Spreading Of Wave Packet Research Articles

Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: Engineering of mobility gaps and multifractal states

In this study, we examine whether periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases that have no counterparts in the static model. Specifically, we consider the Aubry-Andr\'e model, which is a one-dimensional time-independent model with an on-site quasiperiodic potential ${V}_{0}$ and a nearest-neighbor hopping amplitude that is taken to have a staggered form. We add a uniform hopping amplitude that varies in time either sinusoidally or as a square pulse with a frequency $\ensuremath{\omega}$. Unlike the static Aubry-Andr\'e model, which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases for the Floquet eigenstates: a phase with gapless quasienergy bands and only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios that scale with the system size with exponents that are different from the values for both extended and localized states. In addition, we observe intricate reentrant transitions between the different kinds of states when $\ensuremath{\omega}$ and ${V}_{0}$ are varied. The appearance of such transitions is confirmed by the behavior of the Shannon entropy. Many of our numerical results can be understood from an analytic Floquet Hamiltonian derived using a Floquet perturbation theory that uses the inverse of the driving amplitude as the perturbation parameter. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet, and we find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a nonmonotonic dependence on ${V}_{0}$ that does not occur in the static model. Finally, we compare the results for the driven model, which has a static staggered hopping amplitude, with a model that has a static uniform hopping amplitude, and we find some significant differences between the two cases. All of our results are found to be independent of the driving protocol, either sinusoidal or square pulse. We conclude that the interplay of the quasiperiodic potential and driving produces a rich phase diagram that does not appear in the static model.

Dynamic skin effects in non-Hermitian systems

We study the time evolution processes of non-Hermitian systems under the open boundary condition and confirm that the dynamical skin effect exists in non-Hermitian systems analytically, and unveil the mechanism of its formation, which is caused by both the non-Hermitian skin effect and the Hermitian wave packet spreading. Furthermore, we find that in contrast to the uniform speed motion in Hermitian situations, the Gaussian wave packet can be accelerated and amplified during its time evolution in non-Hermitian systems. This additional motion is found to be responsible for the dynamic skin effect.

Floquet band engineering with Bloch oscillations

This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wavepacket but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-Andr\'e-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands or Floquet bands with large Chern numbers due to the interplay between the periodic driving and Bloch oscillations can be obtained, with the band structure and topology extensively tunable by adjusting the ratio of two competing frequencies. To confirm our finding, we further execute the Thouless pumping of one and two interacting bosons in such a lattice system and establish its connection with the topological properties of single- and two-particle Floquet bands.

Where neutrino decoherence lies

Recently, several studies of neutrino oscillations in the vacuum have not found the decoherence long expected from the separation of wave packets of neutrinos in different mass eigenstates. We show that such decoherence will, on the other hand, be present in a treatment including any mechanism which leads to a dependence of the final state on both the neutrino’s emission and absorption time. Using a simplified model in 1+1d, we show that if the positions of the final state particles are measured, or equivalently entangled with the environment, then decoherence will damp neutrino oscillations. We also show that wave packet spreading can cause the decoherence to eventually saturate, without completely suppressing the oscillations. These results are not an artifact of the approximation used: we show that, considering the V-A model in 3+1d, the difference would be simply a total multiplicative factor that would not affect the oscillation probability nor the decoherence.

S0 Lamb Mode Scattering Studies in Laminated Composite Plate Structures with Surface Breaking Cracks: Insights into Crack Opening Behavior

Ultrasonic-guided waves are attractive for rapid inspection of laminated composite structures, where cracks developed transverse to the loading direction are the severe type of damage. This paper presents studies of the interaction of fundamental symmetric S0 Lamb mode with vertical surface-breaking cracks in laminated composite plate structures. Finite element simulations and experimental investigations are used to study the effect of crack depth on S0 wave reflection behavior. Results show a monotonic rise of the reflection coefficient for different crack depths in a manner that is strongly dependent on the orientation of the plies and transverse ply location in the vicinity of the crack. Scattered wave packets in the reflection regime are captured using an in-plane laser. The S0 Lamb mode's sensitivity is numerically presented for the different crack depths in the long wavelength limit. We also observed that the reflected wave mode depicts the information of the corresponding broken interfaces. An attempt was made to show that this behavior relates to the crack-opening behavior in response to in-plane excitation. The reflection coefficient as a characteristic polynomial is proposed for various orientations. It was observed that the dispersion at receiver nodes makes the analysis challenging for distinguishing the signal from crack faces due to the smaller dimension. The study outcomes show its prospect as a promising NDE tool for crack damage detection in thin laminated plate structures.

