Outgoing Wave Packet Research Articles

Wigner time delay revisited

The concept of Wigner time delay was introduced in scattering theory to quantify the delay or advance of an incoming particle in its interaction with the scattering potential. The scattered-wave part of the wave packet, which describes the interacting particle, is delayed/advanced with respect to the non-interacting plane-wave packet. It has been widely assumed that this concept can be transferred to ionization considering it as a half-scattering process. In the present work we show, by analyzing the corresponding wave packets, that this assumption is incorrect. For ionization the outgoing wave packet is a superposition of the continuum states ψk(−)(r,t), which satisfy the incoming-wave boundary condition at large distances r from the origin and which for large time t→∞ form a plane-wave packet. The expansion coefficients in this wave packet are the ionization probability amplitudes. If these amplitudes depend on the scattering phase shift, the plane-wave part of the ionized wave packet may be modified, leading to an ionization analog of the Wigner time delay. However, in most cases such a Wigner time delay is absent for ionization. We illustrate this with two examples: (i) photoionization by a weak field of an atom with the electron bound by a zero-range potential and (ii) strong-field ionization.

Quantum Big Bounce of the Isotropic Universe Using Relational Time

We analyze the canonical quantum dynamics of the isotropic Universe with a metric approach by adopting a self-interacting scalar field as relational time. When the potential term is absent, we are able to associate the expanding and collapsing dynamics of the Universe with the positive- and negative-frequency modes that emerge in the Wheeler–DeWitt equation. On the other side, when the potential term is present, a non-zero transition amplitude from positive- to negative-frequency states arises, as in standard relativistic scattering theory below the particle creation threshold. In particular, we are able to compute the transition probability for an expanding Universe that emerges from a collapsing regime both in the standard quantization procedure and in the polymer formulation. The probability distribution results similar in the two cases, and its maximum takes place when the mean values of the momentum essentially coincide in the in-going and out-going wave packets, as it would take place in a semiclassical Big Bounce dynamics.

Frequency-Selective Surface Based on Negative-Group-Delay Bismuth–Mica Medium

Negative group delay may be observed in dispersive media with anomalous dispersion in a certain frequency range. The fact that an outgoing wave packet precedes an incoming one does not violate the causality principle but is only a consequence of a waveform reshaping. This effect is observed in media such as photonic crystals, hyperbolic and epsilon-near-zero metamaterials, undersized waveguides, subwavelength apertures, side-by-side prisms, and resonant circuits at various frequencies. The current work is devoted to the design of a simple negative-group-delay medium with tunable properties in the THz frequency range. This medium consists of a bismuth-based frequency-selective surface on a dielectric substrate and may be tuned both statically and dynamically. While a geometry variation defines a main form of an effective permittivity dispersion and group delay/group velocity spectra, an external voltage allows one to adjust them with high precision. For the configuration proposed in this work, all frequency regions with noticeable change in group delay/group velocity lie within atmospheric transparency windows, which are to be used in 6G communications. This medium may be applied to THz photonics for a tunable phase-shift compensation, dispersion management in systems of THz signal modulation, and for encoding in next-generation wireless communication systems.

Is Bianchi I a bouncing cosmology in the Wheeler-DeWitt picture?

We provide a quantum picture for the emergence of a bouncing cosmology, according to the idea that a semiclassical behavior of the Universe towards the singularity is not available in many relevant Minisuperspace models. In particular, we study the Bianchi I model in vacuum adopting the isotropic Misner variable as an internal clock for the quantum evolution. The isomorphism between the Wheeler-DeWitt equation in this Minisuperspace representation and the Klein-Gordon one for a relativistic scalar field allows to identify the positive and negative frequency solutions as associated to the collapsing and expanding Universe respectively. We clarify how any Bianchi I localized wave packet unavoidably spreads when the singularity is approached and therefore the semiclassical description of the model evolution in the Planckian region loses its predictability. Then, we calculate the transition amplitude that a collapsing Universe is turned into an expanding one, according to the standard techniques of relativistic quantum mechanics, thanks to the introduction of an ekpyrotic-like matter component which mimics a time-dependent potential term and breaks the frequency separation. In particular, the transition probability of this "Quantum Big Bounce" acquires a maximum value when the mean values of the momenta conjugate to the anisotropies in the collapsing Universe are close enough to the corresponding mean values in the expanding one, depending on the variances of the in-going and out-going Universe wave packets. This symmetry between the pre-Bounce and post-Bounce mean values reflects what happens in the semiclassical bouncing cosmology, with the difference that here the connection of the two branches takes place on a pure probabilistic level.

