Wave Packet Revivals Research Articles

Laser-induced modification of an excited-state vibrational wave packet in neutral H2 observed in a pump-control scheme

We observe and modify a molecular vibrational wave packet in an electronically excited state of the neutral hydrogen molecule. In an extreme-ultraviolet (XUV) time-domain absorption spectroscopy experiment, we launch a vibrational wave packet in the DΠu13pπ state of H2 and track its time evolution via the coherent dipole response. The reconstructed time-dependent dipole from experimentally measured XUV absorption spectra provides access to the revival of the vibrational wave packet, which we control via an intense near-infrared (NIR) pulse. Tuning the intensity of the NIR pulse, we observe the revival of the wave packet to be significantly modified, which is supported by the results of a multilevel simulation as well as an analytical model based on state-specific phase shifts. The NIR field is applied only 7 fs after the creation of the wave packet but influences its evolution up to at least its first revival at 270 fs. This experimental approach for nonlocal-in-time laser modification of quantum dynamics in a pump-control scheme enabled by molecular self-probing is generally applicable to a large range of molecules and materials as it only requires the observation of absorption spectra. Published by the American Physical Society 2024

Wave packet dynamics of entangled q-deformed states

This paper explores the wave packet dynamics of a math-type q-deformed field interacting with atoms in a Kerr-type nonlinear medium. The primary focus is on the generation and dynamics of entanglement using the q-deformed field, with the quantification of entanglement accomplished through the von Neumann entropy. Two distinct initial q-deformed states, the q-deformed Fock state, and the q-deformed coherent state, are investigated. The entanglement dynamics reveal characteristics of periodic, quasi-periodic, and chaotic behaviour. Non-deformed initial states display wave packet near revivals and fractional revivals in entanglement dynamics while introducing q-deformation eliminates these features. The q-deformation significantly influences wave packet revivals and fractional revivals, with even a slight introduction causing their disappearance. For large values of q, the entanglement dynamics exhibit a chaotic nature. In the case of a beam splitter-type interaction applied to the initial deformed Fock state, an optimal deformation parameter q is identified, leading to maximum entanglement exceeding the non-deformed scenario.

Attosecond Probing of Nuclear Vibrations in the D2+ and HeH+ Molecular Ions.

We study the ultrafast photodissociation of small diatomic molecules using attosecond laser pulses of moderate intensity in the (extreme) ultraviolet regime. The simultaneous application of subfemtosecond laser pulses with different photon energies─resonant in the region of the molecular motion─allows one to monitor the vibrational dynamics of simple diatomics, like the D2+ and HeH+ molecular ions. In our real-time wave packet simulations, the nuclear dynamics is initiated either by sudden ionization (D2+) or by explicit pump pulses (HeH+) via distortion of the potential energy of the molecule. The application of time-delayed attosecond pulses leads to the breakup of the molecules, and the information on the underlying bound-state dynamics is imprinted in the kinetic energy release (KER) spectra of the outgoing fragments. We show that the KER-delay spectrograms generated in our ultrafast pump-probe schemes are able to reconstruct the most important features of the molecular motion within a given electronic state, such as the time period or amplitude of oscillations, interference patterns, or the revival and splitting of the nuclear wave packet. The impact of probe pulse duration, which is key to the applicability of the presented mapping scheme, is investigated in detail.

Exact Green's functions for localized irreversible potentials

We study the quantum-mechanical problem of scattering caused by a localized obstacle that breaks spatial and temporal reversibility. Accordingly, we follow Maxwell's prescription to achieve a violation of the second law of thermodynamics by means of a momentum-dependent interaction in the Hamiltonian, resulting in what is known as Maxwell's demon. We obtain the energy-dependent Green's function analytically, as well as its meromorphic structure. The poles lead directly to the solution of the evolution problem, in the spirit of M. Moshinsky's work published in the 1950s. Symmetric initial conditions are evolved in this way, showing important differences between classical and wave-like irreversibility in terms of collapses and revivals of wave packets. Our setting can be generalized to other wave operators, e.g. electromagnetic cavities in a classical regime.

Nonlinear dynamics of positron resonances in a carbon nanotube

We have investigated long-time dynamics of the transverse resonant states occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. This was done by a detailed analysis of quantum carpet, generated by the interference of the resonant states. We found that structure of the carpet depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Close to every fractional revival additional repeated and inverted reconstructed patterns were observed which do not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately, and conclude that dynamics, in this case, is quasi-periodic. This peculiar behavior was traced back to the level of coordination between fluctuations of resonances amplitude and phase functions.

