Wave packet dynamics and control in excited states of molecular nitrogen

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

Direct observation of geometric-phase interference in dynamics around a conical intersection

Conical intersections are ubiquitous in chemistry and physics, often governing processes such as light harvesting, vision, photocatalysis and chemical reactivity. They act as funnels between electronic states of molecules, allowing rapid and efficient relaxation during chemical dynamics. In addition, when a reaction path encircles a conical intersection, the molecular wavefunction experiences a geometric phase, which can affect the outcome of the reaction through quantum-mechanical interference. Past experiments have measured indirect signatures of geometric phases in scattering patterns and spectroscopic observables, but there has been no direct observation of the underlying wavepacket interference. Here we experimentally observe geometric-phase interference in the dynamics of a wavepacket travelling around an engineered conical intersection in a programmable trapped-ion quantum simulator. To achieve this, we develop a technique to reconstruct the two-dimensional wavepacket densities of a trapped ion. Experiments agree with the theoretical model, demonstrating the ability of analogue quantum simulators-such as those realized using trapped ions-to accurately describe nuclear quantum effects.

Dynamics of an excitation-transfer trimer: Interference, coherence, Berry's phase development, and vibrational control of non-adiabaticity

We detail several interesting features in the dynamics of an equilaterally shaped electronic excitation-transfer (EET) trimer with distance-dependent intermonomer excitation-transfer couplings. In the absence of electronic-vibrational coupling, symmetric and antisymmetric superpositions of two single-monomer excitations are shown to exhibit purely constructive, oscillatory, and purely destructive interference in the EET to the third monomer, respectively. In the former case, the transfer is modulated by motion in the symmetrical framework-expansion vibration induced by the Franck-Condon excitation. Distortions in the shape of the triangular framework degrade that coherent EET while activating excitation transfer in the latter case of an antisymmetric initial state. In its symmetrical configuration, two of the three single-exciton states of the trimer are degenerate. This degeneracy is broken by the Jahn-Teller-active framework distortions. The calculations illustrate closed, approximately circular pseudo-rotational wave-packet dynamics on both the lower and the upper adiabatic potential energy surfaces of the degenerate manifold, which lead to the acquisition after one cycle of physically meaningful geometric (Berry) phases of π. Another manifestation of Berry-phase development is seen in the evolution of the vibrational probability density of a wave packet on the lower Jahn-Teller adiabatic potential comprising a superposition of clockwise and counterclockwise circular motions. The circular pseudo-rotation on the upper cone is shown to stabilize the adiabatic electronic state against non-adiabatic internal conversion via the conical intersection, a dynamical process analogous to Slonczewski resonance. Strategies for initiating and monitoring these various dynamical processes experimentally using pre-resonant impulsive Raman excitation, short-pulse absorption, and multi-dimensional wave-packet interferometry are outlined in brief.

High-sensitivity fluorescence-detected multidimensional electronic spectroscopy through continuous pump-probe delay scan

Fluorescence-detected multidimensional electronic spectroscopy (fMES) promises high sensitivity compared to conventional approaches and is an emerging spectroscopic approach toward combining the advantages of MES with the spatial resolution of a microscope. Here, we present a visible white light continuum-based fMES spectrometer and systematically explore the sensitivity enhancement expected from fluorescence detection. As a demonstration of sensitivity, we report room temperature two-dimensional coherence maps of vibrational quantum coherences in a laser dye at optical densities of ∼2-3 orders of magnitude lower than conventional approaches. This high sensitivity is enabled by a combination of biased sampling along the optical coherence time axes and a rapid scan of the pump-probe waiting time T at each sample. A combination of this approach with acousto-optic phase modulation and phase-sensitive lock-in detection enables measurements of room temperature vibrational wavepackets even at the lowest ODs. Alternative faster data collection schemes, which are enabled by the flexibility of choosing a non-uniform undersampled grid in the continuous T scanning approach, are also demonstrated.

Effective normal modes identify vibrational motions which maximally promote vibronic mixing in excitonically coupled aggregates

Controlling energy transfer through vibronic resonance is an interesting possibility. Exact treatment of non-adiabatic vibronic coupling is necessary to fully capture its role in driving energy transfer. However, the exact treatment of vibrations in extended systems is expensive, sometimes requiring oversimplifying approximations to reduce vibrational dimensionality, and do not provide physical insights into which specific vibrational motions promote energy transfer. In this communication, we derive effective normal modes for understanding vibronically enhanced energy transfer in excitonically coupled aggregates. We show that the dynamics of the overall high-dimensional vibronic Hamiltonian can be better understood through one-dimensional Hamiltonians separable along these effective modes. We demonstrate this approach on a trimer toy model to analyze the role of an intermediate "trap" site in mediating energy transfer between electronically uncoupled sites. Bringing uncoupled sites into vibronic resonance converts the "trap" into a "shuttle" for energy transfer. By deconvolving the dynamics along the aggregate normal modes, our approach identifies the specific vibrational motions, which maximally promote energy transfer, against spectator modes, which do not participate in vibronic mixing.

