The dynamics of a THz Rydberg wavepacket

An optically excited Rydberg wavepacket can be generated by exciting the electron from a low-lying state to a coherent superposition of high-lying states with a short broadband optical pulse. A special kind of Rydberg wavepacket is generated in the case of a interaction of a weak THz half cycle pulse with a stationary Rydberg state, called the THz wavepacket. This THz wavepacket is a coherent superposition of the initial Rydberg state and its neighbouring states. We have investigated the time evolution of THz wavepackets by measuring the impact of two in time delayed half cycle pulses ( ≈ 200 V cm^-1) on the population of a stationary (n = 40) Rydberg state in rubidium. The first half cycle pulse creates the THz wavepacket and the second half cycle pulse probes the dynamics of the THz wavepacket. We support our experimental data by numerically solving the Schr?dinger equation and with a semi-classical picture. Whereas an optically excited wavepacket is initially localized, a THz wavepacket is initially delocalized and becomes localized after half a revival time. Received 23 August 2000 and Received in final form 27 March 2001     

Dimension-dependent stimulated radiative interaction of a single electron quantum wavepacket

In the foundation of quantum mechanics, the spatial dimensions of electron wavepacket are understood only in terms of an expectation value – the probability distribution of the particle location. One can still inquire how the quantum electron wavepacket size affects a physical process. Here we address the fundamental physics problem of particle–wave duality and the measurability of a free electron quantum wavepacket. Our analysis of stimulated radiative interaction of an electron wavepacket, accompanied by numerical computations, reveals two limits. In the quantum regime of long wavepacket size relative to radiation wavelength, one obtains only quantum-recoil multiphoton sidebands in the electron energy spectrum. In the opposite regime, the wavepacket interaction approaches the limit of classical point-particle acceleration. The wavepacket features can be revealed in experiments carried out in the intermediate regime of wavepacket size commensurate with the radiation wavelength.     

Measure of the tunnelling time of a single photon through a Fabry-Perot cavity

The displacement of the peak of a wavepacket that crosses an empty Fabry-Perot cavity is measured by using photon pairs generated by parametric down conversion, a Hong-Ou-Mandel (HOM) interferometer and coincidence detection. The Fabry-Perot cavity distorts the photon wavepacket. The HOM interferometer is a good tool to map this distortion. We discuss the corrections which must be made in the two-photon inteference results, in order to achieve the true data researched. Even in the absence of active absorbers media or media with inverted atomic populations, superluminal-like effects connected with the tunnelling phenomena are observed. An interpretation of the experimental results in the causality frame is given.     

Field-Free Molecular Orientation Generated from Cyclic Rotational States by Using Two Trains of Half-Cycle Pulses

We show that two trains of half-cycle pulses （HCPs） with different amplitudes irradiating alternately on polar molecules can achieve a remarkable enhancement of field-free orientation compared with the case of an equal amplitude HCPs train for the same pulse separation. optimal adjustment of the population distribution on This kind of orientation enhancements is mainly due to an every field-free angular momentum eigenstate, in which the populations on the undesired states of high angular momenta are effectively suppressed, and the populations on the desired states of low angular momenta are correspondingly promoted.     

Propagator of an electron in a cavity in the presence of a coherent photonic field

In the present paper we consider the case of an electron under the presence of a single mode field in a cavity linearly polarized in the z-direction. We adopt the dipole approximation and we derive the full propagator of the electron. In the present case we suppose that the field is in a coherent state. The parameters of the propagator involve Mathieu functions. Finally we extract the time evolution of an initially Gaussian wavepacket and its probability density. The present theory is applicable to the interaction of strong fields with atoms. Received 17 March 2000 and Received in final form 19 December 2000     

Exact Timing of Returned Molecular Wavepacket

An ionizing wavepacket of electron will re-visit its parent molecular ion during photoionization by strong laser field. This scenario is associated with physical concepts such as molecular re-scattering/collision, interference, diffraction, molecular clock, and generation of XUV light via high-order harmonic generation. On the workbench of a reduced dimensionality model of molecular hydrogen ions irradiated by laser pulse of 0.01-10.0 a.u. intensities, one-cycle pulsewidth, and 800nm wavelength, by deploying a momentum operator on the time-dependent wavefunction of an ionizing wavepacket, we can determine, in a precise manner, the exact time instant for the re-visiting electron to come back to the cation position. The time value is 57.6% of an optical cycle of the exciting laser pulse. This result may be useful in attosecond pump-probe experiments or molecular clock applications.     