On the exact revival of Morse oscillator wave packets

On the exact revival of Morse oscillator wave packets

Coupled Oscillator Dynamics in Brain EEG Signals: Manifestation of synchronization and Across Frequency Energy Exchange by Neutral Turbulence

Phenomenological models, involving coupled oscillators of both deterministic and stochastic nature, have been invoked to describe the behavior of the EEG signals, with experimental validation. These models derive justification from the fact that the basic electronic unit for potential generation, incorporating capacitive, inductive, and resistive components, as well as the source, is modelled as damped driven oscillator, which can behave independently and may also exhibit synchronized dynamics with others, that can manifest in spatially correlated behavior observed in brain dynamics. Here, using a phase-space approach, we show clear evidence of oscillator dynamics to wave packet collapse and revival in the brain EEG signals, with distinct differences in healthy individuals and epileptic patients. The low frequency components exhibit single oscillator type behavior in a phase-space description, with the potentials as coordinates and their instantaneous changes as the corresponding velocities. The closed paths reveal periodic motion, well described by one linear oscillator or possibly coupled ones with limit cycle dynamics and synchronization at the macroscopic level. The epileptic patients reveal dynamical features of bistability, originating from non-linearity, a prominent feature in the signals from the epileptogenic zone and much enhanced during the periods of seizure. Analogy from the phase-space of oscillator dynamics reveals dominance of potential energy in the signals from the epileptogenic zone, as also in the patients during occurrence of seizure. The acceleration, arising from the change of velocity, is found to be particularly strong in epileptic patients, when the phase space shows bi-stability and bursty behavior. Wave behavior with characteristics of superposition emerges in the frequency range corresponding to the observed unstable periodic orbits that appear at 8-14Hz, centered at 10Hz. A modulated carrier wave is observed for all subjects at 18Hz, higher in width for patients. Coherent wave dynamics, with interference playing a key role in the wave packet collapse and revival, is observed starting from 18Hz, with the coherence getting significantly enhanced around 40-45Hz. Mechanism of intra frequency energy transfer is shown to be neutral turbulence.

Topological behavior of a neutral spin-1/2 particle in a background magnetic field

We present results of a numerical experiment in which a neutral spin-1/2 particle subjected to a static magnetic vortex field passes through a double-slit barrier. We demonstrate that the resulting interference pattern on a detection screen exhibits fringes reminiscent of Aharonov-Bohm scattering by a magnetic flux tube. To gain better understanding of the observed behavior, we provide analytic solutions for a neutral spin-1/2 rigid planar rotor in the aforementioned magnetic field. We demonstrate how that system exhibits a non-Abelian Aharonov-Bohm effect due to the emergence of an effective Wu-Yang (WY)flux tube. We study the behavior of the gauge invariant partition function and demonstrate a topological phase transition for the spin-1/2 planar rotor. We provide an expression for the partition function in which its dependence on the Wilson loop integral of the WY gauge potential is explicit. We generalize to a spin-1 system in order to explore the Wilzcek-Zee (WZ) mechanism in a full quantum setting. We show how degeneracy can be lifted by higher order gauge corrections that alter the semi-classical, non-Abelian, WZ phase. Models that allow analytic description offer a foil to objections that question the fidelity of predictions based on the generalized Born-Oppenheimer approximation in atomic and molecular systems. Though the primary focus of this study concerns the emergence of gauge structure in neutral systems, the theory is also applicable to systems that posses electric charge. In that case, we explore interference between fundamental gauge fields (i.e. electromagnetism) with effective gauge potentials. We propose a possible laboratory demonstration for the latter in an ion trap setting. We illustrate how effective gauge potentials influence wave-packet revivals in the said ion trap.

Dynamical Interference of Shannon Information Entropy: Identification of Wave-Packet Fractional Revivals

Wave packet fractional revivals appear as manifestation of a multiple interference of various components of a wave packet during its long-time evolution in a bounded system. We study the phenomenon of fractional revivals by means of the time-dependent interference of information entropy density associated with a bound-state wave packet, which exhibits the formation of self-similar structures – quantum carpets woven by information entropy. The recurrences of self-similarity in the design of entropic carpet mimic the phenomena of quantum revivals and fractional revivals. We show that information theoretic measures are more sensitive to identify the wave-packet fractional revivals.

Quantum erasing of laser emission in N2.

Cavity-free lasing of N2+ induced by a femtosecond laser pulse at 800 nm is nearly totally suppressed by a delayed twin control pulse. We explain this surprising effect within the V-scheme of lasing without population inversion. A fast transfer of population between nitrogen ionic states X2Σg+ and A2Πu, induced by the second pulse, terminates the conditions for amplification in the system. The appearance of short lasing bursts at delays corresponding to revivals of rotational wave packets is explained along the same lines.

Coherent states of position-dependent mass trapped in an infinite square well

We develop generalized coherent states based on the Gazeau–Klauder formalism for a particle with position-dependent mass trapped in an infinite square well. We study the quantum statistical properties of these states by means of the Mandel parameter and the second-order correlation function. Our analysis reveals that the constructed coherent states exhibit sub-Poissonian statistics. Moreover, theoretical investigations of wave packet revivals and fractional revivals for the pertaining system have been performed by means of the autocorrelation function and temporal evolution of probability density.

