Spreading Of Wave Packet Research Articles

Negative Probability Current in a Freely Falling Quantum Particle

A quantum particle (represented by a Gaussian wave packet) under uniform gravity, projected upward (the conventional positive direction) along the vertical degree of freedom x, may have a negative probability current on a set of points q. This imposes the condition that the position and momentum observables of the state are negatively correlated. We calculate the effect of the negative correlation on the individual contributions to the probability current by the positive and negative momentum amplitudes of the state using an integral representation of the probability current. Negative position-momentum correlation causes a transient attenuation of all contributions to the probability flow, and wave packet spreading is temporarily mitigated.

Dynamical evolution in a one-dimensional incommensurate lattice with PT symmetry

We investigate the dynamical evolution of a parity-time ($\mathcal{PT}$) symmetric extension of the Aubry-Andr\'{e} (AA) model, which exhibits the coincidence of a localization-delocalization transition point with a $\mathcal{PT}$ symmetry breaking point. One can apply the evolution of the profile of the wave packet and the long-time survival probability to distinguish the localization regimes in the $\mathcal{PT}$ symmetric AA model. The results of the mean displacement show that when the system is in the $\mathcal{PT}$ symmetry unbroken regime, the wave-packet spreading is ballistic, which is different from that in the $\mathcal{PT}$ symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different $\mathcal{PT}$ symmetric regimes.

Localization properties of a discrete-time 1D quantum walk with generalized exponential correlated disorder

We study the dynamics of the 1D Hadamard quantum walk featuring generalized exponential correlated phase disorder. We report the existence of distinct dynamical regimes and discuss the prospect of a judicious tuning of the strength of localization of the walker via the degree of correlation. In particular, we unveil that when the typical correlation length is smaller than the chain size, the maximum spreading of the quantum wavepacket is achieved when the underlying disorder displays Gaussian correlations. Our work provides a framework for investigating the weakening of Anderson localization due to correlated disorder and may also find applications in the context of quantum information processing.

Damage localization in composite plates that exploits edge-reflected Lamb waves

Lamb waves can travel a relatively long distance in the plate-like structures. Reflection and scattering may occur when they arrive at an obstacle, and the associated wave packets may contain the information about the obstacle and the whole path they travel through. Those extra reflections change the direction once they meet an obstacle, which enlarges the monitoring zone and enriches the inspecting directions. The motivation and objective of this paper is to exploit the information included in these reflections for damage identification. Firstly, dispersion compensation is applied to the residual between the measured signal and the pre-recorded baseline. Thus the propagation distance of each scattered wave packet could be estimated. On this basis, the sparse reconstruction algorithm is modified to adapt to both direct-scattered waves and indirect-scattered waves for damage identification. Two experimental examples are conducted on CFRP laminates, where damage is correctly identified with the minimum sensor array consisting of one transmitter and one receiver.

Higher harmonic generation from bilayer nanostructures assisted by electron backscattering

In the framework of time-dependent density functional theory, we obtain high-order harmonics of photon energies up to 10 Up from bilayer crystals with an interlayer spacing d = 70 {\AA}. At grazing incidence, a clear double-plateau structure is observed in the harmonic spectrum. The photon energy of the second plateau far beyond atomic-like harmonics can be well explained by the inclusion of backscattering of ionized electrons. Ab initio simulations reveal that the cutoff of the second plateau is continuously extended with an increasing d. Our classical calculations predict that the maximum electronic kinetic energy is linearly dependent on d over a wide range. Moreover, the harmonic yield in the second plateau is significantly enhanced by increases in the wavelength of the driving laser. Owing to the confined spreading of the electronic wave packet, a beneficial wavelength scaling of {\lambda}2.85 is obtained. This study therefore establishes a novel and efficient way of producing high-energy light source based on layered nanostructures.

Density resolved wave packet spreading in disordered Gross-Pitaevskii lattices

We perform novel energy and norm density resolved wave packet spreading studies in the disordered Gross-Pitaevskii (GP) lattice to confine energy density fluctuations. We map the locations of GP regimes of weak and strong chaos subdiffusive spreading in the 2D density control parameter space and observe strong chaos spreading over several decades. We obtain a renormalization of the ground state due to disorder, which allows for a new disorder-induced phase of disconnected insulating puddles of matter due to Lifshits tails. Inside this Lifshits phase, the wave packet spreading is substantially slowed down.

Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy

As recently manifested [], the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the inter-particle interaction is strong enough, thus resulting in a chaotic structure of the many-body eigenstates considered in the non-interacting basis. The semi-analytical approach used here, allows one to estimate the rate of the exponential growth as well as the relaxation time, after which the equilibration (thermalization) emerges. The key ingredient parameter in the description of this process is the width Γ of the local density of states (LDoS) defined by the initially excited state, the number of particles and the interaction strength. In this paper we show that apart from the meaning of Γ as the decay rate of survival probability, the width of the LDoS is directly related to the diagonal entropy and the latter can be linked to the thermodynamic entropy of a system equilibrium state emerging after the complete relaxation. The analytical expression relating the two entropies is derived phenomenologically and numerically confirmed in a model of bosons with random two-body interaction, as well as in a deterministic model which becomes completely integrable in the continuous limit.

Quantum walk versus classical wave: Distinguishing ground states of quantum magnets by spacetime dynamics

We investigate the wavepacket spreading after a single spin flip in prototypical two-dimensional ferromagnetic and antiferromagnetic quantum spin systems. We find characteristic spatial magnon density profiles: While the ferromagnet shows a square-shaped pattern reflecting the underlying lattice structure, as exhibited by quantum walkers, the antiferromagnet shows a circular-shaped pattern which hides the lattice structure and instead resembles a classical wave pattern. We trace these fundamentally different behaviors back to the distinctly different magnon energy-momentum dispersion relations and also provide a real-space interpretation. Our findings point to new opportunities for real-time, real-space imaging of quantum magnets both in materials science and in quantum simulators.

Complete classification of trapping coins for quantum walks on the two-dimensional square lattice

One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, albeit the system is translationally invariant. The effect is dependent on the dimension and the explicit form of the local coin. A four state discrete-time quantum walk on a square lattice is defined by its unitary coin operator, acting on the four dimensional coin Hilbert space. The well known example of the Grover coin leads to a partial trapping, i.e., there exists some escaping initial state for which the probability of staying at the initial position vanishes. On the other hand, some other coins are known to exhibit strong trapping, where such escaping state does not exist. We present a systematic study of coins leading to trapping, explicitly construct all such coins for discrete-time quantum walks on the 2D square lattice, and classify them according to the structure of the operator and the manifestation of the trapping effect. We distinguish three types of trapping coins exhibiting distinct dynamical properties, as exemplified by the existence or non-existence of the escaping state and the area covered by the spreading wave-packet.

Quantum walks with sequential aperiodic jumps.

We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse, and Rudin-Shapiro. We use a generalized Hadamard coin, C[over ̂]_{H}, as well as a generalized Fourier coin, C[over ̂]_{K}. We verify the QW experiences a slowdown of the wave packet spreading, σ^{2}(t)∼t^{α}, by the aperiodic jumps whose exponent, α, depends on the type of aperiodicity. Additional aperiodicity-induced effects also emerge, namely, (1) while the superdiffusive regime (1<α<2) is predominant, α displays an unusual sensibility with the type of coin operator where the more pronounced differences emerge for the Rudin-Shapiro and random protocols and (2) even though the angle θ of the coin operator is homogeneous in space and time, there is a nonmonotonic dependence of α with θ. Fingerprints of the aperiodicity in the hoppings are also found when distributional measures such as the Shannon and von Neumann entropies, the Inverse Participation Ratio, the Jensen-Shannon dissimilarity, and the kurtosis are computed, which allow assessing informational and delocalization features arising from these protocols and understanding the impact of linear and nonlinear correlations of the jump sequence in a quantum walk as well. Finally, we argue the spin-lattice entanglement is enhanced by aperiodic jumps.

Chaotic wave-packet spreading in two-dimensional disordered nonlinear lattices.

We reveal the generic characteristics of wave-packet delocalization in two-dimensional nonlinear disordered lattices by performing extensive numerical simulations in two basic disordered models: the Klein-Gordon system and the discrete nonlinear Schrödinger equation. We find that in both models (a) the wave packet's second moment asymptotically evolves as t^{a_{m}} with a_{m}≈1/5 (1/3) for the weak (strong) chaos dynamical regime, in agreement with previous theoretical predictions [S. Flach, Chem. Phys. 375, 548 (2010)CMPHC20301-010410.1016/j.chemphys.2010.02.022]; (b) chaos persists, but its strength decreases in time t since the finite-time maximum Lyapunov exponent Λ decays as Λ∝t^{α_{Λ}}, with α_{Λ}≈-0.37 (-0.46) for the weak (strong) chaos case; and (c) the deviation vector distributions show the wandering of localized chaotic seeds in the lattice's excited part, which induces the wave packet's thermalization. We also propose a dimension-independent scaling between the wave packet's spreading and chaoticity, which allows the prediction of the obtained α_{Λ} values.

