Quantum Mechanical Phase Research Articles

Coherent electron phase-space manipulation by combined elastic and inelastic light-electron scattering

Abstract Photon-Induced Near-field Electron Microscopy (PINEM), Kapitza-Dirac (KD) gratings, and ponderomotive phase plates are examples of techniques in which the wave function of an electron in free space is manipulated using light fields: Free Electron Quantum Optics (FEQO). These effects are usually treated in separate theoretical frameworks. In this paper we present a unified, two-pronged framework that can be used to describe and numerically evaluate the performance of a number of FEQO-based electron-optical elements. The first part is an extension of an existing analytical treatment of PINEM, based on solving a relativistically corrected Schrödinger equation. The extension covers both second-order contributions to PINEM and the Kapitza-Dirac effect. The second, novel element of the approach is based on electron wavefront reconstruction by evaluating the quantum mechanical phase along a bundle of classical electron trajectories. The quasi-classical (but fully relativistic) approach lends itself to simulating a wide variety of FEQO devices, including the examples mentioned. We apply both approaches to a few specific experimental configurations: mirror-based first-order PINEM, second-order PINEM in very high laser intensity, and Kapitza-Dirac diffraction. The results show excellent agreement between the analytical results and the quasi-classical simulations. Finally, we propose a setup that combines KD and PINEM to allow for simultaneous coherent energy and transverse momentum shaping of an electron beam, and present simulation results thereof.

Complex phases in quantum mechanics

Schrödinger's equation is a local differential equation and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a given Hamiltonian may describe several different physically observable phases, each exhibiting its own characteristic global symmetry.

Mass renormalization in lattice simulations of false vacuum decay

False vacuum decay, a quantum mechanical first-order phase transition in scalar field theories, is an important phenomenon in early Universe cosmology. Recently, real-time semiclassical techniques based on ensembles of lattice simulations were applied to the problem of false vacuum decay. In this context, or any other lattice simulation, the effective potential experienced by long-wavelength modes is not the same as the bare potential. To make quantitative predictions using the real-time semiclassical techniques, it is therefore necessary to understand the redefinition of model parameters and the corresponding deformation of the vacuum state, as well as stochastic contributions that require modeling of unresolved subgrid modes. In this work, we focus on the former corrections and compute the expected modification of the true and false vacuum effective mass, which manifests as a modified dispersion relationship for linear fluctuations about the vacuum. We compare these theoretical predictions to numerical simulations and find excellent agreement. Motivated by this, we use the effective masses to fix the shape of a parametrized effective potential, and explore the modeling uncertainty associated with nonlinear corrections. We compute the decay rates in both the Euclidean and real-time formalisms, finding qualitative agreement in the dependence on the UV cutoff. These calculations further demonstrate that a quantitative understanding of the rates requires additional corrections.

Kagome Lattice Promotes Chiral Spin Fluctuations.

Dynamical spin fluctuations in magnets can be endowed with a slight bent toward left- or right-handed chirality by Dzyaloshinskii-Moriya interactions. However, little is known about the crucial role of lattice geometry on these chiral spin fluctuations and on fluctuation-related transport anomalies driven by the quantum-mechanical (Berry) phase of conduction electrons. Via thermoelectric Nernst effect and electric Hall effect experiments, we detect chiral spin fluctuations in the paramagnetic regime of a kagome lattice magnet; these signals are largely absent in a comparable triangular lattice magnet. Supported by MonteCarlo calculations, we identify lattices with at least two dissimilar plaquettes as most promising for Berry phase phenomena driven by thermal fluctuations in paramagnets.

Geometric phases in kaon decays and baryogenesis

We studied the formalism for construction of Bargmann invariants (BIs) as quantum mechanical geometric phases and identified the CP invariance with the rephasing invariant phases in neutral kaon system, kaon decays, baryogenesis and leptogenesis. We develop this formalism to express the CP violation in terms of the Bargmann invariants, which allow us to interpret them as geometric phases. We then comment on the application of such generalized treatment of CP phases.