Extremely nonlinear Raman interaction of an ultrashort nitrogen ion laser with an impulsively excited molecular wave packet

We report generation of cascaded rotational Raman scattering up to 58th orders in coherently excited CO_2 molecules. The high-order Raman scattering, which produces a quasiperiodic frequency comb with more than 600 sidebands, is obtained using an intense femtosecond laser to impulsively excite rotational coherence and the femtosecond-laser-induced N_2^+ lasing to generate cascaded Raman signals. The novel configuration allows this experiment to be performed with a single femtosecond laser beam at free-space standoff locations. It is revealed that the efficient spectral extension of Raman signals is attributed to the specific spectra-temporal structures of N_2^+ lasing, the ideal spatial overlap of femtosecond laser and N2+ lasing, and the guiding effect of molecular alignment. The Raman spectrum extending above 2000 cm^-1 naturally corresponds to a femtosecond pulse train due to the periodic revivals of molecular rotational wavepackets.

Echo in a single vibrationally excited molecule

Echo is a ubiquitous phenomenon found in many physical systems, ranging from spins in magnetic fields to particle beams in hadron accelerators. It is typically observed in inhomogeneously broadened ensembles of nonlinear objects, and is used to eliminate the effects of environmental-induced dephasing, enabling observation of proper, inherent object properties. Here, we report experimental observation of quantum wave packet echoes in a single isolated molecule. In contrast to conventional echoes, here the entire dephasing-rephasing cycle occurs within a single molecule without any inhomogeneous spread of molecular properties, or any interaction with the environment. In our experiments, we use a short laser pulse to impulsively excite a vibrational wave packet in an anharmonic molecular potential, and observe its oscillations and eventual dispersion with time. A second delayed pulsed excitation is applied, giving rise to an echo: a partial recovery of the initial coherent wavepacket. The vibrational dynamics of single molecules is visualized by time-delayed probe pulse dissociating them one at a time. Two mechanisms for the echo formation are discussed: ac Stark-induced molecular potential shaking and creation of depletion-induced "hole" in the nuclear spatial distribution. Interplay between the optically induced echoes and quantum revivals of the vibrational wave packets is observed and theoretically analyzed. The single molecule wave packet echoes may lead to the development of new tools for probing ultrafast intramolecular processes in various molecules.

Experimental study of the interplay between dynamic localization and Anderson localization

We investigate the interplay between two fundamentally different localization mechanisms in discrete systems: dynamic localization, i.e., resonant wave packet revivals in periodically driven lattices, and Anderson localization, the suppression of transverse transport in the presence of disorder. Using curved femtosecond laser-written photonic lattices as the experimental platform, we directly observe the propagation dynamics for varying degrees of diagonal disorder and characterize the transition between the two regimes of localization.

Femtosecond wave-packet revivals in ozone

Photodissociation of ozone following absorption of biologically harmful solar ultraviolet radiation is the key mechanism for the life protecting properties of the atmospheric ozone layer. Even though ozone photolysis is described successfully by post-Hartree-Fock theory, it has evaded direct experimental access so far, due to the unavailability of intense ultrashort deep ultraviolet radiation sources. The rapidity of ozone photolysis with predicted values of a few tens of femtoseconds renders both ultrashort pump and probe pulses indispensable to capture this manifestation of ultrafast chemistry. Here, we present the observation of femtosecond time-scale electronic and nuclear dynamics of ozone triggered by \ensuremath{\sim}10-fs, \ensuremath{\sim}2-\textmu{}J deep ultraviolet pulses and, in contrast to conventional attochemistry experiments, probed by extreme ultraviolet isolated pulses. An electronic wave packet is first created. We follow the splitting of the excited B-state related nuclear wave packet into a path leading to molecular fragmentation and an oscillating path, revolving around the Franck-Condon point with 22-fs wave-packet revival time. Full quantum-mechanical ab initio multiconfigurational time-dependent Hartree simulations support this interpretation.

Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. I. Time-resolved photoelectron-photoion coincidence spectroscopy.

The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1Bu (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans' correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S1(21Ag) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 11Bu and 21Ag states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S2(11Bu) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1Bu surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.

