equation has only quantized energy thus inducing quantum collapse, we then utilize 𝑯̂ 𝜓 = 𝑬𝜓 + ∑ | cos( 1 𝑛 𝑛 𝑥)⟩ to degenerate eigenstates on a surface tension region to define G shifting quantum growth gravity for reconstructing non-simultaneous time. Originating from gravitational turnover tension between Planck regions and surface tension regions, bio quantum grows in vivo cross folded-surface tension region flow. By the Principle (or Law) of Entropy Degeneration, life relies on negentropy procurements to physically inherit by quantum growth turnover immunity that regenerates by sexual yolk sac (or asexual nucleus) homing. The evolution of long COVID niches and AI/BI is also unveiled.
... It is noted that in the slit surface inversion mechanism of interference experiments, the light bent angles will be much large than Einstein's big mass light bent angle, possibly Einstein himself had already noticed that, since in the Bohr-Einstein debate, Einstein proposed a recoiling double-slit experiment 8 and later Einstein's box. These two designs were quite likely to test why the bent angles after the slit(s) were larger than his gravitational lens. ...
Note: Please see pdf for full abstract with equations.
Inversion energy is parameter-against-gravity-internal-fluctuations, the non-simultaneousness tension among turnover fluctuations is quantizing time. Modified Newtonian Laws, first: 𝑑/𝑑𝑥 cosx =−𝑠𝑖𝑛𝑥, 𝑑/𝑑𝑥 sinx = 𝑐𝑜𝑠𝑥; second: 𝐹⃗=𝑚∙𝑎⃗+|𝑚𝑔⃗∫𝑡𝑔𝜃⋅𝑑𝜃 ⟩↿⇂ third: Wavelength =2/𝑛 L, frequency = n𝑓0. Bio-systems are topological spaces that can process inputs into inversion energy for repetitiveness memory entropy controlling, the capability of equivalent procured inversion energy with memorized trigonometric repetitiveness is bio-inertia. Schrödinger equation has only quantized energy thus inducing quantum collapse, we then utilize equation 𝑯̂𝜓=𝑬𝜓 + Σn|cos(1/𝑛 𝑥)⟩ to degenerate eigenstates on certain surface tension regions to define G shifting quantum growth gravity for lifespan. Originating from quantum gravitational turnover (resistance) tension between Planck regions and surface tension regions, bio quantum grows in vivo cross folded-surface tension region flow. Life relies on trigonometric negentropy procured from elastic entropy generation ground condensates and physically inherit by quantum growth turnover immunity that regenerates by sexual yolk sac (or asexual nucleus) homing. Long COVID niches grow from the NAbs turnover tension is also unveiled.
Multiphoton light-matter interactions invoke a so-called “black box” in which the experimental observations contain the quantum interference between multiple pathways. Here, we employ polarization-controlled attosecond photoelectron metrology with a partial wave manipulator to deduce the pathway interference within this quantum ‘black box” for the two-photon ionization of neon atoms. The angle-dependent and attosecond time-resolved photoelectron spectra are measured across a broad energy range. Two-photon phase shifts for each partial wave are reconstructed through the comprehensive analysis of these photoelectron spectra. We resolve the quantum interference between the degenerate p→d→p and p→s→p two-photon ionization pathways, in agreement with our theoretical simulations. Our approach thus provides an attosecond time-resolved microscope to look inside the “black box” of pathway interference in ultrafast dynamics of atoms, molecules, and condensed matter.
We study single-photon ionization of aligned H$_2^+$ in a high-frequency
low-intensity laser field. We focus on the cases where the laser frequency is near
to or somewhat larger than the ionization potential of the target. The calculated
photoelectron momentum distribution through numerical solution of time-dependent
Schr¨odinger equation shows clear interference patterns. However, different from the
cases of photon energy far larger than the ionization potential usually explored in
experiments, the positions of interference maxima and minima for the present cases
can not be explained by the interference of the electronic wave with the observed
momentum between these two atomic centers of the molecule. By developing a theory
model applicable for ionization of molecules in high-frequency laser field, we show
that the Coulomb potential plays an important role in the momentum component
of the emitting electronic wave near the nuclei, resulting in a remarkable shift of
the interference pattern. A simple expression with Coulomb-modified momentum is
obtained to predict the interference extrema, which gives suggestions for probing the
structure and electron dynamics of the aligned molecule in single-photon ionization
with lower photon energy.