Temporal changes in the distinct scattered wave packets associated with earthquake swarm activity beneath the Moriyoshi-zan volcano, northeastern Japan

We investigated temporal changes in the waveforms of S-coda from triggered earthquakes around the Moriyoshi-zan volcano in northeastern Japan. Seismicity in the area has drastically increased after the 2011 off the Pacific coast of Tohoku earthquake, forming the largest cluster to the north of the volcano. We analyzed distinct scattered wave packets (DSW) that are S-to-S scattered waves from the mid-crust and appeared predominantly at the high frequency range. We first investigated the variation of DSW for event groups with short inter-event distances and high cross-correlation coefficients (CC) in the time window of direct waves. Despite the above restriction, DSW showed temporal changes in their amplitudes and shapes. The change occurred gradually in some cases, but temporal trends were much more complicated in many cases. We also found that the shape of DSW changed in a very short period of time, for example, within ~ 12 h. Next, we estimated the location of the origin of the DSW (DSW origin) by applying the semblance analysis to the data of the temporary small-aperture array deployed to the north of the largest cluster of triggered events. The DSW origin is located between the largest cluster within which hypocentral migration had occurred and the low-velocity zone depicted by a tomographic study. This spatial distribution implies that the DSW origin was composed of geofluid-accumulated midway in the upward fluid movement from the low-velocity zone to the earthquake cluster. Though we could not entirely exclude the possibility of the effect of the event location and focal mechanisms, the temporal changes in DSW waveforms possibly reflect the temporal changes in scattering properties in and/or near the origin. The quick change in DSW waveforms implies that fast movement of geofluid can occur at the depth of the mid-crust.

Multiband effects in equations of motion of observables beyond the semiclassical approach

The equations of motion (EOM) for the position and gauge invariant crystal momentum are considered for multiband wave packets of Bloch electrons. For a localized packet in a subset of bands well-separated from the rest of the band structure of the crystal, one can construct an effective electromagnetic Hamiltonian with respect to the center of the packet. We show that the EOM can be obtained via a projected operator procedure, which is derived from the adiabatic approximation within perturbation theory. These relations explicitly contain information from each band captured in the expansion coefficients and energy band structure of the Bloch states as well as non-Abelian features originating from interband Berry phase properties. This general and transparent Hamiltonian-based approach is applied to a wave packet spread over a single band, a set of degenerate bands, and two linear crossing bands. The generalized EOM hold promise for novel effects in transport currents and Hall effect phenomena.

The origin of the spooky behavior of quantum particles: Time reversal

In this paper, we study the origin of the quantum particle entanglement. Particles will have one mixed wave function as soon as they are created, which are called quantum particle entanglement. Electron spin states are used as an example to discuss this topic. When two electrons are created simultaneously, they have two different mixed quantum spin states. Before the measurement of its spin, we cannot determine its spin state. However, as soon as the spin of one of the electrons is determined (measured), the spin of the other will definitely be in the opposite state, regardless of how far they are away from each other. This paper uses the mechanism that the wave packet spreads as soon as they are created and then the wave packet shrinks when it undergoes a measurement to interpret this spooky phenomenon mentioned above.

Richardson diffusion in neurons.

The dynamics of an initial wave packet affected by random noise is considered in the framework of a comb model. The model is relevant to a diffusion problem in neurons where the transport of ions can be accelerated by an external random field due to synapse fluctuations. In the present specific case, it acts as boundary conditions, which lead to a reaction transport equation with multiplicative noise. The temporal behavior of the mean squared displacement is estimated analytically, and it is shown that the spreading of the initial wave packet corresponds to Richardson diffusion.