Photovoltaic effect by soft phonon excitation

SignificanceThe quantum-mechanical geometric phase of electrons provides various phenomena such as the dissipationless photocurrent generation through the shift current mechanism. So far, the photocurrent generations are limited to above or near the band-gap photon energy, which contradicts the increasing demand of the low-energy photonic functionality. We demonstrate the photocurrent through the optical phonon excitations in ferroelectric BaTiO3 by using the terahertz light with photon energy far below the band gap. This photocurrent without electron-hole pair generation is never explained by the semiclassical treatment of electrons and only arises from the quantum-mechanical geometric phase. The observed photon-to-current conversion efficiency is as large as that for electronic excitation, which can be well accounted for by newly developed theoretical formulation of shift current.

Emergent half-metal at finite temperatures in a Mott insulator

Sustaining exotic quantum mechanical phases at high temperatures is a long-standing goal of condensed matter physics. Among them, half-metals are spin-polarized conductors that are essential for realizing room-temperature spin current sources. However, typical half-metals are low-temperature phases whose spin polarization rapidly deteriorates with temperature increase. Here, we first show that a low-temperature insulator with an unequal charge gap for the two spin channels can arise from competing Mott and band insulating tendencies. We establish that thermal fluctuations can drive this insulator to a half-metal through a first-order phase transition by closing the charge gap for one spin channel. This half-metal has 100% spin polarization at the onset temperature of metallization. Further, varying the strength of electron repulsion can enhance the onset temperature while preserving spin polarization. We outline experimental scenarios for realizing this tunable finite temperature half-metal.

Bubble clustering in cosmological first order phase transitions

False vacuum decay in quantum mechanical first order phase transitions is a phenomenon with wide implications in cosmology and presents interesting theoretical challenges. In the standard approach, it is assumed that false vacuum decay proceeds through the formation of bubbles that nucleate at random positions in spacetime and subsequently expand. In this paper, we investigate the presence of correlations between bubble nucleation sites using a recently proposed semiclassical stochastic description of vacuum decay. This procedure samples vacuum fluctuations, which are then evolved using classical lattice simulations. We compute the two-point function for bubble nucleation sites from an ensemble of simulations, demonstrating that nucleation sites cluster in a way that is qualitatively similar to peaks in random Gaussian fields. We qualitatively assess the phenomenological implications of bubble clustering in early Universe phase transitions, which include features in the power spectrum of stochastic gravitational waves and an enhancement or suppression of the probability of observing bubble collisions in the eternal inflation scenario.

Active Terahertz Modulator and Slow Light Metamaterial Devices with Hybrid Graphene-Superconductor Photonic Integrated Circuits.

Metamaterial photonic integrated circuits with arrays of hybrid graphene–superconductor coupled split-ring resonators (SRR) capable of modulating and slowing down terahertz (THz) light are introduced and proposed. The hybrid device’s optical responses, such as electromagnetic-induced transparency (EIT) and group delay, can be modulated in several ways. First, it is modulated electrically by changing the conductivity and carrier concentrations in graphene. Alternatively, the optical response can be modified by acting on the device temperature sensitivity by switching Nb from a lossy normal phase to a low-loss quantum mechanical phase below the transition temperature (Tc) of Nb. Maximum modulation depths of 57.3% and 97.61% are achieved for EIT and group delay at the THz transmission window, respectively. A comparison is carried out between the Nb-graphene-Nb coupled SRR-based devices with those of Au-graphene-Au SRRs, and significant enhancements of the THz transmission, group delay, and EIT responses are observed when Nb is in the quantum mechanical phase. Such hybrid devices with their reasonably large and tunable slow light bandwidth pave the way for the realization of active optoelectronic modulators, filters, phase shifters, and slow light devices for applications in chip-scale future communication and computation systems.

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem.

The recently developed ab initio multiple cloning (AIMC) approach based on the multiconfigurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to nonadiabatic dynamics with a particular strength in the proper description of decoherence effects because of the branching of vibrational wavepackets at a level crossing. Here, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-field theory to determine the equations of motion for classical trajectories. The multidimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based nonadiabatic coupling approach within the AIMC method, all observables are calculated on-the-fly in the nonadiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level nonadiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

Position-dependent finite symmetric mass harmonic like oscillator: Classical and quantum mechanical study

Abstract We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.