High harmonic spectra computed using time-dependent Kohn–Sham theory with Gaussian orbitals and a complex absorbing potential

High harmonic spectra for H2 and H2 + are simulated by solving the time-dependent Kohn-Sham equation in the presence of a strong laser field using an atom-centered Gaussian representation of the density and a complex absorbing potential. The latter serves to mitigate artifacts associated with the finite extent of the basis functions, including spurious reflection of the outgoing electronic wave packet. Interference between the outgoing and reflected waves manifests as peak broadening in the spectrum as well as the appearance of spurious high-energy peaks after the harmonic progression has terminated. We demonstrate that well-resolved spectra can be obtained through the use of an atom-centered absorbing potential. As compared to grid-based algorithms, the present approach is more readily extensible to larger molecules.

Photoelectron circular dichroism of a model chiral anion.

Photoelectron circular dichroism (PECD) in the one-photon detachment of a model chiral anionic system is studied theoretically by the single center method. The computed chiral asymmetry, characterized by the dichroic parameter β1 of up to about ±3%, is in good accord with the first experimental observations of the effect in photodetachment of amino acid anions [P. Krüger and K. M. Weitzel, Angew. Chem., Int. Ed. 60, 17861 (2021)]. Our findings confirm a general assumption that the magnitude of PECD is governed by the ability of an outgoing photoelectron wave packet to accumulate characteristic chiral asymmetry from the short-range part of the molecular potential.

Decoherence of charge density waves in beam splitters for interacting quantum wires

Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special case of an intersection of topological edge states. We derive an effective impurity model which represents the edge-state intersection within Luttinger liquid theory at low energy. For Luttinger K = 1 / 2 , we compute the exact time-dependent expectation values of the charge density as well as the density-density correlation functions. In general a single incoming charge density wave packet will split into four outgoing wave packets with transmission and reflection coefficients depending on the strengths of the tunnelling processes between the wires at the junction. We find that when multiple charge density wave packets from different directions pass through the intersection at the same time, reflection and splitting of the packets depend on the relative phases of the waves. Active use of this phase-dependent splitting of wave packets may make Luttinger interferometry possible. We also find that coherent incident packets generally suffer partial decoherence from the intersection, with some of their initially coherent signal being transferred into correlated quantum noise. In an extreme case four incident coherent wave packets can be transformed entirely into density-density correlations, with the charge density itself having zero expectation value everywhere in the final state.

Recovery of High-Energy Photoelectron Circular Dichroism through Fano Interference.

It is commonly accepted that the magnitude of a photoelectron circular dichroism (PECD) is governed by the ability of an outgoing photoelectron wave packet to probe the chiral asymmetry of a molecule. To be able to accumulate this characteristic asymmetry while escaping the chiral ion, photoelectrons need to have relatively small kinetic energies of up to a few tens of electron volts. Here, we demonstrate a substantial PECD for very fast photoelectrons above 500eV kinetic energy released from methyloxirane by a participator resonant Auger decay of its lowermost O 1s excitation. This effect emerges as a result of the Fano interference between the direct and resonant photoionization pathways, notwithstanding that their individual effects are negligibly small. The resulting dichroic parameter has an anomalous dispersion: It changes its sign across the resonance, which can be considered as an analogue of the Cotton effect in the x-ray regime.