Significance
Electrons emitted from equivalent centers in isolated molecules via the photoelectric effect interfere, providing an atomic-scale equivalent of the celebrated Young’s double-slit experiment. We have developed a theoretical and experimental framework to characterize such interference phenomena accurately, and we have applied it to the simplest hydrocarbons with different bond lengths and bonding types. We demonstrate that such fundamental observations can be related to crucial structural information, such as chemical bond lengths, molecular orbital composition, and quantitative assessment of many-body effects, with a very high accuracy. The experimental and theoretical tools we use are relatively simple and easily accessible, and our method can readily be extended to larger systems, including molecules of biological interest.
Time-independent and time-dependent theory of radiative and nonradiative
resonant x-ray scattering (RXS) involving dissociative molecular states
is presented. A strong space correlation between excitation and decay is
found. This space correlation has a characteristic length equal to the
path propagated during the lifetime of the core-excited state. It is
shown that for internuclear distances beyond this characteristic length
the RXS signal grows exponentially small. Additional untrivial
properties of the RXS cross section for continuum-bound or
bound-continuum decay transitions are predicted. Selection rules operate
for continuum-bound transitions if the slope of the continuum potential
is small; only transitions to vibrational states with odd quantum
numbers are allowed in the harmonic approximation. We show that the main
contribution to the RXS cross section is obtained at the dissociative
limit if the lifetime of the core-excited state is sufficiently long.
Emission transitions in the molecular region form the wing of the
dissociative resonances. The spectral shape of this wing is in general
oscillatory. The cross sections for both type of transitions are
proportional to the square of the wave function of the vibrational state
involved in the RXS process. The spectral shape copies the space
distribution of the square of this wave function, and so, indirectly,
maps the shape of the corresponding molecular potential. The zeros of
the RXS cross section caused by the nodes of the vibrational wave
function can be used to assign vibrational states. The spectral width of
the RXS resonances involving dissociative molecular states strongly
depends on the features of the interatomic potentials. In the general
case the spectral shapes consist of a narrow part and a broad
background, and will be determined by different limiting factors, such
as the spectral photon shape, the Franck-Condon vibrational
distribution, and the lifetime width for the core-excited states. The
role of these limiting factors depends on the different combinations of
dissociative and bound potentials for the ground state, the core-excited
state, and the optically excited state.
Theory for Doppler effects in resonant x-ray Raman scattering (RXS) is
presented. It is shown that the ``electron'' Doppler effect is important
in nonradiative RXS for decay transitions between continuum nuclear
states lying above the dissociation threshold, and that the averaging of
the RXS cross section over molecular orientations can lead to strong
non-Lorentzian broadenings of the atomiclike resonances. The Doppler
effect is found to give a unique possibility to distinguish dissociating
identical atoms, because different peaks correspond to atoms with
opposite Doppler shifts. Spectral features of the atomiclike profile are
predicted and analyzed. Strong oscillations of the RXS cross section
will occur as a consequence of the interference of the Auger electrons.
Due to the Doppler effect and the interference, the atomiclike profile
can be associated with supernarrow spectral features, the width of which
goes below the lifetime broadening and is practically independent of the
spectral distribution of the incident radiation. As another consequence
of the oscillations and strong anisotropy caused by the interference, we
predict parity selection rules for Auger decay transitions in both bound
and dissociative systems. The corresponding experiments can be realized
by measurements of resonant Auger of surface adsorbed molecules and for
molecules by the electron-ion coincidence technique.
We simultaneously measured the momentum transferred to a free-floating molecular double slit and the momentum change of the atom scattering from it. Our experimental results are compared to quantum mechanical and semiclassical models. The results reveal that a classical description of the slits, which was used by Einstein in his debate with Bohr, provides a surprisingly good description of the experimental results, even for a microscopic system, if momentum transfer is not ascribed to a specific pathway but shared coherently and simultaneously between both.
