Quantum Mechanical Interference Effects Research Articles

Emergence of the Molecular Geometric Phase from Exact Electron-Nuclear Dynamics.

Geometric phases play a crucial role in diverse fields. In molecules, they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wave function experiences quantum-mechanical interference effects. This intriguing effect, closely resembling the magnetic Aharonov-Bohm effect, crucially relies on the adiabatic description of the dynamics, and it is an open issue whether and how it persists in an exact quantum dynamical framework. Recent works suggest that the molecular geometric phase is an artifact of the adiabatic approximation, thereby challenging the entire concept. Here, building upon a recent investigation (Martinazzo, R.; Burghardt, I. Phys. Rev. Lett. 2024, 132, 243002), we address this issue using the exact factorization of the total wave function. We introduce instantaneous gauge-invariant phases separately for the electrons and nuclei and use them to monitor the phase difference between the trailing edges of a wavepacket encircling a conical intersection between adiabatic surfaces. The transition from the time-dependent open-path phase differences to the closed-path limit is examined, revealing how the phase differences in the electronic and nuclear subspaces compensate for each other upon path closure. In this way, we unambiguously demonstrate the role of the geometric phase in the interference process and shed light on its persistence beyond the adiabatic approximation.

Polarization dependence of atomic high-order harmonic generation: Description using a discrete basis

The optical generation of high-order harmonics is known to have a strong polarization dependence: In contrast to linearly polarized excitation, circularly polarized light induces practically no harmonics. In the current paper we focus on atomic targets, the case when a well-established physical picture explains the effect: For circular polarization, the photoionized electrons never return to their parent nuclei, and the energy they gained while being accelerated by the field is not transferred into high-order harmonic radiation. This is essentially a picture that is based on real-space electron trajectories (or the dynamics of the wave functions). Here, we provide an alternative description that uses the discrete Sturmian basis, and points out how quantum mechanical interference effects and selection rules can explain the polarization dependence of the process. This emphasizes the importance of space-time symmetries during the process of high-order harmonic generation.

Ferromagnetism in armchair graphene nanoribbon heterostructures

We study the properties of flat-bands that appear in a heterostructure composed of strands of different widths of graphene armchair nanoribbons. One of the flat-bands is reminiscent of the one that appears in pristine armchair nanoribbons and has its origin in a quantum mechanical destructive interference effect, dubbed `Wannier orbital states' by Lin et al. in Phys. Rev. B 79, 035405 (2009). The additional flat-bands found in these heterostructures, some reasonably closer to the Fermi level, seem to be generated by a similar interference process. After doing a thorough tight-binding analysis of the band structures of the different kinds of heterostructures, focusing in the properties of the flat-bands, we use Density Functional Theory to study the possibility of magnetic ground states when placing, through doping, the Fermi energy close to the different flat-bands. Our DFT results confirmed the expectation that these heterostructures, after being appropriately hole-doped, develop a ferromagnetic ground state that seems to require, as in the case of pristine armchair nanoribbons, the presence of a dispersive band crossing the flat-band. In addition, we found a remarkable agreement between the tight-binding and DFT results for the charge density distribution of the so-called Wannier orbital states.

Steric Effects in the Inelastic Scattering of NO(X) + Ar: Side-on Orientation

The rotationally inelastic collisions of NO(X) with Ar, in which the NO bond-axis is oriented side-on (i.e., perpendicular) to the incoming collision partner, are investigated experimentally and theoretically. The NO(X) molecules are selected in the |j = 0.5, Ω = 0.5, ε = -1, f⟩ state prior to bond-axis orientation in a static electric field. The scattered NO products are then state selectively detected using velocity-map ion imaging. The experimental bond-axis orientation resolved differential cross sections and integral steric asymmetries are compared with quantum mechanical calculations, and are shown to be in good agreement. The strength of the orientation field is shown to affect the structure observed in the differential cross sections, and to some extent also the steric preference, depending on the ratio of the initial e and f Λ-doublets in the superposition determined by the orientation field. Classical and quantum calculations are compared and used to rationalize the structures observed in the differential cross sections. It is found that these structures are due to quantum mechanical interference effects, which differ for the two possible orientations of the NO molecule due to the anisotropy of the potential energy surface probed in the side-on orientation. Side-on collisions are shown to maximize and afford a high degree of control over the scattering intensity at small scattering angles (θ < 90°), while end-on collisions are predicted to dominate in the backward scattered region (θ > 90°).

