Real-Time Observation of Interference between Atomic One-Electron and Two-Electron Excitations

Summary form only given. Wave packets (WPs) has recently emerged as a very active research field in quantum optics. We show here that the evolution of WPs may result in new class of large-scale interference effects: the formation of highly regular spatio-temporal patterns in the QM probability, |/spl Psi/|/sup 2/, with the key mechanism for this being pair interference between the eigen-modes of the system and the degeneracy of this interference. The new patterns have been discovered in the probability density |/spl Psi/|/sup 2/(x,t) of a particle in an infinitely deep square well, by numerical simulations of the evolution of a Gaussian WP; later work by a few groups used other initial conditions and media (e.g. Bose-Einstein condensate and angular WPs). In all these cases, the QM distribution shows a net of canals (minima), and ridges (maxima), running as straight lines in space-time (x,t). Similar patterns in the near field of a diffraction grating, and in matter waves in atom optics reveals a new aspects of the Talbot effect. So far the numerical exploration of these patterns has relied on the specific choice (i) of the initial conditions and (ii) of the square well; no physical explanation of the patterns has been suggested. Recently, we observed a quantum carpet under more general conditions, offered its universal explanation, and predicted distinct curved patterns in general case of an anharmonic potential.

PurposeThe paper explores the spectral solution of a partial differential equation governing nonlinear transmission lines (NLTLs). It aims to present an efficient simulation technique for a nonlinear fractional-order transmission line model and to show the effect of fractional derivatives on the evolution of solitons and wave packets of increasing spatial frequency.Design/methodology/approachThe paper is concerned with the solution of the equation governing NLTLs for both integer and fractional time derivatives. The spectral method shall be considered with Hermite and Malmquist-Takenaka orthogonal functions and integer and fractional implementations of the implicit trapezoidal rule. While the Hermite functions and Malmquist-Takenaka functions are suitable for solitons, the Malmquist-Takenaka functions are selected as these are superior for approximating wave packets of increasing frequency (Iserles, Luong and Webb, 2023). Furthermore, they possess properties that are favourable from a computational viewpoint.FindingsResults will show that the proposed approach is effective for simulating NLTLs with both integer and fractional time derivatives. In particular, fractional derivatives are shown to have a significant effect on the evolution of wave packets on a nonlinear transmission line.Originality/valueThe method is novel in using Malmquist-Takenaka basis functions for a spectral solution of a nonlinear transmission line equation with both integer and fractional time derivatives and for examining the effect of fractional derivatives on wave packets.

In this paper the generation and evolution of an edge-wave packet are studied experimentally and numerically. In the laboratory an edge-wave packet is first generated on a sloping beach by a hinge-type wave-maker. Both the free surface displacement and velocity field are measured along several on-offshore cross sections. Numerical results are also obtained by solving the linear shallow-water wave equations and are compared with experimental data. Numerically predicted wave evolution characteristics are in good agreement with those shown by laboratory data. Analyses of the wave amplitude density spectra of both numerical solutions and experimental data show that wave packets are indeed trapped in the nearshore region and consist of a mixture of Stokes and higher-mode edge waves. Furthermore, the Stokes mode dominates in the low frequency range. Two additional wave-maker designs, i.e., the piston-type and the reverse hinge-type, are investigated numerically. Away from the wave-maker the wave forms (time histories) of the wave packets are insensitive to the details of wave-maker movements. The effects of beach slope on the evolution of wave packets are investigated. The behavior of the velocity field and the attenuation rates of runup amplitudes are also discussed.

We ionized He, Ne and Ar in the tunnelling regime with a linearly polarized laser pulse and measured the ion-recoil momentum distribution on an axis perpendicular to laser polarization for two different wavelengths (λ = 800 nm and λ = 1800 nm). We observed a significantly narrower distribution for 800 nm than for 1800 nm. Classical simulations of the electron wave packet's evolution under the combined influence of the ion's Coulomb potential and the laser field show that the narrowing is caused by Coulomb focusing of the electron wave packet during recollisions. The narrowing is sensitive on the longitudinal momentum of the wave packet after tunnelling, which suggests a way of measuring it. Measurements at 800 nm in circular polarization–for which no recollision occurs–do not exhibit this narrowing of the perpendicular momentum distribution. Simulations for circular polarization show another aspect of Coulomb focusing: the Coulomb potential also affects the wave packet's transverse momentum as it leaves the saddle point immediately after tunnelling.