Counter-propagating wave packets in the quantum transition state approach to reactive scattering.

The quantum transition state concept provides an intuitive and numerically efficient framework for the description of quantum state-resolved reactive scattering and thermal reaction processes. Combining multiconfigurational time-dependent Hartree wave packet dynamics calculations with a flux correlation function based analysis, rigorous full-dimensional calculations of initial state-selected and state-to-state reaction probabilities for six atom reactions are feasible. In these calculations, a set of wave packets is generated in the transition state region, propagated into the asymptotic area, and analyzed. In the present work, an alternative approach which employs counter-propagating sets of wave packets is introduced. Outgoing wave packets started in the transition state region are matched with incoming wave packets generated in the reactant (or product) asymptotic area. Studying the H + CH4 → H2 + CH3 reaction as a prototypical example, one finds that the incoming wave packets can be propagated closely up to the transition state region with minor numerical effort. Employing cross correlation functions of incoming and outgoing wavefunctions, the propagation times required for the outgoing wave packet and thus the numerical costs of the entire calculation can be reduced significantly. Detailed full-dimensional calculations studying initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction are presented to illustrate the new approach. It is found that converged results can be obtained using shorter propagation times of the outgoing wave packets and less single-particle functions.

Electron-electron interaction in graphene at finite Fermi energy

Using the Bethe-Salpeter equation in the leading approximation, we derive the wave equation describing the interaction of two electrons in graphene at arbitrary value of the Fermi energy EF. For the solutions of this equation, we have found the explicit forms of the density and the current which obey the continuity equation. We have traced the evolution of the wave packet during a scattering process. It is shown that the long-living localized quasi-stationary peak may appear at EF < 0. Then this peak decays into a set of wave packets following each other. At t → ∞ a total norm of all outgoing wave packets equals to that of incoming wave packet. At EF = 0 the localized state does not appear. For EF < 0 there is an infinite set of the localized solutions with the finite norms. We clearly demonstrate the qualitative difference of the results obtained on the bases of the Bethe-Salpeter equation and the results following from the wave equation where the Hamiltonian is a sum of the one-particle Hamiltonians and the electron-electron interaction potential.

Design of a dynamic sonar emitter inspired by hipposiderid bats

The ultrasonic emission of the biosonar systems of bats, such as Old World leaf-nosed bats (family Hipposideridae) and the related horseshoe bats (family Rhinolophidae), is characterized by a unique dynamics where baffle shapes (‘noseleaves’) deform while diffracting the outgoing wave packets. As of now, nothing comparable to this dynamics has been used in any related engineering application (e.g. sonar or radar). Prior work with simple concave baffle shapes has demonstrated the impact of the dynamics on the emission characteristics, but it has remained unclear whether this was simply due to the change in aperture size or also influenced by the geometrical shape detail. Hence, it has also remained unclear whether it would be possible to further enhance the time-variant effects reported so far through different static and dynamic geometries. To address this issue, we have created a dynamic emission baffle with biomimetic shape detail modeled after Pratt’s roundleaf bats (Hipposideros pratti). The impact of the dynamic deformation of the shape on the time-variant emission characteristics was evaluated by virtue of the gradient magnitude and the entropy in the gradient orientation. The results have shown that the dynamics results in much larger gradients in signal representation, which change jointly over direction and time.

Cavity-assisted spontaneous emission of a singleΛ-type emitter as a source of single-photon packets with controlled shape

The radiation emitted by a classically pumped three-level $\mathrm{\ensuremath{\Lambda}}$-type emitter in a resonator cavity featuring both radiative and unwanted losses is studied. In particular, the efficiency of one-photon Fock state excitation of the outgoing wave packet and the spatiotemporal shape of the wave packet are investigated. It is shown that, for a given shape of the emitter-cavity interaction, adjusting the shape of the pump pulse renders it possible to generate the emission of one-photon Fock state wave packets of desired shape with high efficiency.