Equivalence of RABBITT and Streaking Delays in Attosecond-Time-Resolved Photoemission Spectroscopy at Solid Surfaces

The dynamics of the photoelectric effect in solid-state systems can be investigated via attosecond-time-resolved photoelectron spectroscopy. This article provides a comparison of delay information accessible by the two most important techniques, attosecond streaking spectroscopy and reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) at solid surfaces, respectively. The analysis is based on simulated time-resolved photoemission spectra obtained by solving the time-dependent Schrödinger equation in a single-active-electron approximation. We show a continuous transition from the few-cycle RABBITT regime to the streaking regime as two special cases of laser-assisted photoemission. The absolute delay times obtained by both methods agree with each other, within the uncertainty limits for kinetic energies &gt;10 eV. Moreover, for kinetic energies &gt;10 eV, both streaking delay time and RABBITT delay time coincide with the classical time of flight for an electron propagating from the emitter atom to the bulk-vacuum interface, with only small deviations of less than 4 as due to quantum mechanical interference effects.

G -factor and well-width fluctuations as a function of carrier density in the two-dimensional hole accumulation layer of transfer-doped diamond

The two-dimensional (2D) hole gas at the surface of transfer-doped diamond shows quantum-mechanical interference effects in magnetoresistance in the form of weak localization and weak antilocalization (WAL) at temperatures below about 5 K. Here we use the quenching of the WAL by an additional magnetic field applied parallel to the 2D plane to extract the magnitude of the in-plane $g$-factor of the holes and fluctuations in the well width as a function of carrier density. Carrier densities are varied between 1.71 and $4.35\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ by gating a Hall bar device with an ionic liquid. Over this range, calculated values of $|g|$ vary between 1.6 and 2.3 and the extracted well-width variation drops from 3 to 1.3 nm rms over the phase coherence length of 33 nm for a fixed geometrical surface roughness of about 1 nm as measured by atomic force microscopy. Possible mechanisms for the extracted variations in the presence of the ionic liquid are discussed.

Collision-induced rovibrational energy transfer in small polyatomic molecules: the role of intramolecular perturbations

ABSTRACTVarious forms of time-resolved optical double-resonance spectroscopy facilitate rotationally resolved measurements of collision-induced intramolecular vibration-to-vibration (V–V) energy-transfer processes, which take a gas-phase polyatomic molecule from one distinct rovibrational energy level to another. Of longstanding mechanistic interest are questions concerning the extent to which such V–V energy transfer (ET) may be influenced by intramolecular perturbations – notably Fermi resonance (and other anharmonic mixing effects) and Coriolis coupling – within polyatomic molecular rovibrational manifolds of interest. It is evident that quantum-mechanical interference effects can arise, either inhibiting or enhancing the probability of collision-induced ET in perturbed rovibrational manifolds of certain small gas-phase polyatomic molecules, notably CO2, D2CO and C2H2. This article focuses on a blend of high-resolution rovibrational spectroscopy (characterising initial and final molecular levels and their intramolecular perturbations) and collision dynamics (with colliding molecules defined in terms of isolated-molecule spectroscopic basis states). It aims to offer fresh insights and to consider some apparent mechanistic anomalies (e.g. collision-induced quasi-continuous background effects in the 4νCH rovibrational manifold of C2H2). Various reported experiments and related theoretical treatments are critically re-examined, in order to pose and address mechanistic questions some of which still challenge detailed understanding.