VPA: Computer program for the computation of the phase shift in atom–atom potential scattering using the Variable Phase Approach

A computer code for the computation of the phase shift in atom–atom and electron–atom potential scattering is presented. The phase shift is the central quantity required for the calculation of all types of scattering cross sections. The program uses the Variable Phase Approach (VPA). This is the only exact method for the direct calculation of the scattering phase shift. All other methods are based on examining the large distance behavior of the exact solution of the Schrödinger equation. Such methods yield the phase shift only modulo π. The absolute value of the phase shift and its variation with scattering energy is, however, needed for a full understanding of the scattering process, such as for instance in the study of shape resonances and Glory oscillations. The VPA has been sparingly used owing to the instability of the underlying equations and the consequent difficulty of writing computer code to solve them. We present a computer code for the efficient implementation of the VPA method for atom–atom scattering problems over a wide range of scattering energies. The code works for potentials which are singular and for those that are non-singular at the origin. An example of the implementation of the code is given for both an interaction potential with an attractive well and for a purely repulsive potential. Program summaryProgram title: VPA:Variable Phase ApproachCPC Library link to program files: https://dx.doi.org/10.17632/zh248d2362.1Code Ocean capsule: https://dx.doi.org/10.24433/CO.8146850.v1Licensing provisions: GNU General Public License 3 (GPL)Programming language: Fortran 90Nature of problem: To compute the quantum mechanical phase shift in an atom–atom or an electron–atom potential scattering problem. The interaction potential, dependent on a single radial coordinate, is defined by the user.Solution method: The Variable Phase Approach is used. This is the only available method for the direct calculation of the phase shift. The initial internuclear separation for the integration is chosen with the help of the analytical solution for a hard sphere core for all orbital angular momentum quantum numbers L of interest. The first-order nonlinear equation is integrated numerically with a modified LSODA19,20 program. The analytic formula for calculation of the Jacobian of the equation is also provided.Additional comments including restrictions and unusual features: Computer codes for the atom–atom interaction potential, POTENT1, and for its derivative with respect to the inter nuclear separation, DPOTENT1, must be supplied by a user. The calculation of the spherical Bessel and Neumann functions required is performed explicitly for large l angular momentum quantum numbers where the standard upward iterative generation of the functions becomes unstable.

Stochastic fractal and Noether's theorem.

We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments either survives with probability p or disappears with probability 1-p. It describes a stochastic dyadic Cantor set that evolves in time, and eventually becomes a fractal. We investigate this phenomenon, through analytical methods and Monte Carlo simulation, for a generic class of models, where segment breakup points follow a symmetric beta distribution with shape parameter α, which also determines the fragmentation rate. For a fractal dimension d_{f}, we find that the d_{f} th moment M_{d_{f}} is a conserved quantity, independent of p and α. While the scaling exponents do not depend on p, the self-similar distribution shows a weak p dependence. We use the idea of data collapse-a consequence of dynamical scaling symmetry-to demonstrate that the system exhibits self-similarity. In an attempt to connect the symmetry with the conserved quantity, we reinterpret the fragmentation equation as the continuity equation of a Euclidean quantum-mechanical system. Surprisingly, the Noether charge corresponding to dynamical scaling is trivial, while M_{d_{f}} relates to a purely mathematical symmetry: Quantum-mechanical phase rotation in Euclidean time.

Non-linear Terahertz driving of plasma waves in layered cuprates

The hallmark of superconductivity is the rigidity of the quantum-mechanical phase of electrons, responsible for superfluid behavior and Meissner effect. The strength of the phase stiffness is set by the Josephson coupling, which is strongly anisotropic in layered cuprates. So far, THz light pulses have been used to achieve non-linear control of the out-of-plane Josephson plasma mode, whose frequency lies in the THz range. However, the high-energy in-plane plasma mode has been considered insensitive to THz pumping. Here, we show that THz driving of both low-frequency and high-frequency plasma waves is possible via a general two-plasmon excitation mechanism. The anisotropy of the Josephson couplings leads to markedly different thermal effects for the out-of-plane and in-plane response, linking in both cases the emergence of non-linear photonics across Tc to the superfluid stiffness. Our results show that THz light pulses represent a preferential knob to selectively drive phase excitations in unconventional superconductors.