Entropy of the information retrieved from black holes

The retrieval of black hole information was recently presented in two interesting proposals in the ‘Hawking Radiation’ conference: a revised version by Hooft of a proposal he initially suggested 20 years ago and, a new proposal by Hawking. Both proposals address the problem of black hole information loss at the classical level and derive an expression for the scattering matrix. The former uses gravitation back reaction of incoming particles that imprints its information on the outgoing modes. The latter uses supertranslation symmetry of horizons to relate a phase delay of the outgoing wave packet compared to their incoming wave partners. The difficulty in both proposals is that the entropy obtained from them appears to be infinite. By including quantum effects into the Hawking and Hooft’s proposals, I show that a subtlety arising from the inescapable measurement process, the quantum Zeno effect, not only tames divergences but it actually recovers the correct 1/4 of the area Bekenstein–Hawking entropy law of black holes.

Quantifying the noseleaf and pulse dynamics in rhinolophid and hipposiderid bats

Horseshoe bats (Rhinolophidae) and Old-World leaf-nosed bats (Hipposideridae) are two related bat families that emit their biosonar pulses nasally and diffract the outgoing wave-packets with elaborate baffle shapes (“noseleaves”). Since the noseleaf surfaces are frequently in motion during pulse emission, an experimental setup has been established to characterize the dynamics in their geometry in conjunction with the effects that this dynamics may have on the ultrasonic pulses. To achieve this goal, greater horseshoe bats (Rhinolophus ferrumequinum), great roundleaf bats (Hipposideros armiger), and Pratt's roundleaf bats (Hipposideros pratti) were trained to emit biosonar pulses while seated on a platform. At least 10 landmarks were placed on the noseleaves of the animals to track the dynamic geometry of these structures with an array of four high-speed video cameras (frame rate 400 Hz). Pairs of video frames were used to reconstruct the 3d trajectories of the noseleaf landmarks, and from these trajectori...

Dynamics of biosonar systems in Horseshoe bats

Horseshoe bats have an active ultrasonic sonar system that allows the animals to navigate and hunt prey in structure-rich natural environments. The physical components of this biosonar system contain an unusual dynamics that could play a key role in achieving the animals’ superior sensory performance. Horseshoe bat biosonar employs elaborate baffle shapes to diffract the outgoing and incoming ultrasonic wave packets; ultrasound is radiated from nostrils that are surrounded by noseleaves and received by large outer ears. Noseleaves and pinnae can be actuated while ultrasonic diffraction takes place. On the emission side, two noseleaf parts, the anterior leaf and the sella, have been shown to be in motion in synchrony with sound emission. On the reception side, the pinnae have been shown to change their shapes by up to 20% of their total length within ∼100 milliseconds. Due to these shape changes, diffraction of the incoming and outgoing waves is turned into a dynamic physical process. The dynamics of the diffraction process results in likewise dynamic device characteristics. If this additional dynamic dimension was found to enhance the encoding of sensory information substantially, horseshoe bat biosonar could be a model for the use of dynamic physical processes in sensing technology.

Wave-packet dynamics and valley filter in strained graphene

The time evolution of a wave packet in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudomagnetic field, on the wave-packet trajectories and zitterbewegung are analyzed. Combining the effects of strain with those of an external magnetic field produces an effective magnetic field which is large in one of the Dirac cones, but can be practically zero in the other. We construct an efficient valley filter, where for a propagating incoming wave packet consisting of momenta around the $K$ and ${K}^{\ensuremath{'}}$ Dirac points, the outgoing wave packet exhibits momenta in only one of these Dirac points while the components of the packet that belong to the other Dirac point are reflected due to the Lorentz force. We also found that the zitterbewegung is permanent in time in the presence of either external or strain-induced magnetic fields, but when both the external and strain-induced magnetic fields are present, the zitterbewegung is transient in one of the Dirac cones, whereas in the other cone the wave packet exhibits permanent spatial oscillations.

