Selective preparation of ground state wave-packets: a theoretical analysis of femtosecond pump-dump-probe experiments on the potassium dimer

We present simulations on pump-dump-probe experiments performed on the potassium dimer. The interaction of two time-delayed laser pulses prepares vibrational wave packets in the electronic ground state. The quantum calculations reveal to what extent it is possible to prepare a ground state superposition of states with high versus low vibrational quantum numbers by changing the pump-dump delay time. It is shown that transient signals may exhibit interference effects which are due to characteristics of ground state wave-packets composed of two components showing different vibrational dynamics. In this way the signals are able to yield information about vibrational overtone motion. Received 27 September 2000 and Received in final form 21 November 2000     

The stability of magnetobipolarons in low-dimensional systems

We investigate the stability condition of large bipolarons confined in a parabolic potential containing certain parameters and a uniform magnetic field. The variational wave function is constructed as a product form of electronic parts, consisting of center of mass and internal motion, and a part of coherent phonons generated by Lee-Low-Pines transformation from the vacuum. An analytical expression for the bipolaron energy is found, from which the ground and excited-state energies are obtained numerically by minimization procedure. The bipolaron stability region is determined by comparing the bipolaron energy with those of two separate polarons, which is already calculated within the same approximation. It is shown that the results obtained for the ground state energy of bipolarons reduce to the existing works in zero magnetic field. In the presence of a magnetic field, the stability of bipolarons is examined, for three types of low-dimensional system, as function of certain parameters, such as the magnetic-field, the electron-phonon coupling constant, Coulomb repulsion and the confinement strength. Numerical solutions for the energy levels of the ground and first excited states are examined as functions of the same parameters. Received 7 March 2002 and Received in final form 22 April 2002 Published online 25 June 2002     

Ultrafast multidimensional dynamics of strong hydrogen bonds

The laser driven dynamics of the OH(D) stretching vibration in phthalic acid monomethylester is investigated. The combination of a 55-dimensional all-Cartesian reaction surface Hamiltonian and the time-dependent self-consistent field approach is shown to provide a microscopic picture of intramolecular vibrational energy redistribution taking place upon interaction with an external laser field. Choosing suitable zeroth-order vibrational states and combinations thereof a quasi-periodic in-phase and out-of-phase oscillatory behavior is observed manifesting energy flow on different time scales. The fingerprints of this behavior in transient absorption spectroscopy are also discussed. Received 24 August 2000 and Received in final form 11 October 2000     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. II. Quantum bipolarons

We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the vicinity of the adiabatic limit. Several approaches to investigate the quantum mobility of polarons and bipolarons are proposed for this model. First, the quantum fluctuations are treated as perturbations of the mean-field (or adiabatic) approximation of the electron-phonon coupling in order to calculate the bipolaron bands. It is found that the bipolaron mass generally remains very large except in the vicinity of the triple point of the phase diagram (see [1]), where the bipolarons have several degenerate configurations at the adiabatic limit (single site (S0), two sites (S1) and quadrisinglet (QS)), while the polarons are much lighter. This degeneracy reduces the bipolaron mass significantly. Next we improve this result by variational methods (modified Toyozawa Exponential Ansatz or TEA) valid for larger quantum perturbations away from the adiabatic limit. We first test this new method for the single polaron. We find that the triple point of the phase diagram is washed out by the lattice quantum fluctuations which thus suppress the light bipolarons. Further improvements of the method by hybridization of several TEA states do not change this conclusion. Next we show that some model variations, for example a phonon dispersion may increase the stability of the (QS) bipolaron against the quantum lattice fluctuations. We show that the triple point of the phase diagram may be stable to quantum lattice fluctuations and a very sharp mass reduction may occur, leading to bipolaron masses of the order of 100 bare electronic mass for realistic parameters. Thus we argue that such very light bipolarons could condense as a superconducting state at relatively high temperature when their interactions are not too large, that is, their density is small enough. This effect might be relevant for understanding the origin of the high superconductivity of doped cuprates far enough from half filling. Received 15 September 1999     