Generalized uncertainty principle and its implications on geometric phases in quantum mechanics

We study the implications of the generalized uncertainty principle (GUP) with a minimal measurable length on some quantum mechanical interferometry phenomena, such as the Aharonov–Bohm, Aharonov–Casher, COW and Sagnac effects. By resorting to a modified Schrödinger equation, we evaluate the lowest-order correction to the phase shift of the interference pattern within two different GUP frameworks: the first one is characterized by the redefinition of the physical momentum only, and the other is a Lorentz covariant GUP which also predicts non-commutativity of spacetime. The obtained results allow us to fix upper bounds on the GUP deformation parameters which may be tested through future high-precision interferometry experiments.

Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane

In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi2Sr2CaCu2O8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern.

Geometrical Hall effect and momentum-space Berry curvature from spin-reversed band pairs

When nanometric, noncoplanar spin textures with scalar spin chirality (SSC) are coupled to itinerant electrons, they endow the quasiparticle wavefunctions with a gauge field, termed Berry curvature, in a way that bears analogy to relativistic spin-orbit coupling (SOC). The resulting deflection of moving charge carriers is termed geometrical (or topological) Hall effect. Previous experimental studies modeled this signal as a real-space motion of wavepackets under the influence of a quantum-mechanical phase. In contrast, we here compare the modification of Bloch waves themselves, and of their energy dispersion, due to SOC and SSC. Using the canted pyrochlore ferromagnet Nd$_2$Mo$_2$O$_7$ as a model compound, our transport experiments and first-principle calculations show that SOC impartially mixes electronic bands with equal or opposite spin, while SSC is much more effective for opposite spin band pairs.

Out-of-plane corrugations in graphene based van der Waals heterostructures

Graphene, the first truly two-dimensional material isolated, is never perfectly flat. Even when it is sandwiched between other atomically flat crystals, it still slightly ripples. These out-of-plane corrugations, deformations of the graphene layer into the third dimension, have profound implications on graphene's properties. They reduce the mobility of electrons moving within graphene just like bumps on a road slow down a car. Here, the authors demonstrate the presence of such corrugations by studying the quantum mechanical phase electrons acquire in the presence of a magnetic field.

Time-energy uncertainty relation for neutrino oscillations in curved spacetime

We derive the Mandelstam–Tamm time–energy uncertainty relation for neutrino oscillations in a generic stationary curved spacetime. In particular, by resorting to Stodolsky covariant formula of the quantum mechanical phase, we estimate gravity effects on the neutrino energy uncertainty. Deviations from the standard Minkowski result are explicitly evaluated in Schwarzschild, Lense–Thirring and Rindler (uniformly accelerated) geometries. Finally, we discuss how spacetime could affect the characteristic neutrino oscillation length in connection with the recent view of flavor neutrinos as unstable particles.

Complete reconstruction of bound and unbound electronic wavefunctions in two-photon double ionization

To be complete, the characterization of the photoionization process of atoms and molecules requires the extraction of all quantum-mechanical phases and amplitudes. So far, complete experiments have accessed only the ionization process of neutral atoms and molecules. Here we report the quantum-mechanically complete characterization of the single and double ionization of neon to yield doubly charged ions. The first ionization step by intense, polarized extreme ultraviolet light from a free-electron laser leaves the ion in a polarized state (that is, one in which the angular momentum of the ion is aligned in space). By controlling the polarization of the light, we determine the bound and continuum components of the system in the first and second ionization steps leading to the formation of doubly charged neon ions. We test the validity of our approach by characterizing the influence of autoionizing ionic states on the two-photon double-ionization mechanism. Our results are important for understanding the physics of the interaction of extreme ultraviolet radiation with ions. Photoionization is one of the most important photophysical events. This process can now be characterized in a quantum-mechanically complete manner by use of polarization-controlled extreme-ultraviolet light derived from a free-electron laser