Isotopomer selective optimization of <Superscript>39</Superscript>K<Superscript>85</Superscript>Rb<Superscript>+</Superscript> and <Superscript>41</Superscript>K<Superscript>87</Superscript>Rb<Superscript>+</Superscript> using optimal control

We report on isotope selective three-photon ionization of two isotopomers of KRb by applying evolution strategies. The particularity of this experiment is based on the high resolution phase and amplitude modulation of the fs-laser pulses provided by a 2 × 640 pixel pulse shaper. The optimization in a closed feedback loop performed with spectrally broad pulses centered at 840 nm shows high enhancements of one isotopomer at the expense of the other isotopomer and vice versa. From the optimal laser field we aim to gain details about the selective ionization sequence and the wavepacket evolution on the involved vibrational states.     

The dynamics and stabilities of Bose-Einstein condensates in deep optical lattices

The dynamics and stabilities of Bose-Einstein condensate (BEC) trapped in a deep one-dimensional periodic optical lattices with three-body interactions are investigated. By using the tight-binding approximation, the Bloch and the Bogoliubov excitation stabilities and the dynamics of the BEC wavepacket with the effects of the three-body interactions are studied. The critical conditions for occurrence of the dynamical/Landau instabilities, self-trapping/diffusion/breather of wavepacket, and localized soliton are obtained analytically. The results show that the boundaries of the dynamical instability and Landau instability are modified significantly due to the presence of the three-body interactions. It is also revealed that, the initial wavepacket width, the initial momentum, especially, the strength of the three-body force have strong effect on the critical conditions which are used to describe the dynamics of the wavepacket. It is shown that the regions of self-trapping, diffusion, and breather for BEC wavepacket in the parameter space are modified dramatically by the three-body interactions. The analytical results are confirmed by the direct numerical solutions of the discrete GPE.     

Carrier conduction through the quantum barrier region in a heterostructure barrier varactor induced by an ac bias

By solving the time-dependent Schrödinger equation, we have studied the quantum transport of a wavepacket in a GaAs/AlGaAs heterostructure barrier varactor (HBV) diode induced by an ac bias. The current conduction of a wavepacket is complicated due to the superposition of many different stationary states. When the oscillating frequency of the external bias is relatively low, the motion of the wavepacket follows the electric field induced by the external bias. When the frequency is too high (over 1000 GHz for the GaAs/AlGaAs HBV structure under investigation), the wavepacket becomes effectively confined by the oscillating bias, and the conduction current is significantly reduced.     

Reliable Lateral Manipulation of Single Adatom on Metal fcc（lll） Surfaces with a Single-Atom Tip

Using molecular statistics simulations based on the embedded atom method potential, we investigate the reliability of the lateral manipulation of single Pt adatom on Pt（111） surface with a single-atom tip for different tip heights （tip-surface distance） and tip orientations. In the higher tip-height range, tip orientation has little influence on the reliability of the manipulation, and there is an optimal manipulation reliability in this range. In the lower tip- height range the reliability is sensitive to the tip orientation, suggesting that we can obtain a better manipulation reliability with a proper tip orientation. These results can also be extended to the lateral manipulation of Pd adatom on P d （111） surface.     

The influence of the anion vibrational temperature on the fs dynamics in a NeNePo experiment

A negative-neutral-positive (NeNePo) femtosecond charge-reversal experiment studying the temperature-dependent relaxation dynamics of linear Ag₃ is described. A wavepacket is prepared on the potential-energy surface of the electronic ground state of the neutral trimer by photodetachment from an anion ensemble held at different, well-defined temperatures between 20 K and 350 K. The wavepacket dynamics is probed by resonant two-photon ionization. The cooled octopole ion trap developed to prepare the cold anions is described. The relaxation dynamics of the initially linear Ag₃ from a saddle point of the potential-energy surface into the triangular equilibrium configuration shows a significant dependence on the anion temperature, which is rationalized in terms of a simple model. We demonstrate that a low anion vibrational temperature results in the generation of “narrower” wavepackets on the neutral potential-energy surface. This allows us to probe coherent effects more sensitively. Received: 10 January 2000 / Published online: 24 July 2000     

Laser Controlling Wavepacket Trains of a Paul Trapped Ion

We have studied the quantum and classical motions of a single Paul trapped ion interacting with a time-periodic laser field. By using the test-function method, we construct n exact solutions of quantum dynamics that describe the generalized squeezed coherent states with the expectation orbits being the corresponding classical ones. The space-time evolutions of the exact probability densities show some wavepacket trains. It is demonstrated analytically that by adjusting the laser intensity and frequency, we can control the center motions of the wavepacket trains. We also discuss the other physical properties such as the expectation value of energy, the widths and heights of the wavepackets, and the resonance loss of stability.     