Excited state dynamics of molecules studied with femtosecond time-resolved mass spectrometry and photoelectron imaging

Study of quantum states of molecules, especially the evolution of excited states can help to understand their basic features and the interactions among different states. Furthermore, the information about the chemical reaction process and the interactions among several reaction channels can be obtained. Femtosecond time-resolved mass spectrometry (TRMS) and time-resolved photoelectron imaging (TRPEI), which combine pump-probe technique with time of flight mass spectrometry and photoelectron imaging, are powerful tools for detecting the molecular quantum state and for studying the molecular quantum state interaction and molecular ultrafast dynamics. With these methods, the photochemistry and photophysics mechanism of isolated molecule reaction process can be investigated on a femtosecond time scale. The principles of TRMS and TRPEI are introduced here in detail. On the basis of substantial research achievements in our group, the applications of TRMS and TRPEI are presented in the study of ultrafast internal conversion and intersystem crossing, wavepacket evolution dynamics at excited states of polyatomic molecules, energy transfer process of polyatomic molecules, ultrafast photodissociation dynamics and structural evolution dynamics of molecular excited states. In the study of ultrafast internal conversion and intersystem crossing, the methyl substituted benzene derivatives and benzene halides are discussed as typical molecular systems. In the study of wavepacket evolution dynamics at excited states of polyatomic molecules, the real-time visualization of the dynamic evolution of CS2 4d and 6s Rydberg wave packet components, the vibrational wave packet dynamics in electronically excited pyrimidine, the rotational wave packet revivals and field-free alignment in excited o-dichlorobenzene are reported. In order to discuss the energy transfer process of polyatomic molecules, the intramolecular vibrational energy redisctribution between different vibrational states in p-difluorobenzene in the S1 low-energy regime and the intramolecular energy transfer between different electronic states in excited cyclopentanone are presented. For the study of ultrafast photodissociation dynamics, the dissociation constants and dynamics of the A band and even higher Rydberg states are investigated for the iodine alkanes and iodine cycloalkanes. Structural evolution dynamics of molecular excited states is the main focus of our recent research. The structural evolution dynamics can be extracted from the coherent superposition preparation of quantum states and the observation of quantum beat phenomenon, by taking 2, 4-difluorophenol and o-fluorophenol as examples. Time-dependent photoelectron peaks originating from the planar and nonplanar geometries in the first excited state in 2, 4-difluorophenol exhibit the clear beats with similar periodicities but a phase shift of π rad, offering an unambiguous picture of the oscillating nuclear motion between the planar geometry and the nonplanar minimum. Also, the structural evolution dynamics in o-fluorophenol via the butterfly vibration between planar geometry and nonplanar minimum is mapped directly. Finally, the potential developments and further possible research work and future directions of these techniques and researches are prospected.

Ro-vibrational revival of the molecular hydrogen wave packet by a two-color pump in four-wave Raman mixing

Ro-vibrational revival of the molecular hydrogen wave packet by a two-color pump in four-wave Raman mixing

Investigation of the photodetached electronic wave packet dynamics in a magnetic field near a surface

The electronic wave packet dynamics photodetached from H− ion in a magnetic field near an elastic surface has been studied by using the time-dependent perturbation theory combined with the semiclassical closed orbit theory for the first time. Firstly, we put forward an analytic formula for calculating the autocorrelation function of this system. Then we calculate and analyze the autocorrelation function in great detail. It is demonstrated that the quantum wave packet revival phenomenon is significant when the laser pulse width is far less than the period of the detached electron’s closed orbit. As the pulse width is close to the period of the detached electron’s closed orbit, the quantum wave packet revival phenomenon becomes weakened. When the laser pulse width is bigger than the period of the closed orbit of the detached electron, the adjacent revival peaks in the autocorrelation function begin to merge and the quantum revival phenomenon disappears. In addition, the magnetic field strength can also affect the autocorrelation function of this system. As the magnetic field strength is relatively small, the quantum wave packet revival phenomenon is weak. With the increase of the magnetic field strength, the number of the reviving peaks in the autocorrelation function becomes increased and the quantum wave packet revival phenomenon becomes significant. Therefore, we can control the quantum wave packet revival in the autocorrelation function of this system by changing the laser pulse width and the external magnetic field strength. This study can guide the future experimental research on the wave packet dynamics of atoms or ions in the external fields or surfaces.

Isotope-selective molecular alignment induced by optimal laser pulses

ABSTRACTFluence-specified optimal control simulation is applied to C16O/C18O and 14N2/15N2 mixtures to numerically design laser pulses that best achieve isotope-selective alignment. The degree of control is measured in terms of selectivity, which is defined by the difference in the degree of alignment between a heavy isotopologue (HI) and a light isotopologue (LI). Optimal pulses are composed of several subpulses that cooperate with the so-called revivals of the rotational wave packets. Although the two mixtures have slightly different molecular parameters and isotope shifts, it turns out that the optimal pulses share common multi-pulse structures. We also develop a pulse-partitioning analysis to quantitatively and systematically examine the role of inter-subpulse cooperation in the improvement of the isotope-selective alignment. According to the analyses, we find that the ‘coherent’ and the ‘incoherent’ inter-subpulse cooperation almost equally contribute to the improvement of the degree of alignment (HI) as well as that of anti-alignment (LI).