Chaos-assisted localization and delocalization of a particle in a driven optical lattice

Abstract We investigate quantum chaotic dynamics of a single particle held in a weak amplitude- and tilt-modulated optical lattice with frequency resonance, by using the classical-quantum mixing method. Based on the macroscopic heteroclinic orbit tending to the chaotic “sea” of classical phase space, the quantum chaotic coherent states of the microscopic system are constructed, which show classical-quantum correspondence well. We illustrate the chaotic parameter regions and demonstrate that chaos causes the spread of wave packets and transfers the multiple quantum levels into a single chaotic band. The quantum expected orbit sensitively depends on the initial conditions and system parameters, meaning the famous quantum butterfly effect. Such an effect may lead to the chaotic dynamical localization or delocalization with a certain probability, which can be experimentally observed by matching the driving parameters and initial conditions.

Wave Packet Spreading with Disordered Nonlinear Discrete-Time Quantum Walks.

We use a novel unitary map toolbox-discrete-time quantum walks originally designed for quantum computing-to implement ultrafast computer simulations of extremely slow dynamics in a nonlinear and disordered medium. Previous reports on wave packet spreading in Gross-Pitaevskii lattices observed subdiffusion with the second moment m_{2}∼t^{1/3} (with time in units of a characteristic scale t_{0}) up to the largest computed times of the order of 10^{8}. A fundamental and controversially debated question-whether this process can continue ad infinitum, or has to slow down-stands unresolved. Current experimental devices are not capable to even reach 1/10^{4} of the reported computational horizons. With our toolbox, we outperform previous computational results and observe that the universal subdiffusion persists over an additional four decades reaching "astronomic" times 2×10^{12}. Such a dramatic extension of previous computational horizons suggests that subdiffusion is universal, and that the toolbox can be efficiently used to assess other hard computational many-body problems.

Nonlinear symmetry breaking of Aharonov-Bohm cages

We study the influence of mean field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wavepacket spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes, and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry breaking transition is readily observable in femtosecond laser-written waveguide arrays.

Wavelength dependence of high-order harmonic yields in solids

We theoretically investigate the wavelength dependence of high-order harmonic yields in solids driven by a mid-infrared laser field. By solving the three-dimensional two-band density matrix equations in the wavelength range of $2.0--7.5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$, it is shown that, in the limit of slow dephasing (dephasing time ${T}_{2}\ensuremath{\rightarrow}\ensuremath{\infty}$), the high-order harmonic yield from a crystal follows a scaling of ${\ensuremath{\lambda}}^{\ensuremath{-}4}$ for a fixed energy interval. The ${\ensuremath{\lambda}}^{\ensuremath{-}4}$ scaling is attributed to the wave-packet spreading (${\ensuremath{\lambda}}^{\ensuremath{-}3}$) for the overall yield and the energy distribution effect (${\ensuremath{\lambda}}^{\ensuremath{-}1}$) due to the increase of the cutoff. For the crystal with a finite dephasing time ${T}_{2}$, we find that the exponential factor $x$ of ${\ensuremath{\lambda}}^{\ensuremath{-}x}$ increases with a decay of ${T}_{2}$. An apparent and rapid fluctuation on a fine wavelength mesh is also observed in the harmonic yields. The fine-scale oscillation originates from the quantum interference effect, and the corresponding modulation period $\ensuremath{\delta}\ensuremath{\lambda}$ scales as ${\ensuremath{\lambda}}^{\ensuremath{-}1}$.

Transient Dynamics of Super Bloch Oscillations of a 1D Holstein Polaron under the Influence of an External AC Electric Field

AbstractTheoretical formalism for DC‐field polaron dynamics is extended to the dynamics of a 1D Holstein polaron in an external AC electric field using multiple Davydov trial states. Effects of carrier–phonon coupling on detuned and resonant scenarios are investigated for both phase and nonzero phase. For slightly off‐resonant or detuned cases, a beat between the usual Bloch oscillations and an AC driving force results in super Bloch oscillations, that is, rescaled Bloch oscillations in both the spatial and the temporal dimension. Super Bloch oscillations are damped by carrier–phonon coupling. For resonant cases, if the carrier is created on two nearest‐neighboring sites, the carrier wave packet spreads with small‐amplitude oscillations. Adding carrier–phonon coupling localizes the carrier wave packet. If an initial broad Gaussian wave packet is adopted, the centroid of the carrier wave packet moves with a certain velocity and with its shape unchanged. Adding carrier–phonon coupling broadens the carrier wave packet and slows down the carrier movement. Our findings may help provide guiding principles on how to manipulate the dynamics of the super Bloch oscillations of carriers in semiconductor superlattice and optical lattices by modifying DC and AC field strengths, AC phases, and detuning parameters.