Gaussian Wave Packet Research Articles

Propagation properties of collinear self-decelerating Airy–Elegant–Laguerre–Gaussian wave packets in free space

ABSTRACTBased on the analytical expression of the spatiotemporal collinear self-decelerating Airy Elegant–Laguerre–Gaussian (AiELG) wave packets by solving the (3+1)D free-space Schrödinger equation, we have investigated the collinear self-decelerating AiELG propagation properties in detail. Analysis results show that the different spatiotemporal profiles can be accessed by selecting a different mode number or relative amplitude. The spatiotemporal profiles will rotate if the mode parameter or mode number in the propagation. The wave packets will also rotate when the relative phase are varied. The direction of the energy flow of collinear wave packets is in helical clockwise distribution if mode number or mode parameter A>0, otherwise, the direction is in helical anticlockwise distribution if mode number or mode parameter A<0, which is the reason of rotation of the wave packets during propagation. The spatiotemporal hollow self-decelerating AiELG wave packets are accessed with .

Low-temperature annihilation rate for quasilocalized excitons in monolayer MoS2

The strong Coulomb forces in monolayer transition metal dichalcogenides ensure that optical excitation of band electrons gives rise to Wannier-Mott excitonic states, each of which can be conceptualized as a composite of a Gaussian wavepacket corresponding to center-of-mass motion and an orbital state corresponding to the motion of the electron and hole about the center-of-mass. Here, we show that at low temperature in monolayer MoS2, given quasi-localized excitons and consequently a significant inter-exciton spacing, the excitons undergo dipole-dipole interaction and annihilate one another in a manner analogous to Auger recombination. To construct our model, we assume that each exciton is localized in a region whose length is on the same scale as the excitonic diameter, thus causing the exciton to behave in a fermionic manner, while the distance between neighboring excitons is much larger than the exciton diameter. We construct the orbital ladder operators for each exciton and apply Fermi's Golden Rule to derive the overall recombination rate as a function of exciton density.

High-order harmonic generation from diatomic molecules in an orthogonally polarized two-color laser field

We study high-order harmonic generation (HHG) from aligned ${{\mathrm{H}}_{2}}^{+}$ and oriented ${\mathrm{HeH}}^{2+}$ and ${\mathrm{HeH}}^{+}$ molecular ions in orthogonally polarized two-color laser pulses composed of an intense fundamental field and a time-delayed weak second-harmonic field. By numerical solution of the time-dependent Schr\"odinger equation, we find that for a fixed alignment angle, as the delay between the two colors varies on a subcycle scale, the HHG intensity from ${{\mathrm{H}}_{2}}^{+}$ shows a pronounced groove in a specific delay region, which turns out to be a two-center interference effect. HHG from asymmetric molecules shows an obvious orientation dependence where the interference effect can be observed only when the tunneling occurs on the helium side. The physical origin of these phenomena is deduced by modeling the two-color HHG intensity of ${{\mathrm{H}}_{2}}^{+}$ using classical and quantum models and by modeling that of asymmetric molecules with the help of field-free collisions of Gaussian wave packets with the core.

The frame bundle picture of Gaussian wave packet dynamics in semiclassical mechanics

Recently Ohsawa (Lett Math Phys 105:1301–1320, 2015) has studied the Marsden–Weinstein–Meyer quotient of the manifold T^*mathbb {R}^ntimes T^*mathbb {R}^{2n^2} under a mathrm {O}(2n)-symmetry and has used this quotient to describe the relationship between two different parametrisations of Gaussian wave packet dynamics commonly used in semiclassical mechanics. In this paper, we suggest a new interpretation of (a subset of) the unreduced space as being the frame bundle {mathcal {F}}(T^*mathbb {R}^n) of T^*mathbb {R}^n. We outline some advantages of this interpretation and explain how it can be extended to more general symplectic manifolds using the notion of the diagonal lift of a symplectic form due to Cordero and de León (Rend Circ Mat Palermo 32:236–271, 1983).

Some remarks on analytical solutions for a damped quantum parametric oscillator

The time-dependent Schrödinger equation for quadratic Hamiltonians has Gaussian wave packets as exact solutions. For the parametric oscillator with frequency ω(t), the width of these wave packets must be time-dependent. This time-dependence can be determined by solving a complex nonlinear Riccati equation or an equivalent real nonlinear Ermakov equation. All quantum dynamical properties of the system can easily be constructed from these solutions, e.g., uncertainties of position and momentum, their correlations, ground state energies, etc. In addition, the link to the corresponding classical dynamics is supplied by linearizing the Riccati equation to a complex Newtonian equation, actually representing two equations of the same kind: one for the real and one for the imaginary part. If the solution of one part is known, the missing (linear independent) solution of the other can be obtained via a conservation law for the motion in the complex plane. Knowing these two solutions, the solution of the Ermakov equation can be determined immediately plus the explicit expressions for all the quantum dynamical properties mentioned above. The effect of a dissipative, linear velocity dependent friction force on these systems is discussed.

