Wave packet interferometry without phase-locking

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.

We develop a wave packet interferometry description of multidimensional ultrafast electronic spectroscopy for energy-transfer systems. After deriving a general perturbation-theory-based expression for the interference signal quadrilinear in the electric field amplitude of four phase-locked pulses, we analyze its form in terms of the underlying energy-transfer wave packet dynamics in a simplified oriented model complex. We show that a combination of optical-phase cycling and polarization techniques will enable the experimental isolation of complex-valued overlaps between a “target” vibrational wave packet of first order in the energy-transfer coupling J, characterizing the one-pass probability amplitude for electronic energy transfer, and a collection of variable “reference” wave packets prepared independently of the energy-transfer process. With the help of quasiclassical phase-space arguments and analytic expressions for local signal variations, the location and form of peaks in the two-dimensional interferogram are interpreted in terms of the wave packet surface-crossing dynamics accompanying and giving rise to electronic energy transfer.

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.

We propose a generalCina, Jeffrey A. framework for calculating and interpreting multidimensional electronic spectroscopy signals in terms of the wave-packet-shaping, amplitude-transferring effects of femtosecond laser pulses on time-dependent molecular states. The chapter sets up basic expressionsKiessling, Alexis J. for two-dimensional wave-packet interferometry (WPI) experiments on an electronic energy-transfer (EET) system as a quantum yield-weighted sum of contributing overlaps between multi-pulse wave packets. Further, we identify the ranges of interpulse delay within which each overlap is not excluded by its order of pulse action from contributing to the WPI signal. Example calculations are carried out for the case of a spatially oriented, weakly-coupled EET dimer. Semiclassical analyses of the necessary conditions for phase-space coincidence between the bra and ket, the dynamical consequences of a site-energy difference between the two chromophores, and the sensitivity of contributions accessing or originating from doubly electronically excited states of the dimer to the possible presence of an exciton shift all provide physical interpretations of individual wave-packet overlaps.

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.

We investigate the control of electronic energy transfer in molecular dimers through the preparation of specific vibrational coherences prior to electronic excitation, and its observation by nonlinear wave-packet interferometry (nl-WPI). Laser-driven coherent nuclear motion can affect the instantaneous resonance between site-excited electronic states and thereby influence short-time electronic excitation transfer (EET). We first illustrate this control mechanism with calculations on a dimer whose constituent monomers undergo harmonic vibrations. We then consider the use of nl-WPI experiments to monitor the nuclear dynamics accompanying EET in general dimer complexes following impulsive vibrational excitation by a subresonant control pulse (or control pulse sequence). In measurements of this kind, two pairs of polarized phase-related femtosecond pulses following the control pulse generate superpositions of coherent nuclear wave packets in optically accessible electronic states. Interference contributions to the time- and frequency-integrated fluorescence signals due to overlaps among the superposed wave packets provide amplitude-level information on the nuclear and electronic dynamics. We derive the basic expression for a control-pulse-dependent nl-WPI signal. The electronic transition moments of the constituent monomers are assumed to have a fixed relative orientation, while the overall orientation of the complex is distributed isotropically. We include the limiting case of coincident arrival by pulses within each phase-related pair in which control-influenced nl-WPI reduces to a fluorescence-detected pump-probe difference experiment. Numerical calculations of pump-probe signals based on these theoretical expressions are presented in the following paper [J. D. Biggs and J. A. Cina, J. Chem. Phys. 131, 224302 (2009)].

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.

Ultrashort, nearly unipolar electric field pulses are used to produce novel dynamic states in Rydberg atoms. A single 500 fsec field pulse redistributes essentially all of the population from a single stationary Rydberg state to hundreds of different final states. The dynamic evolution of the nonstationary wave packet is monitored using a second, time-delayed pulse. The time-dependent momentum-space probability distribution of the wave packet can be retrieved experimentally using a classical impulse approximation.

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 discuss new aspects of generating and observing electronic wave packets in Rydberg systems. A new scheme of observing wave packets in a pump and probe configuration with time-delayed correlation broad-bandwidth laser pulses is proposed and wave packet generation in near threshold multiphoton ionization is discussed.

We investigate coherent population transfer in double-$\ensuremath{\Lambda}$ and diamond-type four-level systems driven by two pairs of time-delayed laser pulses. We show that the relative phase between the pulses induces interference so that the adiabatic passage dynamics is only possible for a particular phase. Both pulse area and phase are control knobs that can be used to prepare specific coherent superpositions using counterintuitive and intuitive pulse sequences. Since the diamond-type four-level system maps the Hamiltonian of two interacting two-level systems, the schemes can be used to manipulate entanglement. In particular we propose robust schemes to prepare specific entangled states by phase control with time-delayed pulse sequences.

We present one-color nonlinear wavepacket interferometry (WPI) signal calculations for a system of two electronic levels and one vibrational degree of freedom. We consider two cases, a displaced harmonic oscillator system, which can be treated analytically, and a model photodissociative system, whose WPI signal must be calculated by numerical wavepacket propagation. We show how signals obtained with different combinations of intrapulse-pair phase shifts can be combined to isolate the complex-valued overlap between a given onepulse target wavepacket and a variable three-pulse reference wavepacket. We demonstrate that with a range of inter- and intrapulse-pair delays the complex overlaps and variable reference states can be used to reconstruct the target wavepacket. We compare our results with previous methods for vibronic state reconstruction based on linear WPI and discuss further generalizations of our method.

We present results of real-time tracking of atomic two-electron dynamics in an autoionizing transient wave packet in krypton. A coherent superposition of two Fano resonances is excited with a femtosecond extreme-ultraviolet pulse. The evolution of the corresponding wave packet is subsequently probed with a delayed infrared pulse. In our specific case, we get access to the interference between one- and two-electron excitation channels in the launched wave packet, which is superimposed on its decay through autoionization. A simple model is able to account for the observed dynamical evolution of this wave packet.

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.

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.