Wave packet spreading with periodic, Fibonacci quasiperiodic, and random nonlinear discrete-time quantum walks

Wave packet spreading with periodic, Fibonacci quasiperiodic, and random nonlinear discrete-time quantum walks

Aharonov-Bohm cages, flat bands, and gap labeling in hyperbolic tilings

Aharonov-Bohm caging is a localization mechanism stemming from the competition between the geometry and the magnetic field. Originally described for a tight-binding model in the dice lattice, this destructive interference phenomenon prevents any wavepacket spreading away from a strictly confined region. Accordingly, for the peculiar values of the field responsible for this effect, the energy spectrum consists of a discrete set of highly degenerate flat bands. In the present work, we show that Aharonov-Bohm cages are also found in an infinite set of hyperbolic dice tilings defined on a negatively curved hyperbolic plane. We detail the construction of these tilings and compute their Hofstadter butterflies by considering periodic boundary conditions on high-genus surfaces. As recently observed for some regular hyperbolic tilings, these butterflies do not manifest the self-similar structure of their Euclidean counterparts but still contain some gaps. We also consider the energy spectrum of hyperbolic kagome tilings (which are the dual of hyperbolic dice tilings), which displays interesting features, such as highly degenerate states arising for some particular values of the magnetic field. For these two families of hyperbolic tilings, we compute the Chern number in the main gaps of the Hofstadter butterfly and propose a gap labeling inspired by the Euclidean case. Finally, we also study the triangular Husimi cactus, which is a limiting case in the family of hyperbolic kagome tilings, and we derive an exact expression for its spectrum versus magnetic flux.

Wave-packet spreading in disordered soft architected structures.

We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice, which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of Deng et al. [Nat. Commun. 9, 1 (2018)]. This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site), which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered, and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media.

Comparison of the semiclassical and quantum dynamics of the Bianchi I cosmology in the polymer and GUP extended paradigms

We compare in some detail Polymer Quantum Mechanics and the Generalized Uncertainty Principle approach to clarify to what extent we can treat them on the same footing. We show that, while on a semiclassical level they may be formulated as similar modifications of the Poisson algebra, on a quantum level they intrinsically differ because PQM implies no absolute minimal uncertainty on position. Then we implement these schemes to Bianchi I cosmology on a semiclassical level deforming only the algebra of the Universe volume, searching for alternative formulations able to account for the modified Friedmann equations emerging in Brane Cosmology and Loop Quantum Cosmology. On a pure quantum level, we implement the two approaches through their original setups and reduce the two resulting Wheeler–DeWitt equations to the same morphological structure, showing how the polymer formalism is associated with a bouncing dynamics while in the Generalized Uncertainty Principle case the singularity is still present. The implications of the wavepacket spreading are also discussed in both approaches, outlining that, when the singularity survives, the Planckian era must necessarily be approached by a fully quantum (non-peaked) state of the Universe.

Passage of a vortex electron over an inclined grating

We study Smith-Purcell radiation from a conducting grating generated by an inclined passage of a shaped electron wave packet with an electric quadrupole moment in the nonparaxial regime. Spreading of an asymmetric wave packet induces quadrupole corrections to the radiation field. Although the nonparaxial corrections stay small, they are dynamically enhanced during the interaction of the electron with the grating whose length exceeds the Rayleigh length of the packet. To simplify the possible experimental setup where such effects could be measured, we study the dependence of these effects on the inclination angle, i.e., the angle between the mean velocity of the packet and the surface of the grating. There is a minimal angle such that the multipole expansion always stays valid at the grating surface. In such a regime, the quadrupole contribution to the Smith-Purcell radiation can become the leading one, which represents a quantum effect impossible for classical pointlike electrons. Thus, the impact of the wave-packet shape (vortex structure or nonspherical shape) can be observed experimentally by comparing the radiation for different orientations of the grating in the single-electron regime.

On free fall of quantum matter

We propose an approach that allows to systematically take into account gravity in quantum particle physics. It is based on quantum field theory and the general principle of relativity. These are used to build a model for quantum particles in curved spacetime. We compute by its means a deviation from a classical geodesic in the Earth’s gravitational field. This shows that free fall depends on quantum- matter properties. Specifically, we find that the free-fall universality and the wave-packet spreading are mutually exclusive phenomena. We then estimate the Eötvös parameter for a pair of atoms freely falling near the Earth’s surface, provided that the wave-packet spreading is more fundamental than the weak equivalence principle.