Interference between two resonant transitions with distinct initial and final states connected by radiative decay

The resonant line shape from driving a transition between two states, $|\rm{a}\rangle$ and $|\rm{b}\rangle$, can be distorted due to a quantum-mechanical interference effect involving a resonance between two different states, $|\rm{c}\rangle$ and $|\rm{d}\rangle$, if $|\rm{c}\rangle$ has a decay path to $|\rm{a}\rangle$ and $|\rm{d}\rangle$ has a decay path to $|\rm{b}\rangle$. This interference can cause a shift of the measured resonance, despite the fact that the two resonances do not have a common initial or final state. As an example, we demonstrate that such a shift affects measurements of the atomic hydrogen 2S$_{1/2}$-to-2P$_{1/2}$ Lamb-shift transition due to 3S-to-3P transitions if the 3S$_{1/2}$ state has some initial population.

The coupled system of (5)[formula omitted] and (5)1Πu electronic states in Rb2

We present deperturbation analysis of the mutually perturbed (5)1Σu+←X1Σg+ and (5)1Πu ← X1Σg+ band systems of Rb2 molecule, recorded under rotational resolution by polarization labelling spectroscopy technique. The L-uncoupling interaction causes large shifts of rovibrational energy levels in the low parts of both excited states, which manifest themselves in very irregular patterns of spectral lines. Besides, intensity anomalies among P(J) and R(J) lines are observed and identified as quantum mechanical interference effects. The coupled channels treatment of the (5)1Σu+ and (5)1Πu states allows to reproduce positions of majority of the observed spectral lines within the experimental uncertainty as well as to explain the unusual intensity distribution.

Metal-insulator transition in tin doped indium oxide (ITO) thin films: Quantum correction to the electrical conductivity

Tin doped indium oxide (ITO) thin films are being used extensively as transparent conductors in several applications. In the present communication, we report the electrical transport in DC magnetron sputtered ITO thin films (prepared at 300 K and subsequently annealed at 673 K in vacuum for 60 minutes) in low temperatures (25-300 K). The low temperature Hall effect and resistivity measurements reveal that the ITO thin films are moderately dis-ordered (kFl∼1; kF is the Fermi wave vector and l is the electron mean free path) and degenerate semiconductors. The transport of charge carriers (electrons) in these disordered ITO thin films takes place via the de-localized states. The disorder effects lead to the well-known ‘metal-insulator transition’ (MIT) which is observed at 110 K in these ITO thin films. The MIT in ITO thin films is explained by the quantum correction to the conductivity (QCC); this approach is based on the inclusion of quantum-mechanical interference effects in Boltzmann’s expression of the conductivity of the disordered systems. The insulating behaviour observed in ITO thin films below the MIT temperature is attributed to the combined effect of the weak localization and the electron-electron interactions.

Interference effects and Stark broadening in XUV intrashell transitions in aluminum under conditions of intense XUV free-electron-laser irradiation

Quantum mechanical interference effects in the line broadening of intrashell transitions are investigated for dense plasma conditions. Simulations that involved $LSJ$-split level structure and intermediate coupling discovered unexpected strong line narrowing for intrashell transitions $L$-$L$ while $M$-$L$ transitions remained practically unaffected by interference effects. This behavior allows a robust study of line narrowing in dense plasmas. Simulations are carried out for XUV transitions of aluminum that have recently been observed in experiments with the FLASH free-electron laser in Hamburg irradiating solid aluminum samples with intensities greater than ${10}^{16}$ W/cm${}^{2}$. We explore the advantageous case of Al that allows, first, simultaneous observation of $M$-$L$ transitions and $L$-$L$ intrashell transitions with high-resolution grating spectrometers and, second, has a convenient threshold to study interference effects at densities much below solid. Finally, we present simulations at near solid density where the line emission transforms into a quasicontinuum.