Short-Wave Asymptotics for Gaussian Beams and Packets and Scalarization of Equations in Plasma Physics

We study Gaussian wave beam and wave packet types of solutions to the linearized cold plasma system in a toroidal domain (tokamak). Such solutions are constructed with help of Maslov’s complex germ theory (short-wave or semi-classical asymptotics with complex phases). The term “semi-classical” asymptotics is understood in a broad sense: asymptotic solutions of evolutionary and stationary partial differential equations from wave or quantum mechanics are expressed through solutions of the corresponding equations of classical mechanics. This, in particular, allows one to use useful geometric considerations. The small parameter of the expansion is h = λ / 2 π L where λ is the wavelength and L the dimension of the system. In order to apply the asymptotic algorithm, we need this parameter to be small, so we deal only with high-frequency waves, which are in the range of lower hybrid waves used to heat the plasma. The asymptotic solution appears to be a Gaussian wave packet divided by the square root of the determinant of an appropriate Jacobi matrix (“complex divergence”). When this determinant is zero, focal points appear. Our approach allows one to write out asymptotics near focal points. We also claim that this approach is very practical and leads to formulas that can be used for numerical simulations in software like Wolfram Mathematica, Maple, etc. For the particular case of high-frequency beams, we present a recipe for constructing beams and packets and show the results of their numerical implementation. We also propose ideas to treat the more difficult general case of arbitrary frequency. We also explain the main ideas of asymptotic theory used to obtain such formulas.

Propagation of the chirped-Airy–Gaussian–Hermite–Laguerre–Gaussian wave packets in free space

We investigate the propagation properties of the chirped-Airy–Gaussian–Hermite–Laguerre–Gaussian (CAGHLG) wave packets analytically and numerically. We mainly discuss the features of the wave packets with various chirped conditions, modes and angles. The results reveal that the intensity distributions and the phase patterns of the CAGHLG wave packets change with different modes. Meantime, the CAGHLG wave packets can realize the transformation of correlation wave packets by altering angle. Additionally, we obtain two kinds of inversions of the CAGHLG wave packets by choosing appropriate chirp factors in the course of transmission.

Computer model of the two-pinhole interference experiment using two-dimensional Gaussian wave-packets

The two-slit interference experiment has been modeled a number of times using Gaussian wave-packets and the Bohm–de Broglie causal interpretation. Here we consider the experiment with pinholes instead of slits and model the experiment in terms of two-dimensional Gaussian wave-packets and the Bohm–de Broglie causal interpretation.

Machine learning and signed particles, an alternative and efficient way to simulate quantum systems

AbstractRecently neural networks have been applied in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. Important advantages were introduced, such as the reduction of the amount of memory required for the simulation of a quantum system by avoiding the storage of the kernel in a multi‐dimensional array, as well as attainment of consistent speedup by the ability to realize the computation only on the cells occupied by signed particles. An inherent limitation was the number of hidden neurons to be equal to the number of cells of the discretized real space. In this work, anew network architecture is presented, decreasing the number of neurons in its hidden layer, thereby reducing the complexity of the network and achieving an additional speedup. The approach is validated on a onedimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier.

Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model

Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrödinger equation of Dysthe (Proc. R. Soc. Lond. A, vol. 369 (1736), 1979, pp. 105–114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of $\unicode[STIX]{x1D716}$ and $\unicode[STIX]{x1D6E5}$, for $\unicode[STIX]{x1D716}$ the linear prediction of the maximum slope at focusing and $\unicode[STIX]{x1D6E5}$ the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of $\unicode[STIX]{x1D716}-\unicode[STIX]{x1D6E5}$ phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air–sea interaction processes is discussed.

Real-time evolution method and its application to the 3α cluster system

A new theoretical method is proposed to describe the ground and excited cluster states of atomic nuclei. The method utilizes the equation-of-motion of the Gaussian wave packets to generate the basis wave functions having various cluster configurations. The generated basis wave functions are superposed to diagonalize the Hamiltonian. In other words, this method uses the real time as the generator coordinate. The application to the $3\alpha$ system as a benchmark shows that the new method works efficiently and yields the result consistent with or better than the other cluster models. Brief discussion on the structure of the excited $0^+$ and $1^-$ states is also made.