Theoretical two-center interference patterns produced (i) by the K-shell photoionization process of the N2 molecule and (ii) by the Auger decay process of the K-shell hole state of the N2 molecule are compared for the case of equal photo- and Auger-electron energies of about 360 eV. The comparison shows that both the angular distribution of the photoelectrons and the angular distribution of the Auger electrons of equal energy in the molecular frame are primarily defined by the Young interference. The experimental data for the angular resolved K-shell Auger electrons as a function of the kinetic-energy release (KER) obtained earlier [ Phys. Rev. A 81 043426 (2010)] have been renormalized in order to visualize the angular variation in the regions of low Auger-electron intensities. That renormalized data are compared with the corresponding theoretical results. From the known behavior of the potential energy curves, the connection between the KER and the internuclear distance can be established. Since the Young interference pattern is sensitive to the internuclear distance in the molecule, from the measured KER dependence of the Young interference pattern one can trace the behavior of the Auger-electron angular distribution for different molecular terms as a function of internuclear distance. The results of that analysis are in a good agreement with the corresponding theoretical predictions.
An overview is presented of the theory of X-ray Raman scattering. Second-order perturbation theory for the interaction between matter and light is used as a common starting point, and the consequences of this theory are analytically and numerically analyzed for a variety of experimental situations. The review focuses on results from radiative and nonradiative scattering experiments conducted with 2nd and 3rd generation synchrotron radiation sources during the last couple of years, dealing with atomic, molecular, solid state and surface adsorbate targets. After giving a brief synopsis of relevant experimental techniques, some basic theoretical concepts and principles of X-ray Raman scattering are described, followed by a presentation of the various particular aspects associated with the resonant X-ray scattering process. That is: polarization – interference – role of symmetry – symmetry breaking and energy dependence – dissociation and time dependent interpretations – duration time and frequency detuning – formation of band profiles – Doppler effects – screening and chemical shifts – elastic scattering – solid state theory – application to surface adsorbates – absorption in the Raman mode – direct processes versus resonant X-ray scattering – many channel theory. Each aspect is described by a qualitative picture, a mathematical analysis, and by illustrative examples from experiment combined in some cases with results from simulations. Simple systems are chosen to demonstrate the consequences of various aspects of the theory.
ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.
The principle of complementarity refers to the ability of
quantum-mechanical entities to behave as particles or waves under
different experimental conditions. For example, in the famous
double-slit experiment, a single electron can apparently pass through
both apertures simultaneously, forming an interference pattern. But if a
`which-way' detector is employed to determine the particle's path, the
interference pattern is destroyed. This is usually explained in terms of
Heisenberg's uncertainty principle, in which the acquisition of spatial
information increases the uncertainty in the particle's momentum, thus
destroying the interference. Here we report a which-way experiment in an
atom interferometer in which the `back action' of path detection on the
atom's momentum is too small to explain the disappearance of the
interference pattern. We attribute it instead to correlations between
the which-way detector and the atomic motion, rather than to the
uncertainty principle.
Dissociation pathways for complex polyatomic molecules can sometimes be obscure due to the multitude of degrees of freedom involved. Here, we suggest the description of a dissociation mechanism implying multimode dynamics on the barrierless potential energy surface. The mechanism is elaborated from the X-ray spectroscopic analysis of the ultrafast nuclear motion in core−shell excited molecules. We infer that in large molecules, dissociation pathways are observed to deviate from the two-body dissociation coordinate due to the internal motion of light linkages, which alters dissociation rates and may yield heavy products on very short time scales. The mechanism is exemplified with the case of 1-bromo-2-chloroethane, where the rotation of the C2H4-moiety leads to the dissociation of C−Cl or C−Br bonds in Cl2p or Br3d core-excited states, whose lifetimes last only ∼7 fs.
Initial observations by Samson of the far-uv photoabsorption by molecules suggest that the spectrum of photoelectrons emerging from a multicenter molecular field is modulated by interferences. This effect is discussed in terms of Huygens' approach and of a partial-wave analysis with a Born-approximation calculation. It is compared with processes of diffraction by molecules. It appears related to the onset of photo-ionizing transitions to states of increasing orbital momenta which occurs at increasing photon energies.