Monitoring the evolution of intersite and interexciton coherence in electronic excitation transfer via wave-packet interferometry

We detail an experimental strategy for tracking the generation and time-development of electronic coherence within the singly excited manifold of an energy-transfer dimer. The technique requires that the two monomers have nonparallel electronic transition-dipole moments and that these possess fixed orientations in space. It makes use of two-dimensional wave-packet interferometry (WPI or whoopee) measurements in which the A, B, C, and D pulses have respective polarizations e, e, e, and e'. In the case of energy-transfer coupling that is weak or strong compared to electronic-nuclear interactions, it is convenient to follow the evolution of intersite or interexciton coherence, respectively. Under weak coupling, e could be perpendicular to the acceptor chromophore's transition dipole moment and the unit vector e' would be perpendicular to the donor's transition dipole. Under strong coupling, e could be perpendicular to the ground-to-excited transition dipole to the lower exciton level and e' would be perpendicular to the ground-to-excited transition dipole to the upper exciton level. If the required spatial orientation can be realized for an entire ensemble, experiments of the kind proposed could be performed by either conventional four-wave-mixing or fluorescence-detected WPI methods. Alternatively, fluorescence-detected whoopee experiments of this kind could be carried out on a single energy-transfer dimer of fixed orientation. We exhibit detailed theoretical expressions for the desired WPI signal, explain the physical origin of electronic coherence detection, and show calculated observed-coherence signals for model dimers with one, two, or three internal vibrational modes per monomer and both weak and strong energy-transfer coupling.

Quantum dynamics and spectroscopy of dihalogens in solid matrices. II. Theoretical aspects and G-MCTDH simulations of time-resolved coherent Raman spectra of Schrödinger cat states of the embedded I2Kr18 cluster

This study presents quantum dynamical simulations, using the Gaussian-based multiconfigurational time-dependent Hartree (G-MCTDH) method, of time-resolved coherent Raman four-wave-mixing spectroscopic experiments for the iodine molecule embedded in a cryogenic crystal krypton matrix [D. Picconi et al., J. Chem. Phys. 150, 064111 (2019)]. These experiments monitor the time-evolving vibrational coherence between two wave packets created in a quantum superposition (i.e., a "Schrödinger cat state") by a pair of pump pulses which induce electronic B Πu30⁺⟵XΣg+1 transitions. A theoretical description of the spectroscopic measurement is developed, which elucidates the connection between the nonlinear signals and the wave packet coherence. The analysis provides an effective means to simulate the spectra for several different optical conditions with a minimum number of quantum dynamical propagations. The G-MCTDH method is used to calculate and interpret the time-resolved coherent Raman spectra of two selected initial superpositions for a I₂Kr₁₈ cluster embedded in a frozen Kr cage. The time- and frequency-dependent signals carry information about the molecular mechanisms of dissipation and decoherence, which involve vibrational energy transfer to the stretching mode of the four "belt" Kr atoms. The details of these processes and the number of active solvent modes depend in a non-trivial way on the specific initial superposition.

Ab Initio Transient Vibrational Spectral Analysis

Pump probe spectroscopy techniques have enabled the direct observation of a variety of transient molecular species in both ground and excited electronic states. Time-resolved vibrational spectroscopy is becoming an indispensable tool for investigating photoinduced nuclear dynamics of chemical systems of all kinds. On the other hand, a complete picture of the chemical dynamics encoded in these spectra cannot be achieved without a full temporal description of the structural relaxation, including the explicit time-dependence of vibrational coordinates that are substantially displaced from equilibrium by electronic excitation. Here we present a transient vibrational analysis protocol combining ab initio direct molecular dynamics and time-integrated normal modes introduced in this work, relying on the recent development of analytic time-dependent density functional theory (TDDFT) second derivatives for excited states. Prototypical molecules will be used as test cases, showing the evolution of the vibrational signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems.

Two-Photon-Excited Fluorescence-Encoded Infrared Spectroscopy

We report on a method for performing ultrafast infrared (IR) vibrational spectroscopy using fluorescence detection. Vibrational dynamics on the ground electronic state driven by femtosecond mid-infrared pulses are detected by changes in fluorescence amplitude resulting from modulation of a two-photon visible transition by nuclear motion. We examine a series of coumarin dyes and study the signals as a function of solvent and excitation pulse parameters. The measured signal characterizes the relaxation of vibrational populations and coherences but yields different information than conventional IR transient absorption measurements. These differences result from the manner in which the ground-state dynamics are projected by the two-photon detection step. Extensions of this method can be adapted for a variety of increased-sensitivity IR measurements.