Wave-packet dynamics in multilayer phosphorene

We investigate the dynamics of Gaussian wave packets in multilayer black phosphorus (BP). Time-dependent average position and velocity are calculated analytically and numerically by using a continuum model and a method based on the split-operator technique, respectively. By analyzing the wave-packet trajectories with nonvanishing initial momentum along $y$ direction, we observed transient spatial oscillations due to the effect known as zitterbewegung (ZBW). We also demonstrated, based on the Heisenberg picture and by the calculation of the velocity operators, that the trembling motion along the $y$ direction at small times is unavoidable even for null initial momentum. We verified that the ZBW is directly related to the splitting of the wave packet into two parts moving with opposite velocities, as similar to graphene, and the linear dependence on ${k}_{y}$ in out-of-diagonal terms in the Hamiltonian. In addition for phosphorene systems, the two portions of the propagated wave packets have an asymmetric shape for unbalanced $\left({[1,0]}^{T}\right)$ and phased different $\left({[1,i]}^{T}\right)$ initial pseudospin components, playing an important role in the amplitude, frequency and duration time of the transient oscillations. Electrons in the vicinity of the Fermi energy traveling in $N$-layer phosphorene also exhibit qualitatively similar trembling motion and transient character as found in the monolayer case, except by the oscillation phase difference and final group velocity achieved after the transient behavior. As a consequence of the anisotropy on the $N$-layer BP energy bands, effective masses and group velocities along the $x$ and $y$ directions, the wave packet propagates nonuniformly along the different directions and deforms into an elliptical shape. By comparing our analytical results with those ones obtained by the split-operator technique, we verified a good qualitative and quantitative agreement between them, except for very larger values of wave vector and after long time steps.

Open system dynamics using Gaussian-based multiconfigurational time-dependent Hartree wavefunctions: Application to environment-modulated tunneling.

A variational approach for the quantum dynamics of statistical mixtures is developed, which is based upon the representation of the natural states of the mixture in terms of hybrid Gaussian-based Multiconfiguration Time-Dependent Hartree (G-MCTDH) wavefunctions. The method, termed ρG-MCTDH, is combined with a treatment of dissipation and decoherence based on the nonstochastic open-system Schrödinger equations. The performance and the convergence properties of the approach are illustrated for a two-dimensional tunneling system, where the primary tunneling coordinate, represented by flexible single-particle functions, is resonantly coupled to a second harmonic mode, represented by Gaussian wave packets. The harmonic coordinate is coupled to the environment and two different processes are studied: (i) vibrational relaxation at zero temperature described by a master equation in the Lindblad form and (ii) thermalization induced by the Caldeira-Leggett master equation. In the second case, the evolution from a quantum tunneling regime to a quasistationary classical-limit distribution, driven by the heat bath, is visualized using a flux analysis.

α and triton clustering in Cl35

Coupling of cluster and deformed structures are important for dynamics of nuclear structure. Threshold energy has been discussed to explain cluster structures coupling to deformed states but relation between threshold energy and excitation energy has open problems. Negative-parity superdeformed (SD) states were observed by a $\gamma$-spectroscopy experiment in $^{35}$Cl but its detailed structure is unclear. By analyzing coupling of cluster structures in deformed states and high-lying cluster states in $^{35}$Cl, cluster structures coupling to deformed states and excitation energy of high-lying cluster states are investigated. The antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM) are used. An AMD wave function is a Slater determinant of Gaussian wave packets. By energy variational calculations with constraints on deformation and clustering, wave functions of deformed structures and $\alpha$- and $t$-cluster structures are obtained. Adopting those wave functions as GCM basis, wave functions of ground and excited states are calculated. Various deformed bands are obtained and predicted. A $K^\pi = \frac{1}{2}^-$ deformed band, which corresponds to the observed SD band, dominates deformed structure and compact $\alpha$- and $t$-cluster structure components. Particle-hole configurations of the dominant components with deformed and cluster structures are similar. In high-lying states, almost pure $\alpha$- and $t$-cluster states are obtained in negative-parity states, and excitation energies of the $t$-cluster states are higher than those of $\alpha$-cluster states. In conclusions, particle-hole configurations of cluster structure with small intercluster distance are important for coupling to low-energy deformed states. Threshold energies reflect to excitation energies of high-lying almost pure cluster states.