Stability of low-dimensionally-confined bipolarons

In the limit of strong electron-phonon coupling, we provide a unified insight into the stability criterion for bipolaron formation in low-dimensionally confined media. The model that we use consists of a pair of electrons immersed in a reservoir of bulk LO phonons and confined within an anisotropic parabolic potential box, whose barrier slopes can be tuned arbitrarily from zero to infinity. Thus, encompassing the bulk and all low-dimensional geometric configurations of general interest, we obtain an explicit tracking of the critical ratio of dielectric constants below which bipolarons can exist. Received 15 September 1999 and Received in final form 20 March 2000     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction , which tends to break them, generates many different ground-states. There are four domains in the phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small , large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large , large g); or 3) be a “quadrisinglet state” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. Received 10 December 1998     

Laser pulse control of ultrafast electron transfer reactions

The optimal control (OC) scheme for molecular dynamics is applied to the study of ultrafast bridge mediated electron transfer (ET). Utilizing the methods of dissipative quantum dynamics in combination with the OC approach the guided charge motion in a donor-bridge-acceptor system including a single active vibrational coordinate is studied. The control field drives the optical transition from the electronic ground-state of the ET system into the donor-level and can be used to prepare special electronic and vibrational states. In particular, it is demonstrated that charge localization becomes possible at the acceptor or bridge molecule as well as in the electronic ground-state of the ET system. Received 30 August 2000 and Received in final form 25 October 2000     

Numerical studies of the vibrational isocoordinate rule in chalcogenide glasses

Many properties of alloyed chalcogenide glasses can be closely correlated with the average coordination of these compounds. This is the case, for example, of the ultrasonic constants, dilatometric softening temperature and the vibrational densities of states. What is striking, however, is that, at a given average coordination, these properties are nevertheless almost independent of the elemental composition. Here, we report on some numerical verification of this experimental rule as applied to the vibrational density of states. We find that this rule is not exact but holds qualitatively well over a wide range of compositions and local chemical correlations. Received 25 April 2000     

Intensity and detuning dependence of fine structure changing collisions in a 85 Rb magneto-optical trap

In an experimental study, the multi-ionisation of metallic clusters (Na_n) has been analysed in collisions with light ions in low charge states (H⁺, He⁺, He²⁺, O³⁺) at collision velocities below 1 a.u. Cluster ions are produced in charge states up to 5+. The average charge of the nano-particles is found to increase linearly with the variation of projectile velocity and the square of the effective projectile charge, well in agreement with the electronic stopping power of the bulk material. A fraction of 50% to 30% of the total projectile energy loss (decreasing with velocity) is transferred into vibrational modes in good agreement with recent theoretical predictions. Received 8 November 2000 and Received in final form 26 January 2001     

Non-Markovian relaxation in an open quantum system

Non-Markovian dynamics in open quantum systems is characterized by a time-non-locality in the equation of motion valid for the reduced density operator. An expansion of this density matrix equation with respect to Laguerre polynomials is used to tackle the time-non-locality. The applicability and the numerical limitations of the method are discussed in detail. In order to illuminate the characteristics of non-Markovian dynamics the reference example is studied of a single quantum degree of freedom moving in a harmonic potential and being embedded in a heat bath. If interpreted as the photoinduced dynamics of nuclear motion in polyatomic molecules we can suggest two clear signatures of non-Markovian dynamics observable in ultrafast optical experiments, firstly a pronounced and somewhat irregular oscillatory behavior of the vibrational level populations, and secondly a separation of the vibrational wavepacket into a double-structure. Received 12 April 2000 and Received in final form 2 September 2000     

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     

Resonance and composition effects on the Raman scattering from silver-gold alloy clusters

Low-frequency Raman scattering experiments have been performed on thin films consisting of pure gold or gold-silver alloy clusters embedded in alumina matrix. It is clearly shown that the quadrupolar vibrational modes are observed by Raman scattering because of the effect of resonance with the excitation of the electronic surface dipolar plasmon. This is due to the strong coupling between the collective electronic dipolar excitation and the quadrupolar vibrational modes. This effect of resonance does not exist with the core electron excitations. The mixing of the conduction electron dipolar excitation (surface plasmon) with the core electrons leads to the quenching of the resonant Raman scattering. Received 16 November 2000     

Nonlinear electron-lattice interaction on excited states in polythiophene

In consideration of the effects of the square term of the electron-lattice interaction and the bond-bending term, the energy spectra and the localized vibrational modes around a bipolaron of the polythiophene are investigated based on the one-dimensional and two-dimensional extension SSH model. The results show that, with the influence of the square term, the energy gap increases, the frequencies of all the localized vibrational modes around a bipolaron decrease and their localizations also shift. It is noted that, an even-parity mode has been found which corresponds to absorption peak at 1220 cm⁻¹. When the bond-bending term is considered, the frequencies of the localized modes increase and five new localized modes appear. Among them, one Raman active mode and three infrared active modes may correspond the observed RRS absorption peaks at 1047 cm⁻¹ and three infrared absorption peaks at 370, 1020, 1120 cm⁻¹ in the experiments.     