The influence of femtosecond laser parameters on the wavepacket and population of the diabatic excited states of NaLi

Using the three-state model and time-dependent wavepacket method, the influence of the parameters of the intense femtosecond laser field on the wavepacket dynamic process of the double-minimum potential state 5¹Σ⁺ and the population of the ground and diabatic electronic states of NaLi are investigated. The calculations show that different femtosecond laser parameters result in different influences on the evolution of the wavepacket and the population of NaLi. With increasing laser intensity and wavelength the diabatic coupling strength between A and B states first strengthens and then weakens. The population interchanges between A and B states when the laser pulse disappears. The above results provide the suggestions and useful information for one to achieve quantum manipulation of the molecule in an experiment.     

Quantum nondemolition measurement of transverse atomic position in Kapitza-Dirac atomic beam scattering

It is demonstrated that one can measure the distribution of the transverse position of an atom crossing one or more optical cavities by monitoring the phase of the standing wave fields in the cavities. For the atom-field interaction the Kapitza-Dirac regime is assumed; it is shown that in this regime the method represents a quantum nondemolition measurement of the atomic position. On the other hand it can be applied to prepare narrow distributions of the transverse atomic position. In order to show this, a numerical simulation is performed, which illustrates the collapse of a broad initial Gaussian wavepacket, which can be coherent or incoherent, to a distribution with narrow peaks. Preparing the cavity fields in a squeezed state, one can greatly enhance the impact of the cavity field measurements on the atomic density matrix.     

Highly localized vibronic wavepackets in large reactive molecules

The ultrafast dynamics of the internal conversion of S₁ azulene and the excited-state intramolecular proton transfer in 2-(2^′-hydroxyphenyl)benzothiazole (HBT) were investigated by pump–probe spectroscopy with tunable pulses as short as 20 fs. In both cases we find very pronounced oscillatory contributions to the transients, which are due to vibrational wavepacket motion in the excited state. The damping times are on the order of 1 ps even for these large reactive molecules in solution at room temperature. For azulene only 2 out of 48 vibrational modes participate and in HBT only 4 out of 69. This high degree of localization of the wavepacket seems to be a general feature, and supports hopes that even for systems of chemical interest coherent control might be possible. Received: 24 January 2000 / Published online: 24 July 2000     

Subvacuum effects of the quantum field on the dynamics of a test particle

We study the effects of the electromagnetic subvacuum fluctuations on the dynamics of a nonrelativistic charged particle in a wavepacket. The influence from the quantum field is expected to give an additional effect to the velocity uncertainty of the particle. In the case of a static wavepacket, the observed velocity dispersion is smaller in the electromagnetic squeezed vacuum background than in the normal vacuum background. This leads to the subvacuum effect. The extent of reduction in velocity dispersion associated with this subvacuum effect is further studied by introducing a switching function. It is shown that the slow switching process may make this subvacuum effect insignificant. We also point out that when the center of the wavepacket undergoes non-inertial motion, reduction in the velocity dispersion becomes less effective with its evolution, no matter how we manipulate the nonstationary quantum noise via the choice of the squeeze parameters. The role of the underlying fluctuation–dissipation relation is discussed.     

Dissociative adsorption of H2: Time-dependent quantum studies

In this short review we consider some selected results for the dissociation of hydrogen on metal surfaces. In particular we focus our attention on the effects that surface corrugation have on the dissociation and also how rotations and vibrations couple in the interaction region. Results from time dependent quantum wavepacket calculations have been particularly helpful in forming our ideas of how diatomics dissociate. We describe this method along with two examples of propagation schemes. The power of limited dimensional models to rationalize experimental observations is clearly demonstrated.     

Control of wavepacket dynamics in mixed alkali metal clusters by optimally shaped fs pulses

We have performed adaptive feedback optimization of phase-shaped femtosecond laser pulses to control the wavepacket dynamics of small mixed alkali-metal clusters. An optimization algorithm based on Evolutionary Strategies was used to maximize the ion intensities. The optimized pulses for NaK and Na₂K converged to pulse trains consisting of numerous peaks. The timing of the elements of the pulse trains corresponds to integer and half integer numbers of the vibrational periods of the molecules, reflecting the wavepacket dynamics in their excited states. Received 4 December 2001