The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials

The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials

Pseudospin-dependent Zitterbewegung in monolayer graphene

We propose a spintronic device based on a narrow nanoribbon patterned from a monolayer graphene (MLG) sheet, embedded between a film of hexagonal boron nitride and a SiO2 substrate, all comprised under a three top-gated structure, to explore spin-dependent quantum transport of Dirac fermions. We developed a theoretical procedure for describing the pseudospin-related effects and the dynamics of Dirac fermions represented by a one-dimensional Gaussian wave packet (1DGWP), which is electrostatically confined in the device. The free-space 1DGWP time evolution follows expected features. Meanwhile, due to the weak breakdown of the real-spin degeneracy, the 1DGWP barely splits inside the under-barrier region governed by the extrinsic Rashba spin–orbit interaction (SOI-R). Most importantly, departing from the pristine MLG, we have found evidence of trembling antiphase oscillations in the probability density time-distribution for each sublattice state, which we have called the pseudospinorial Zitterbewegung effect (PZBE). The PZBE appears modulated with robust transient character and with a decay time in the femtosecond scale. Interestingly, several features of the PZBE become tunable, even its complete disappearance at the vicinity of the Dirac points or at a symmetric pseudospin configuration. For the proposed quasi-1D MLG device, we have captured evidence of the familiar Klein tunneling and the unusual anti-Klein tunneling, whose interplay for 2D MLG under tunable SOI-R was reported recently.

Synthesis of Directional Wave Packets from Shot Records

Using directional waves is advantageous in subsurface seismic imaging because such waves are localized in space and time. Hence, the recorded data contain information mostly about the illuminated targets. However, most seismic field data are physically generated by point sources that excite wavefield propagating into all directions and interact with all parts of the medium. How to convert point-source wavefields into a wavefield due to a directional wave packet without physically exciting it, is the subject of investigation here. In particular, we investigate the Gaussian wave packet (GWP) which is a directional wave packet localized in space and time. GWP is an exact solution of the wave equation and it differs from the widely used asymptotic solutions such as Gaussian Beams or Gaussian Packets. The spatial localization and propagation direction of GWP are controlled by parameters chosen by users. We propose a method to synthesize GWP field data in complex media using recorded shot records of point sources based on the reverse-time concept. To assess the quality of the synthesized GWP data, we study the influences from point-source wavelets and the spatial interval between point sources. Finally, we present the constructed GWP fields in two numerical examples. We also show one application of the GWP data in seismic imaging using multiples.

Quantum path computing: computing architecture with propagation paths in multiple plane diffraction of classical sources of fermion and boson particles

Quantum computing (QC) architectures utilizing classical or coherent resources with Gaussian transformations are classically simulable as an indicator of the lack of QC power. Simple optical set-ups utilizing wave-particle duality and interferometers achieve QC speed-up with the cost of exponential complexity of resources in time, space or energy. However, linear optical networks composed of single photon inputs and photon number measurements such as boson sampling achieve solving problems which are not efficiently solvable by classical computers while emphasizing the power of linear optics. In this article, quantum path computing (QPC) set-up is introduced as the simplest optical QC satisfying five fundamental properties all-in-one: exploiting only the coherent sources being either fermion or boson, i.e., Gaussian wave packet of standard laser, simple set-up of multiple plane diffraction (MPD) with multiple slits by creating distinct propagation paths, standard intensity measurement on the detector, energy efficient design and practical problem solving capability. MPD is unique with non-Gaussian transformations by realizing an exponentially increasing number of highly interfering propagation paths while making classical simulation significantly hard. It does not require single photon resources or number resolving detection mechanisms making the experimental implementation of QC significantly low complexity. QPC set-up is utilized for the solutions of specific instances of two practical and hard number theoretical problems: partial sum of Riemann theta function and period finding to solve Diophantine approximation. Quantumness of MPD with negative volume of Wigner function is numerically analyzed and open issues for the best utilization of QPC are discussed.

Amplitude and Phase of Wave Packets in a Linear Potential.

We theoretically study and successfully observe the evolution of Gaussian and Airy surface gravity water wave packets propagating in an effective linear potential. This potential results from a homogeneous and time-dependent flow created by a computer-controlled water pump. For both wave packets we measure the amplitudes and the cubic phases appearing due to the linear potential. Furthermore, we demonstrate that the self-acceleration of the Airy surface gravity water wave packets can be completely canceled by a linear potential.

Investigation of valence band reconstruction methods for attosecond streaking data from surfaces.

We analyze simulated streaked valence band photoemission with atomic streaking theory-based reconstruction methods to investigate the differences between atomic gas-phase streaking and valence band surface streaking. The careful distinction between atomic and surface streaking is a prerequisite to justify the application of atomic streaking theory-based reconstruction methods to surface streaking measurements. We show that neglecting the band structure underestimates the width of reconstructed photoelectron wavepackets, consistent with the Fourier transform limit of the band spectrum. We find that a fit of Gaussian wavepackets within the description of atomic streaking is adequate to a limited extent. Systematic errors that depend on the near-infrared skin depth, an inherently surface-specific property, are present in temporal widths of wavepackets reconstructed with atomic streaking theory-based methods.