The role of quantum-mechanical interference and quasi-classical effects in conjugated hydrocarbons

The nature of the chemical bond in conjugated hydrocarbons is analyzed through the generalized product function energy partitioning (GPF-EP) method, which allows the calculation of the quantum-mechanical interference and quasi-classical contributions to the energy. The method is applied to investigate the differences between the chemical bonding in conjugated and non-conjugated hydrocarbon isomers and to evaluate the contribution from the energy components to the stabilization of the molecules. It is shown that in all cases quantum-mechanical interference has the effect of concentrating π electron density between the two carbon atoms directly involved in the (C-C)π bonds. For the conjugated isomers, this effect is accompanied by a substantial reduction of electron density in the π space of the neighbouring (C-C)σ bond. On the other hand, quasi-classical effects are shown to be responsible for the extra stabilization of the conjugated isomers, in which a decrease of the π space kinetic reference energy seems to play an important role. Finally, it is shown that the polarization of p-like orbitals in compounds with alternating single and double bonds ultimately increases electron density in the π space of the neighbouring (C-C)σ bond. Therefore, quasi-classical effects, rather than covalent ones, seem to be responsible for several properties of conjugated molecules, such as thermodynamic stability, planarity and (C-C)σ bond shortening. The shortcomings of the delocalization concept are discussed.

Chemical Bonding in the N2 Molecule and the Role of the Quantum Mechanical Interference Effect

The chemical bond in the N(2) molecule is analyzed from the perspective of the quantum mechanical interference effect by means of the recently developed generalized product function energy partitioning (GPF-EP) scheme. The analysis is carried out at the GVB-PP and SC levels, which constitute interpretable independent particle models, while ensuring the correct dissociation behavior for the molecule. The results suggest that some current ideas concerning the bond in the N(2) molecule should be revised. It is shown that, in the absence of the interference effect, there is no chemical bond in the N(2) molecule. The influence of the basis set on the energy partitioning is also evaluated. The interference contributions to the energy are substantially less sensitive to the choice of the basis set than the reference energy, making the investigation of the relative importance of inteference effects in larger systems feasible.

Energy partitioning for generalized product functions: The interference contribution to the energy of generalized valence bond and spin coupled wave functions

The main driving force for the formation of the covalent bond is the quantum-mechanical interference effect among one-electron states, as has been suggested in several works by the use of partition schemes to calculate the interference contributions to the energy. However, due to some difficulties associated with the original approaches, calculations were only carried out for a few, mostly diatomic molecules. In this work, we propose a general approach of partitioning based on generalized product functions with generalized valence bond at the perfect pairing approximation and spin-coupled groups, which should allow the investigation of a broader array of molecules, and hopefully, shed light on the nature of the chemical bond in molecules with unusual chemical features. Among other things, this approach lends itself naturally to the investigation of interference in individual bonds or groups of bonds in a molecule.

Quantum-mechanical description of in-medium fragmentation

We present a quantum-mechanical description of quark-hadron fragmentation in a nuclear environment. It employs the path-integral formulation of quantum mechanics, which takes care of all phases and interferences and contains all relevant time scales, such as production, coherence, and formation. The cross section includes the probability of prehadron (colorless dipole) production both inside and outside the medium. Moreover, it also includes inside-outside production, which is a typical quantum-mechanical interference effect (like twin-slit electron propagation). We observe a substantial suppression caused by the medium, even if the prehadron is produced outside the medium and no energy loss is involved. This important source of suppression is missed in the usual energy-loss scenario interpreting the effect of jet quenching observed in heavy ion collisions. This may be one reason for the too large gluon density reported by such analyses.

Spin Injection Efficiency at the Source/Channel Interface of Spin Transistors

Almost all spintronic transistors (e.g., spin field-effect transistors, spin bipolar transistors, and spin-enhanced MOSFETs) require high efficiency of spin injection from a ferromagnetic contact into a semiconductor channel for proper operation. In this paper, we calculate the efficiency of spin injection from a realistic nonideal ferromagnetic contact into the semiconductor quantum wire channel of a spintronic transistor, taking into account the presence of an axial magnetic field (caused by either the ferromagnetic contact or external agents) and spin orbit interaction. In our calculations, the temperature is assumed to be low enough that phonon scattering is weak and transport is phase-coherent, although not ballistic because of elastic scattering caused by impurities and defects. We consider a single impurity in the channel and show that the conductance depends strongly on the exact location of this impurity because of quantum mechanical interference effects. This is a nuisance since it exacerbates device variability. The ldquosignrdquo of the impurity potential, i.e., whether it is attractive or repulsive, also influences the channel conductance. Surprisingly, at absolute zero temperature, the spin injection efficiency can reach 100% at certain gate biases, even though the ferromagnetic injector is nonideal. However, this efficiency drops rapidly with increasing temperature.

