Creating and probing electronic wave packets using half-cycle pulses.

With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the ‘Förster sphere’ (R < RF) this dependence transforms to the formula for electric dipole interaction energy ΔEd − d = C3/R3 and for R > RF it transforms to the formula for the van der Waals interaction energy ΔEVdW = −C6/R6. The van der Waals constant C6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J. The numerical values of the irreducible components of tensor C6 were calculated for rubidium atoms in the same Rydberg states |nlJM〉 with large quantum numbers n. We present the calculated resonance interaction energy of two rubidium atoms in the states |43D5/2M〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P3/2M〉 and of the other in the state |41F7/2M〉.

We have demonstrated that superradiance and superfluorescence states can be created in a selective manner in n=20 Rydberg states of Na atoms using a sub-ps, uni-polar half-cycle field pulse.

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.

Summary form only given. Unipolar half-cycle pulses (HCPs) can be used to alter the momentum distribution of atomic electrons over subpicosecond timescales. Previously, momentum kicks from HCPs were used to produce electronic wave packets from highly excited Rydberg eigenstates. In addition, these pulses have been used to kick bound electrons into the continuum, making it possible to monitor the time-dependent momentum distribution of electronic wave packets. Conversely, our most recent experiments have shown that HCPs can extract momentum from free electrons, facilitating their capture by positive ions. In the experiments, calcium atoms in the singlet 4s4p level are photoionized into the continuum using a 1.5ps, 390-nm laser pulse.

We investigate population transfer across the barrier in a double-well potential, induced by a pair of time-delayed single-lobe half-cycle pulses. We apply this setup both to a one-dimensional (1D) quartic model potential and to a three-dimensional potential representing HCN-->HNC isomerization. Overall the results for the two systems are similar, although in the 3D system some additional features appear not seen in the 1D case. The generic mechanism of population transfer is the preparation by the pump pulse of a wave packet involving delocalized states above the barrier, followed by the essentially 1D motion of the delocalized part of wave packet across the barrier, and the eventual de-excitation by the dump pulse to localized states in the other well. The correct timing is given by the well-to-well passage time of the wave packet and its recurrence properties, and by the signs of the field lobes which determine the direction and acceleration or deceleration of the wave packet motion. In the 3D system an additional pump-pump-dump mechanism linked to wave packet motion in the reagent well can mediate isomerization. Since the transfer time and the pulse durations are of the same order of magnitude, there is also a marked dependence of the dynamics and the transfer yield on the pulse duration. Our analysis also sheds light on the pronounced carrier envelope phase dependence previously observed for isomerization and molecular dissociation with one-cycle and sub-one-cycle pulses.

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.

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.

This article demonstrates that coherent states in Rydberg atoms can be produced and stabilized by combining a circularly polarized microwave field with a static, perpendicular magnetic field. These electronic wavepackets owe their stability to atomic analogs of the Lagrange equilibria which confine Jupiter's Trojan asteroids. While these “Trojan” wavepackets may slowly decay due to tunneling, a more significant source of dispersion will arise if the tails of the wavepacket penetrate appreciably into the non-linear or chaotic parts of phase space. In the laboratory frame, if these dispersive factors can be minimized — and this may be accomplished using magnetic fields — the electronic wavepacket will travel along a circular Kepler orbit while remaining localized radially and angularly for a finite — but large — number of Kepler periods. In this sense, the system is a classical Bohr atom.

The time evolution of Stark wave packets in Rydberg atoms under the influence of colored noise is analyzed. The Stark wave packets are generated by exposing $K(350p)$ Rydberg atoms to an electric field step. Their time evolution is monitored using a half-cycle probe pulse that is applied after a variable time delay. The noise is generated by randomly modulating the amplitude of the static field. We show that noise results in an enhanced and irreversible dephasing of Stark quantum beats, as monitored by the damping of the beat amplitude. This source of decoherence is most effective when the characteristic frequency of the noise power spectrum matches the orbital frequency of the Rydberg electron. Noise driven resonant $\ensuremath{\Delta}n=1$ transitions broaden the energy distribution thereby accelerating the dephasing.

The results of essential improvement of the microwave spectrometer for investigation of spectra of Rydberg state atoms are presented. The spectrometer was equipped by a new time domain (waveform) acquisition system, which allowed us to apply time selection of useful signal. Such solution significantly improved signal-to-noise ratio of recorded spectra. The result of test measurement of a microwave transition between Rydberg states of magnesium atom is presented.

We propose an approximate method for modeling the so-called Trojan wave packets of Rydberg states in a hydrogen-like atom subjected to a circularly polarized microwave field and a constant magnetic field. The method implies the reduction of the Schrodinger wave equation to a set of ordinary nonlinear differential equations for the parameters of the wave packet. Earlier we applied this method to solve the Schrodinger-like parabolic equation in nonlinear optics to describe misaligned beams in waveguide systems. The optimal values of the wave packet initial parameters are obtained. The numerical solution of the obtained differential equations show, that for these parameters the Trojan wave packet moves along a circle orbit.

Unidirectional half-cycle pulses (HCP) are ideally suitable for shaping, driving, and probing atomic wave packets in momentum space. The shortest HCP presently available have a width of about $500\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ restricting the manipulation of electronic wave packets to those in high-lying Rydberg states. The nonlinear harmonic response of atoms to strong two-color infrared laser pulses with frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ opens up the opportunity to form trains of ultrafast HCP's on an attosecond time scale. In the present contribution, we investigate the influence of macroscopic propagation effects onto the production of HCP and show that trains of unidirectional attosecond HCP's could be produced under experimentally realistic conditions.

We apply the method of “coherence observation by interference noise” (COIN) to molecular wave packet interferometry. In contrast to conventional wave packet interferometry, where one has to control precisely the relative phase between the pair of time-delayed laser pulses, COIN employs a sequence of randomly phased laser pulses. Whereas in this case the mean signal does not reflect anymore the coherent evolution of a localized wave packet, the fluctuations around this mean still mimic the dynamics of the propagating wave packet. We demonstrate the feasibility of wave packet interferometry without phase–locking by simulating fluorescence interferograms for the Na2– molecule.

Systematic observation of tunneling field-ionization in highly excited Rb Rydberg atoms

Energy potentials with double-well structures are typical in atoms and molecules systems. A manipulation scheme using Half Cycles Pulses (HCPs) is proposed to transfer a Gaussian wave packet between the two wells. On the basis of quantum mechanical simulations, the time evolution and the energy distribution of the wave packet are evaluated. The effect of time parameters, amplitude, and number of HCPs on spatial and energy distribution of the final state and transfer efficiency are investigated. After a carefully tailored HCPs sequence is applied to the initial wave packet localized in one well, the final state is a wave packet localized in the other well and populated at the lower energy levels with narrower distribution. The present scheme could be used to control molecular reactions and to prepare atoms with large dipole moments.