Local field corrections for light absorption by fullerenes

Semi-empirical atom-atom potential energy calculations based on pairwise additive interactions are performed and, after applying the Born-Oppenheimer approximation to separate high frequency vibrational modes from low frequency orientational and translational modes, the infrared vibrational spectra of CO₂ and N₂O monomers trapped in an argon matrix at a temperature of 5 K are determined. It is shown that only a double substitutional site in argon can accommodate N₂O, whereas CO₂ is trapped in two distinct sites, of single and double substitutional types. The model shows that splitting of the degenerate mode occurs for both molecules in the double site. In the ground electronic state, the vibrational frequency shifts due to the matrix and the vibrational transition moments for low-lying levels are determined using the contact transformation method, as used for gas phase calculations. Calculated energy levels compare well with observed ones and the theory also predicts some unobserved levels. Moreover, calculations show no significant changes in the dipole moments of both CO₂ and N₂O trapped molecules. Received 22 March 2000 and Received in final form 10 May 2000     

Very fast relaxation in polycarbonate glass

Relaxations in amorphous bis-phenol A polycarbonate are studied by neutron scattering, as a function of temperature below the glass transition. Two different processes are observed. One is very fast, with a characteristic time (∼ 0.3 ps), that is independent of temperature and momentum transfer. Conversely the other is slower, with a time which is dependent on temperature and momentum transfer. The very fast localized anharmonic motion is interpreted by the overdamping of low-frequency vibrational modes, by nearby dynamic holes. The slower relaxation is thermally activated and momentum transfer dependent. It corresponds to molecular group motions and possibly to the short-time regime of the segmental relaxation. Received 29 February 2000 and Received in final form 13 June 2000     

Structural and vibrational properties of C36 and its oligomers (C36) M = 2, 3, 4 by tight-binding molecular dynamics

Non-orthogonal tight-binding molecular-dynamics is employed to calculate structural and vibrational properties of C₃₆ and its oligomers (C₃₆) _{M = 2, 3, 4} . The lowest energy configuration of the C ₃₆ cage is confirmed to have D _6h symmetry. For the dimer, too, the D _2h structure reported in the literature is found. The vibrational spectrum is identified with the power spectrum of the displacement autocorrelation function. Additional vibrational properties are extracted from the dynamical matrix. For the monomer, fair agreement with available ab initio calculations is achieved, with comparatively smaller deviations in the Raman-frequencies than for published semi-empirical calculations. The features of the vibrational modes are correlated with the structural properties of the oligomers. Received 24 November 2000 and Received in final form 24 August 2001     

Comparison of dephasing times for vibrational and rotational coherent anti-Stokes Raman scattering: implications for velocimetry

Time-domain coherent anti-Stokes Raman scattering experiments have been carried out by probing vibrational and pure rotational lines of nitrogen in the Doppler broadened regime. The theoretical analysis of the transient responses outlines the role of the geometrical effects. For pure rotational CARS, it is shown that the main contribution to the dephasing of the Raman coherence results from the change in direction between the pump and anti-Stokes wave vectors whereas the difference between the modulus of these two wave vectors accounts for dephasing in vibrational CARS. Furthermore, we demonstrate that the range of operation of time-domain CARS velocimetry is extended by probing pure rotational lines. The predictions are validated by experiments which are performed both in a static gas cell and in a Mach 10 supersonic flow. Received: 30 March 2000 / Revised version: 9 June 2000 / Published online: 13 September 2000     

Lifetimes of metastable states in Sr II

The lifetimes of the 4d ²D _3/2,5/2 levels of Sr⁺ have been determined both experimentally and theoretically. The experiment was performed at an ion storage ring utilising collinear laser excitation. The calculation was performed by the Hartree-Fock method including relativistic effects and core polarisation. The obtained lifetimes (which are about 0.4 s) are discussed in detail and compared with earlier published results. In addition, calculated lifetimes of a large number of excited states in Sr⁺ are included. Received 15 February 2000 and Received in final form 20 March 2000