Frequency Map Analysis of Spatiotemporal Chaos in the Nonlinear Disordered Klein–Gordon Lattice

We study the characteristics of chaos evolution of initially localized energy excitations in the one-dimensional nonlinear disordered Klein–Gordon lattice of anharmonic oscillators, by computing the time variation of the fundamental frequencies of the motion of each oscillator. We focus our attention on the dynamics of the so-called “weak chaos” and “strong chaos” spreading regimes [Laptyeva et al., 2010], for which Anderson localization is destroyed, as the initially restricted excitation at the central region of the lattice propagates in time to more lattice sites. Based on the fact that large variations of the fundamental frequencies denote strong chaotic behavior, we show that in both regimes chaos is more intense at the central regions of the wave packet, where also the energy content is higher. On the other hand, the oscillators at the wave packet’s edges, through which the energy propagation happens, exhibit regular motion up until the time they gain enough energy to become part of the highly excited portion of the wave packet. Eventually, the percentage of chaotic oscillators remains practically constant, despite the fact that the number of excited sites grows as the wave packet spreads, but the portion of highly chaotic sites decreases in time. Thus, albeit the number of chaotic oscillators is constantly growing the strength of their chaotic behavior decreases, indicating that although chaos persists it is becoming weaker in time. We show that the extent of the zones of regular motion at the edges of the wave packet in the strong chaos regime is much smaller than in the weak chaos case. Furthermore, we find that in the strong chaos regime the chaotic component of the wave packet is not only more extended than in the weak chaos one, but in addition the fraction of strongly chaotic oscillators is much higher. Another important difference between the weak and strong chaos regimes is that in the latter case a significantly larger number of frequencies is excited, even from the first stages of the evolution. Moreover, our computations confirmed the shifting of fundamental frequencies outside the normal mode frequency band of the linear system in the case of the so-called “selftrapping” regime where a large part of the wave packet remains localized.

Optimal control of photodissociation of phenol using genetic algorithm

Photodissociation dynamics of the OH bond of phenol is studied with an optimally shaped laser pulse. The theoretical model consists of three electronic states (the ground electronic state, ππ* state, and πσ* state) in two nuclear coordinates (the OH stretching coordinate as a reaction coordinate, r, and the CCOH dihedral angle as a coupling coordinate, θ). The optimal UV laser pulse is designed using the genetic algorithm, which optimizes the total dissociative flux of the wave packet. The latter is calculated in the adiabatic asymptotes of the S0 and S1 electronic states of phenol. The initial state corresponds to the vibrational levels of the electronic ground state and is defined as |nr, nθ⟩, where nr and nθ represent the number of nodes along r and θ, respectively. The optimal UV field excites the system to the optically dark πσ* state predominantly over the optically bright ππ* state with the intensity borrowing effect for the |0, 0⟩ and |0, 1⟩ initial states. For the |0, 0⟩ initial condition, the photodissociation to the S1 asymptotic channel is favored slightly over the S0 asymptotic channel. Addition of one quantum of energy along the coupling coordinate increases the dissociation probability in the S1 channel. This is because the wave packet spreads along the coupling coordinate on the πσ* state and follows the adiabatic path. Hence, the S1 asymptotic channel gets more (∼11%) dissociative flux as compared to the S0 asymptotic channel for the |0, 1⟩ initial condition. The |1, 0⟩ and |1, 1⟩ states are initially excited to both the ππ* and πσ* states in the presence of the optimal UV pulse. For these initial conditions, the S1 channel gets more dissociative flux as compared to the S0 channel. This is because the high energy components of the wave packet readily reach the S1 channel. The central frequency of the optimal UV pulse for the |0, 0⟩ and |0, 1⟩ initial states has a higher value as compared to the |1, 0⟩ and |1, 1⟩ initial states. This is explained with the help of an excitation mechanism of a given initial state in relation to its energy.

Unusual wave-packet spreading and entanglement dynamics in non-Hermitian disordered many-body systems

Non-Hermiticity and dephasing, collaborating in an unusual wave packet dynamics, realizes unconventional entanglement evolution in a disordered, interacting and asymmetric (non-reciprocal) quantum medium. Taking the Hatano-Nelson model as a concrete example, we first consider how wave packet spreads in a non-Hermitian disordered system for demonstraing that it is very different from the Hermitian case. Interestingly, a cascade like wave packet spreading as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its non-monotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems, and show that the many-body dynamics is governed by a principle different from the Hermitian case. The size dependence of the results suggests with the increase of disorder, a unusual area-volume-area law crossover of the maximal entanglement entropy. To analyze the effects of disorder on a firm basis, using the Hermitian limit as a benchmark, we employ a quasi-periodic disorder (Aubry-Andr\'{e} model) in the analyses.

