Clocking Ultrafast Wave Packet Dynamics in Molecules through UV-Induced Symmetry Breaking

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.

We present a method for probing ultrafast nuclear dynamics in molecules using transient enhancement of high-order harmonic generation (HHG). The method exploits strong dependence of the overall harmonic yield in a fixed spectral range on the nuclear separation in a molecule, which is shown to take place for both aligned and randomly oriented molecules. Our numerical simulations show that this method is capable of monitoring long-term evolution of the nuclear vibrational wave packets in molecules, even in light-weight ones, with very high time resolution. By the example of D2+ vibrational wave packet launched via tunnelling ionization of D2 and probed by a time-delayed 8 fs laser pulse with λ = 800 nm and the peak intensity of 1014 W cm-2, we show that the time-delay dependence of the high harmonic signal exhibits pronounced features, which are due to the collapses and revivals of the nuclear wave packet. The time-frequency analysis of the pump–probe signal reveals structures with a periodicity down to 6 fs, which correspond to the fractional revivals of orders 1/5 and 1/10. With the laser parameters used, the deuteron motion during the probe pulse is shown to have almost negligible effect on the resulting signal.

We derive stochastic master equations for a quantum system interacting with a Bose field prepared in a superposition of continuous-mode coherent states. To determine a conditional evolution of the quantum system, we use a collision model with an environment given as an infinite chain of not interacting between themselves qubits prepared initially in an entangled state being a discrete analogue of a superposition of coherent states of the Bose field. The elements of the environment chain interact with the quantum system in turn one by one, and they are subsequently measured. We determine a conditional evolution of the quantum system for continuous in time observations of the output field as a limit of discrete recurrence equations. We consider the stochastic master equations for a counting as well as for a diffusive stochastic process.

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.

In this paper, a new state called superposition of three-mode photon-added trio coherent state is introduced and its nonclassical properties are studied. Based on the negative values of the Wigner function, we find that the nonclassical as well as non-Gaussian characteristics of the superposition of three-mode photon-added trio coherent state are more obvious than that of the original trio coherent state. The superposition of three-mode photon-added trio coherent state always appears three-mode sum squeezing while the trio coherent state does not. It also shows that the superposition of three-mode photon-added trio coherent state is genuinely entangled. The entanglement degree of this state is more improved compared with the trio coherent state. It becomes bigger and bigger through nonlocally increasing the number of added photons.

At the 1990 UFP conference the observation of several kinds of wave packets was reported [1]. All these wavepackets have in common that the wavefunction is localised due to a coherent superposition of eigenstates. The localised ‘particle’ evolves in course of time. The oscillation time of the wavepacket is determined by the inverse spacing of the states out of which the wavepacket is formed. We reported on the localisation of an atomic electron wavefunction by coherent superposition of Rydberg states. Also the observation of exciton wavepackets was reported, as well as the observations of optic phonons in the time domain. At an earlier conference the CalTech group reported already the observation of the oscillation of vibrational wavepackets in diatomic molecules [2].

Forward and backward electron/proton ionization/dissociation spectra from one-dimensional non-Born-Oppenheimer H2 molecule exposed to ultrashort intense laser pulses ( W/cm2, λ = 800 nm) have been computed by numerically solving the time-dependent Schrodinger equation. The resulting above-threshold ionization and above-threshold dissociation spectra exhibit the characteristic forward-backward asymmetry and sensitivity to the carrier-envelope phase (CEP), particularly for high energies. A general framework for understanding CEP effects in the asymmetry of dissociative ionization of H2 has been established. It is found that the symmetry breaking of electron-proton distribution with π periodic modulation occurs for all CEPs except for ( integer) and the largest asymmetry coming from the CEP of . At least one of the electron and proton distributions is asymmetric when measured simultaneously. Inspection of the nuclear and electron wave packet dynamics provides further information about the relative contribution of the gerade and ungerade states of to the dissociation channel and the time delay of electrons in asymmetric ionization. © 2014 Wiley Periodicals, Inc.

When an atom interacts with an intense laser pulse which generates electric fields comparable to the atomic (Coulombic) field, high order processes become dominant as for example multiphoton ionization(1) and above threshold ionization(2). In some particular circumstances however, coherence phenomena may be at the origin of a substantial inhibition of ionization and lead to the stabilization of the atom. In this contribution, we analyze in detail a physical mechanism which is responsible for strong suppression of ionization(3). We show that the intense field excitation of the atom may generate a new kind of spatially extended wave packet through virtual transitions from the initial state via high-lying Rydberg and continuum states to a coherent superposition of Rydberg states with a small initial overlap with the nucleus. Conventional atomic wave packets(4) are created by direct short pulse excitation of overlapping Rydberg states from a compact initial source which ensures a large initial overlap with the nucleus and a substantial ionization. By contrast, our wave packet stems from extended high-lying states which are accessed virtually through Raman coupling rather than directly through short pulse excitation from compact low-lying states.