Transport of a wave packet via an open quantum dot: on the correspondence with classical billiards

We use the Korteweg–de Vries (KdV) equation, supplemented with several forcing/friction terms, to describe the evolution of wind-driven water wave packets in shallow water. The forcing/friction terms describe wind-wave growth due to critical level instability in the air, wave decay due to laminar friction in the water at the air–water interface, wave stress in the air near the interface induced by a turbulent wind and wave decay due to a turbulent bottom boundary layer. The outcome is a modified KdV–Burgers equation that can be a stable or unstable model depending on the forcing/friction parameters. To analyse the evolution of water wave packets, we adapt the Whitham modulation theory for a slowly varying periodic wave train with an emphasis on the solitary wave train limit. The main outcome is the predicted growth and decay rates due to the forcing/friction terms. Numerical simulations using a Fourier spectral method are performed to validate the theory for various cases of initial wave amplitudes and growth and/or decay parameter ranges. The results from the modulation theory agree well with these simulations. In most cases we examined, many solitary waves are generated, suggesting the formation of a soliton gas.

Floquet states represent intrinsic modes of ionization of an atom in a monochromatic field of constant intensity. To describe atomic wave packets evolving in realistic laser pulses, linear superpositions of Floquet states are required (“multistate Floquet theory”). This gives the possibility of following the evolution of wave packets in terms of the Floquet states that are populated during the pulse. We study here the way in which the Floquet states present in the representation of the wave packet manifest themselves in the excess-photon ionization spectra (EPI/ATI). For the purpose of illustration we choose a 1D atomic model with a soft-core Coulomb potential. We calculate the totality of the Floquet states, at all intensities needed, and generate the corresponding “Floquet map”. We then calculate the EPI spectra for wave packets evolving from the ground state under different types of pulses. By analyzing the location of the lines in the spectrum, and their shapes, we show that they can be associated, in a clear cut and predictable way, to Floquet states responsible for the emission. The understanding of the underlying physics can lead to tailoring laser pulses, such as to obtain EPI signals in a controlled way. Whereas our analysis is applied to theoretical spectra, it would apply, just as well, to experimental ones.

The wave packet perturbation energy propagation and accumulation signal during continuing heavy rain process in west of Sichuan Basin from September 22, 2008 to September 27, 2008 is analyzed and predicted in wave-packet propagation diagnosis method by making use of NCEP/NCAR reanalysis materials. According to the analysis, the distribution and propagation of wave packet can obviously reflect features of generation, lasting and ending of the rain. The high value area of the wave packet is basically consistent with heavy rain areas. The heavy rain process is generally generated in high value period or high phase of the wave packet perturbation energy accumulation. According to the meridional and zonal propagation features of the wave packet value, the continuing heavy rain process in west of Sichuan Basin from September 22, 2008 to September 27, 2008 was mainly affected by West Pacific subtropical high, cold air in northern regions and plateau regions, two water vapor channels from Bay of Bengal and South Sea to the basin as well as Typhoon Hagupit. The evolution of wave packet is meaningful for prediction.

We demonstrate an experimental approach to read and write populations and relative phases of vibrational eigenstates within a wave packet created in the $B$ state of the iodine molecule by using a pair of phase-locked femtosecond laser pulses. Our highly stabilized optical interferometer provides attosecond stability and resolution in the interpulse delay. The stability and resolution have realized an exquisite tuning of the interference of two vibrational wave packets to manipulate the relative populations and the relative quantum phases among the vibrational eigenstates within the wave packets. These populations and phases have been retrieved by measuring fluorescence from the upper $E$ state induced by another nanosecond (ns) or femtosecond (fs) probe laser pulse. The bandwidth of the ns probe pulse is narrow enough to select only a small portion of the rotational progression of a particular vibrational band of the $E\ensuremath{-}B$ transition. By scanning the probe wavelength, we measure the population distribution of the vibrational eigenstates within the wave packet. The fs probe pulse is used to measure quantum beats arising from the temporal evolution of the wave packet. Combining these two complementary measurements, we can read both population and phase information written and stored in the wave packet.

Recent TOPEX/Poseidon observations show an enhanced (weakened) westward propagation of long planetary Rossby waves at extratropics (Tropics) and they usually propagate faster in the western basin than in the eastern basin in all major oceans. The evolution of a long planetary wave packet in a continuously stratified ocean in response to the various forcing functions is analytically investigated using the wave packet theory. For a wave packet with a large vertical scale, the stratification variation and the vertical shear of the mean zonal current act in concert, causing the wave packet to propagate directly against the mean zonal current—called the counter-Doppler-shift (CDS) effect. It is found that the speed ratio between the zonal baroclinic zonal current and the classic theory increases with the latitude, the eastward zonal current, and the local vertical scale. The vertical scale of a wave packet plays a critical role in the propagation, the structure, and spatial-scale development of a wave...