Energy transport in one-dimensional oscillator arrays with hysteretic damping

Energy transport in 1-dimensional oscillator arrays has been extensively studied to date in the conservative case, as well as under weak viscous damping. When driven at one end by a sinusoidal force, such arrays are known to exhibit the phenomenon of supratransmission, i.e. a sudden energy surge above a critical driving amplitude. In this paper, we study 1-dimensional oscillator chains in the presence of hysteretic damping, and include nonlinear stiffness forces that are important for many materials at high energies. We first employ Reid's model of local hysteretic damping, and then study a new model of nearest neighbor dependent hysteretic damping to compare their supratransmission and wave packet spreading properties in a deterministic as well as stochastic setting. The results have important quantitative differences, which should be helpful when comparing the merits of the two models in specific engineering applications.

Universal dynamical scaling laws in three-state quantum walks.

We perform a finite-time scaling analysis over the detrapping point of a three-state quantum walk on the line. The coin operator is parametrized by ρ that controls the wave packet spreading velocity. The input state prepared at the origin is set as a symmetric linear combination of two eigenstates of the coin operator with a characteristic mixing angle θ, one of them being the component that results in full spreading occurring at θ_{c}(ρ) for which no fraction of the wave packet remains trapped near the initial position. We show that relevant quantities, such as the survival probability and the participation ratio assume single parameter scaling forms at the vicinity of the detrapping angle θ_{c}. In particular, we show that the participation ratio grows linearly in time with a logarithmic correction, thus, shedding light on previous reports of sublinear behavior.

Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators

Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent articles, including pseudodifferential, Fourier integral and metaplectic operators, with applications to the analysis of Schrödinger-type evolution equations. It has been proved that such operators are approximately diagonalized by Gabor wave packets. While the latter are expected to undergo some spreading phenomenon, there is no record of this issue in the aforementioned results. In this note we prove refined estimates for the Gabor matrix of metaplectic operators, also of generalized type, where sparsity, spreading and dispersive properties are all noticeable. We provide applications to the propagation of singularities for the Schrödinger equation.

Optimal control for suppressing wave-packet spreading with strong nonresonant laser pulses

We use nonlinear optimal control simulation to systematically examine how to suppress wave-packet spreading with strong nonresonant near-infrared (NIR) laser pulses through a case study of a vibrational wave packet in the $B$ state of ${\mathrm{I}}_{2}$. As the degree of spreading of the vibrational wave packet is controllable by adjusting the pump pulse shape, the vibrational wave packet may be regarded as a prototype system to study spreading suppression by using nonresonant laser pulses. We quantitatively define spreading suppression in terms of the probability of finding the wave packet in the analytically defined, initially excited state at every vibrational period. From optimal control simulation and simulation by using model Gaussian pulse trains that mimic optimal pulses, we conclude that a simple periodic NIR pulse train without highly tuned temporal widths, amplitudes, or irradiation timings can almost perfectly stop the wave-packet spreading over a long control period, provided that the degree of spreading is not too large.

Intense quasi-monochromatic resonant harmonic generation in the multiphoton ionization regime

Resonant high-order harmonics, which result in quasi-monochromatic extreme ultraviolet light with coherent intensity enhancement involving autoionizing resonances, have been demonstrated from laser-ablated plumes in the tunnel-ionization regime. Here, we demonstrate resonant harmonics in the previously unexplored multiphoton-ionization regime. We demonstrate an intense resonant harmonic from gallium with an intensity enhancement ratio of 714 relative to the neighboring harmonics, achieved without the need for extreme ultraviolet filtering methods, thus preventing a typical photon flux loss of more than 70%. Three-dimensional time-dependent Schrödinger equation calculations reveal that this increase in the enhancement ratio is due to the low electron wave packet spreading in the multiphoton-ionization regime. These results reveal a method for increasing the intensity and monochromaticity of intense multimicrojoule femtosecond extreme ultraviolet light and will also facilitate understanding of the involvement of autoionizing resonances in generating resonant harmonics in the multiphoton-ionization regime.

Quantum diffusion of massive Dirac fermions induced by symmetry breaking

We show that when a two-dimensional $(2\mathrm{D})$ Dirac fermion moves in disordered environments, the weak time-reversal symmetry breaking by a small mass gives rise to the diffusive wave propagation, i.e., that the wave-packet spread obeys the diffusive law of Einstein, up to a---practically inaccessible---exponentially large length. Strikingly, the diffusion constant is larger than that given by the Boltzmann kinetic theory, and grows unboundedly as the energy-to-mass ratio increases. This diffusive phenomenon is of quantum nature and different from weak antilocalization. It implies a new type of transport in topological insulators at zero temperature.