Time-Resolved Femtosecond Photoelectron Spectroscopy by Field-Induced Surface Hopping

We present the extension of our field-induced surface hopping method for the description of the photoionization process and the simulation of time-resolved photoelectron spectra (TRPES). This is based on the combination of nonadiabatic molecular dynamics "on the fly" in the framework of TDDFT generalized for open shell systems under the influence of laser fields with the approximate quantum mechanical description of the photoionization process. Since arbitrary pulse shapes can be employed, this method can be also combined with the optimal control theory in order to steer the photoionization or to shape the outgoing electronic wavepackets. We illustrate our method for the simulation of TRPES on the prototype system of Ag(3), which involves excitation from the equilibrium triangular geometry, as well as excitation from the linear transition state, where in both cases nonadiabatic relaxation takes place in a complex manifold of electronic states. Our approach represents a generally applicable method for the prediction of time-resolved photoelectron spectra and their analysis in systems with complex electronic structure as well as many nuclear degrees freedom. This theoretical development should serve to stimulate new ultrafast experiments.

Bond breaking in light-induced potentials

We study the photodissociation of ICl(-) under moderately strong (TW/cm(2)) and short (below picosecond) laser pulses. Using a single resonant pump pulse, the photodissociation spectra shows two barely overlapping bands corresponding to Frank-Condon excitation and dissociation in two electronic states. By adding a nonresonant stronger control pulse we show that (1) the photodissociation bands can be blueshifted and (2) the asymptotic state of the fragments depends on the chosen pulse sequence. If the pump pulse precedes the control pulse or the control pulse straddles the pump pulse, the outgoing wave packet has components in the two dissociation channels, whereas if the control pulse precedes the pump pulse, the photodissociation proceeds selectively in a single channel.

Cavity-assisted spontaneous emission as a single-photon source: Pulse shape and efficiency of one-photon Fock-state preparation

Within the framework of exact quantum electrodynamics in dispersing and absorbing media, we have studied the quantum state of the radiation emitted from an initially in the upper state, prepared two-level atom in a high-$\mathit{Q}$ cavity, including the regime where the emitted photon belongs to a wave packet that simultaneously covers the areas inside and outside the cavity. For both continuing atom-field interaction and short-term atom-field interaction, we have determined the spatiotemporal shape of the excited outgoing wave packet and calculated the efficiency of the wave packet to carry a one-photon Fock state. Furthermore, we have made contact with quantum noise theories where the intracavity field and the field outside the cavity are regarded as approximately representing independent degrees of freedom such that two separate Hilbert spaces can be introduced.

A rigorous analysis of high-order electromagnetic invisibility cloaks**Research partially supported by CONACYT under Project P42553-F.

There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al that are based on the transformation approach. They obtained their results using first-order transformations. In recent papers, Hendi et al and Cai et al considered invisibility cloaks with high-order transformations. In this paper, we study high-order electromagnetic invisibility cloaks in transformation media obtained by high-order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. We prove that for any incident plane wave, at any frequency, the scattered wave is identically zero. We also consider the scattering of finite-energy wave packets. We prove that the scattering matrix is the identity, i.e., that for any incoming wave packet the outgoing wave packet is the same as the incoming one. This proves that the invisibility cloaks cannot be detected in any scattering experiment with electromagnetic waves in high-order transformation media, and in particular in the first-order transformation media of Pendry et al. We also prove that the high-order invisibility cloaks, as well as the first-order ones, cloak passive and active devices. The cloaked objects completely decouple from the exterior. Actually, the cloaking outside is independent of what is inside the cloaked objects. The electromagnetic waves inside the cloaked objects cannot leave the concealed regions and vice versa, the electromagnetic waves outside the cloaked objects cannot go inside the concealed regions. As we prove our results for media that are obtained by transformation from general anisotropic materials, we prove that it is possible to cloak objects inside general crystals.