We study the space-time evolution of ``flavor'' neutrino wave-packets at finite temperature and density in the early Universe prior to BBN. We implement non-equilibrium field theory methods and linear response to study the space-time evolution directly from the effective Dirac equation in the medium. There is a rich hierarchy of time scales associated with transverse and longitudinal dispersion and coherence. A phenomenon of ``freezing of coherence'' is a result of a competition between longitudinal dispersion and the separation of wave-packets of propagating modes in the medium. Near a resonance the coherence and oscillation time scales are enhanced by a factor $1/\sin2\theta$ compared to the vacuum. Collisional relaxation via charged and neutral currents occurs on time scales much shorter than the coherence time scale and for small vacuum mixing angle, shorter than the oscillation scale. Assuming that the momentum spread of the initial wave packet is determined by the large angle scattering mean free path of charged leptons, we find that the transverse dispersion time scale is the shortest and is responsible for a large suppression in both the survival and transition probabilities on time scales much shorter than the Hubble time. For small mixing angle the oscillation time scale is \emph{longer} than the collisional relaxation scale. The method also yields the evolution of right-handed wave packets. Corrections to the oscillation frequencies emerge from wave-packet structure as well as from the energy dependence of mixing angles in the medium.

Summary form only given. A small-area femtosecond pulse propagates in a dispersive medium in a coherent fashion, if the relaxation times of the medium are compared with the pulse length for a long time. As a result, the pulse will be reshaped. This has been described by linear dispersion theory. Using Rydberg states of a molecular or an atomic gas as dispersive medium, the large spectral width of the femtosecond pulse can overlap with more than one level simultaneously. In this case, the shape of the propagated pulse reflects the temporal evolution of the Rydberg wave packet formed by the resonant Rydberg states.

We present numerical simulations of the evolution of a large-amplitude electrostatic wave packet in a hot collisionless plasma. When resonant particles are trapped by the wave potential during a transit time, the number of lobes in the packet is observed to increase. This is explained in terms of an equation of propagation for the packet amplitude and a dispersion relation involving the trapped particles.

Wave packets of time-harmonic disturbances in a laminar separated flow behind a backward-facing step on flat plate are investigated. Experimental data are obtained through hot-wire measurements in a low-turbulent subsonic wind tunnel. The results show that the oscillations generated locally in the separation region are transported upstream which makes an essential difference between the separation bubble under self-excitation and the attached boundary layer

Surface polaritons, light-matter hybrid excitations at material interfaces, are extensively studied for their strong field confinement and high propagation velocities, which are ideal for nanoscale waveguide and sensor applications [1], [2]. While near-field microscopy is known to map polariton propagation mostly in the frequency domain, real-space field-resolved detection of broadband-pulse-launched polaritons (spacetime imaging) can offer new insights into their properties [3], [4]. Here, we investigate terahertz surface plasmon polaritons (SPPs) in graphene using spacetime imaging and manipulate their dynamics by ultrafast photoexcitation [5]. A terahertz pulse coupled into the sharp metallic tip of a near-field microscope launches surface polaritons (Fig. 1a). Using electro-optic detection, we extract the electric field profile of SPPs that reflect off graphene edges. By analyzing these waveforms at different distances to a graphene edge, we can directly trace the spatiotemporal evolution of the SPP wave packet, providing insights into the group and phase velocities of the polariton wave packet, as well as damping (Fig. 1 b). Thus, the position and gradient of the polariton dispersion within the probed spectral range can be inferred (Fig. 1c), even for strongly damped polariton modes. Additionally, our straight-forward analysis can be expanded to full 2D images, mapping distinct propagation directions at different edges (Fig. 1 d). Access to the time domain also enables us to probe nonequilibrium dynamics with femtosecond accuracy. Photoexciting graphene with ultrafast visible light pulses transiently changes its conductivity. This allows us to control the SPP amplitude on subcycle timescales (Fig. 1 e) - much faster than electrostatic gating - offering a potential new avenue for ultrafast plasmonic logic devices. Beyond graphene, our approach can be readily extended to a wide range of materials including anisotropic polaritons in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha-\text{MoO}_{3}$</tex> and black phosphorus, or topological insulator surface modes, and other systems where electro-optic sampling of the scattered electric field can be employed.