Quantum-interference effects in the o 1Πu(v=1)∼b 1Πu(v=9) Rydberg–valence complex of molecular nitrogen

Two distinct high-resolution experimental techniques, 1 UV laser-based ionization spectroscopy and synchrotron-based XUV photoabsorption spectroscopy, have been used to study the o Rydberg–valence complex of 14N2, providing new and detailed information on the perturbed rotational structures, oscillator strengths, and predissociation linewidths. Ionization spectra probing the b state of 14N2, which crosses o1Πu(v=1) between J = 24 and J = 25, and the o1Πu(v=1), b,1Πu(v=9), and b states of 14N15N, have also been recorded. In the case of 14N2, rotational and deperturbation analyses correct previous misassignments for the low-J levels of o(v=1) and b(v=9). In addition, a two-level quantum-mechanical interference effect has been found between the o–X(1, 0) and b–X(9, 0) transition amplitudes which is totally destructive for the lower-energy levels just above the level crossing, making it impossible to observe transitions to b(v=9,J=6). A similar interference effect is found to affect the o(v=1) and b(v=9) predissociation linewidths, but, in this case, a small non-interfering component of the b(v=9) linewidth is indicated, attributed to an additional spin–orbit predissociation by the repulsive state.

The K239 2Σg+3 state: Observation and analysis

The K239 2Σg+3 state has been observed by perturbation-facilitated infrared-infrared double resonance spectroscopy and two-photon excitation. Resolved fluorescence spectra into the aΣu+3 state have been recorded. The observed vibrational levels have been assigned as the v=23–25, 27, 28, 31–33, 38–45, 47, and 53 levels by comparing the observed and calculated spectra of the 2Σg+3→aΣu+3 transitions. Molecular constants have been obtained using a global fitting procedure with a comprehensive set of experimental data. Fine and hyperfine splittings have been resolved in the excitation spectra. Perturbations between the 2Σg+3 and 2Πg3 states were observed. The hyperfine patterns of the 2Σg+3 levels are strongly affected by the perturbation. The perturbation-free and weakly perturbed levels follow the case bβS coupling scheme, while the perturbed levels follow case bβJ coupling. A Fermi contact constant, bF=65±10MHz, has been obtained. Intensity anomalies of rotational lines appeared both in the 2Σg+3∼2Πg3←bΠu3 excitation spectra and in the 2Σg+3∼2Πg3→aΣu+3 resolved fluorescence spectra. These intensity anomalies can be explained in terms of a quantum-mechanical interference effect.

Polarization dependence of X-ray emission spectroscopy

The polarization dependence of X-ray emission spectroscopy (XES) is studied on the angle dependence of incident and emitted X-ray. The Kramers–Heisenberg formula is employed to describe the optical process. It is shown that the quantum mechanical interference effect is directly observable in magnetic circular dichroism (MCD) spectra in a special geometrical configuration. It is also shown that by making use of the linearly polarized X-ray, information on the symmetry of ground states of materials is directly determinable from simple selection rules. Potential possibilities of X-ray spectrum with a polarized photon are demonstrated.

Experimental verification of line- and band-shape asymmetry in the Schumann–Runge system of O2

High-resolution, laser-based photoabsorption cross-section measurements in the weakly absorbing windows between the (11,0) and (16,0) Schumann–Runge bands of O2 have been performed at liquid-nitrogen temperature and the results compared with corresponding coupled-channel Schrödinger-equation (CSE) and line-by-line model calculations. While the symmetric-line- shape-based line-by-line model cross sections differ significantly from experiment, the excellent agreement found between the CSE and experimental window cross sections serves to confirm clearly for the first time the CSE-model predictions of band shape asymmetry and quantum-mechanical interference effects, especially in the (11,0)–(14,0) band region.