We calculate the second-order moments, the Robertson-Schrödinger uncertainty product, and the Mandel factor for various superpositions of coherent phase states with opposite arguments, comparing the results with similar superpositions of the usual (Klauder-Glauber-Sudarshan) coherent states. We discover that the coordinate variance in the analog of even coherent states can show the most strong squeezing effect, close to the maximal possible squeezing for the given mean photon number. On the other hand, the Robertson-Schrödinger (RS) uncertainty product in superpositions of coherent phase states increases much slower (as function of the mean photon number) than in superpositions of the usual coherent states. A nontrivial behavior of the Mandel factor for small mean photon numbers is discovered in superpositions with unequal weights of two components. An exceptional nature of the even and odd superpositions is demonstrated.

Symmetry breaking and control of bond selective dissociation can be achieved by means of ultrashort few-cycle-infrared (IR) and ultraviolet (UV) laser pulses. The mechanism is demonstrated for the oriented model system, FHF-, by nuclear wave packets which are propagated on two-dimensional potential energy surfaces calculated at the QCISD/d-aug-cc-pVTZ level of theory. The IR laser pulse is optimized to drive the wave packet coherently along alternate bonds. Next, a well-timed ultrashort UV laser pulse excites the wave packet, via photodetachment of the negative bihalide anion, to the bond selective domain of the neutral surface close to the transition state. The excited wave packet is then biased to evolve along the pre-excited bond toward the target product channel, rather than bifurcating in equal amounts. Comparison of the vibrational frequencies obtained within our model with harmonic and experimental frequencies indicates substantial anharmonicities and mode couplings which impose restrictions on the mechanism in the domain of ultrashort laser fields. Extended applications of the method to randomly oriented or to asymmetric systems XHY- are also discussed, implying the control of product directionality and competing bond-breaking.

A time-dependent theoretical method is used to describe a UV pump–UV probe strategy to trace, at a femtosecond time scale, the motion of vibrational wave packets created in excited states of the hydrogen molecule by measuring single ionization probabilities. We use a spectral method to solve the time-dependent Schrodinger equation in full dimensionality, including correlation and all electronic and vibrational degrees of freedom. A pump pulse initially creates a vibrational wave packet in the intermediate electronic excited states of $$\hbox{H}_2$$ . The frequency of the probe is chosen to ionize the target leaving the ion in a bound vibrational state. By varying the time delay between pulses, non-dissociative single ionization is enhanced or suppressed. Energy differential ionization probabilities are reported and compared with a model based on the Franck–Condon approximation.

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.

A coherent superposition of two electronic states of ozone (ground and Hartley B) is prepared with a UV pump pulse. Using the multiconfiguration time-dependent Hartree approach, we calculate the subsequent time evolution of the two corresponding nuclear wave packets and the coherence between them. The resulting wave packet shows an oscillation between the two chemical bonds. Even more interesting, the coherence between the two electronics states reappears after the laser pulse is switched off, which could be observed experimentally with an attosecond probe pulse.

In Rhodobacter sphaeroides R-26 reaction centers (RCs) the nuclear wave packet induced by 25 fs excitation at 90 K moves on the primary electron donor P* potential energy hypersurface with initial frequency at approximately 130 cm(-1) (monitored by stimulated emission measurement). At the long-wavelength side of P* stimulated emission at 935 nm the wave packet is transferred to the surface with P(+)B(A)(-) character at 120, 380, 1.2 fs, etc. delays (monitored by measurement of the primary electron acceptor B(A)(-) band at 1020 nm). However, only beginning from 380 fs delay and later the relative stabilization of the state P(+)B(A)(-) is observed. This is accompanied by the electron transfer to bacteriopheophytin H(A) (monitored by H(A) band measurement at 760 nm). The most active mode of 32 cm(-1) in the electron transfer and its overtones up to the seventh were found in the Fourier transform spectrum of the oscillatory part of the kinetics of the P* stimulated emission and of the P(+)B(A)(-) and P(+)H(A)(-) formation. This mode and its overtones are apparently populated via the 130 cm(-1) vibrational mode. The deuteration of the sample shifts the fundamental frequency (32 cm(-1)) and all overtones by the same factor of approximately 1.3. This mode and its overtones are suppressed by a factor of approximately 4.7 in the dry film of RCs. The results obtained indicate that the 32 cm(-1) mode might be related to a rotation of hydrogen-containing groups (possibly the water molecule) participating in the modulation of the primary electron transfer from P* to B(A)(-) in at least 35% of RCs. The Brookhaven Protein Data Bank (1PRC) displays the water molecule located at the position HOH302 between His M200 (axial ligand for P(B)) and the oxygen of ring V of B(A) which might be a part (approximately 35%) of the molecular pathway for electron transfer from P* to B(A).