Excited-state wavepacket and potential reconstruction by coherent anti-Stokes Raman scattering

We propose a methodology for reconstructing polyatomic excited-state molecular wavepackets and potential energy surfaces by multiple pulse optical spectroscopy.

Fifth-order three-dimensional electronic spectroscopy using a pump-probe configuration

We present the theoretical details and experimental demonstration of fifth-order three-dimensional (3D) electronic spectroscopy using a pump-probe beam geometry. This is achieved using a pulse shaper and appropriate phase cycling schemes. We show how 8-step and 27-step phase cycling schemes can measure purely absorptive 3D spectra as well as 3D spectra for the individual fifth-order processes that contribute to the purely absorptive spectrum. 3D spectra as a function of two separate controllable waiting time periods can be obtained. The peak shapes and positions of the peaks in the experimental measurement correspond well to theory.

Weak-field, multiple-cycle carrier envelope phase effects in laser excitation

Although the absolute or carrier envelope phase (CEP) of a laser pulse is usually assumed to be effective for ultrashort and/or ultrastrong pulses only, it is demonstrated that these limitations can eventually be removed. Therefore, the excitation of a model positively charged homonuclear diatomic molecule, in which four electronic states are coupled by the laser field, is studied. In an initial step, nuclear wave packets in two dissociative states are prepared. Upon reaching the fragment channel, a weak pulse interacts with the system and prepares CEP-dependent asymmetries associated with electron density localized on one or the other fragmentation product.

Two-dimensional vibronic spectroscopy of coherent wave-packet motion

We theoretically study two-dimensional (2D) spectroscopic signals obtained from femtosecond pulse interactions with diatomic molecules. The vibrational wave-packet dynamics is monitored in the signals. During the motion in anharmonic potentials the wave packets exhibit vibrational revivals and fractional revivals which are associated with particular quantum phases. The time-dependent phase changes are identified by inspection of the complex-valued 2D spectra. We use the Na(2) molecule as a numerical example and discuss various pulse sequences which yield information about vibrational level structure and phase relationships in different electronic states.

Rotational coherence imaging and control for CN molecules through time-frequency resolved coherent anti-Stokes Raman scattering

Numerical wave packet simulations are performed for studying coherent anti-Stokes Raman scattering (CARS) for CN radicals. Electronic coherence is created by femtosecond laser pulses between the X(2)Σ and B(2)Σ states. Due to the large energy separation of vibrational states, the wave packets are superpositions of rotational states only. This allows for a specially detailed inspection of the second- and third-order coherences by a two-dimensional imaging approach. We present the time-frequency domain images to illustrate the intra- and intermolecular interferences, and discuss the procedure to rationally control and experimentally detect the interferograms in solid Xe environment.

Femtosecond interferometry of molecular dynamics – the role of relative and absolute phase of two individual laser pulses

Dynamical implications of the dissociation of a molecular ion under the influence of interferometrically generated light fields have been investigated by numerical solution of time dependent Schrödinger equations. As an example the dissociation of DCl+ ions by means of two interfering 7 fs laser pulses at 800 nm has been chosen. We demonstrate that product branching ratios D+:Cl+ can be manipulated from 10:1 to 1:10 not only by adjusting the appropriate delay time in the time-shifted two-pulse approach, but also by choosing the proper carrier envelope phase (CEP) of the two partial light fields. The effects of the phase shift related to the time shift and that of the CEP can be clearly distinguished.

Complete reconstruction of the wave function of a reacting molecule by four-wave mixing spectroscopy

Probing the real time dynamics of a reacting molecule remains one of the central challenges in chemistry. Here we show how the time-dependent wave function of an excited-state reacting molecule can be completely reconstructed from resonant coherent anti-Stokes Raman spectroscopy. The method assumes knowledge of the ground potential but not of any excited potential. The excited-state potential can in turn be constructed from the wave function. The formulation is general for polyatomics and applies to bound as well as dissociative excited potentials. We demonstrate the method on the Li(2) molecule.

Multidimensional optical spectroscopy of a single molecule in a current-carrying state

The nonlinear optical signals from an open system consisting of a molecule connected to metallic leads, in response to a sequence of impulsive pulses, are calculated using a superoperator formalism. Two detection schemes are considered: coherent stimulated emission and incoherent fluorescence. The two provide similar but not identical information. The necessary superoperator correlation functions are evaluated either by converting them to ordinary (Hilbert space) operators which are then expanded in many-body states, or by using Wick's theorem for superoperators to factorize them into nonequilibrium two point Green's functions. As an example we discuss a stimulated Raman process that shows resonances involving two different charge states of the molecule in the same signal.

Optical N-wave-mixing spectroscopy with strong and temporally well-separated pulses: the doorway-window representation

We have extended the doorway-window representation of optical pump-probe spectroscopy with weak pulses toward N-wave-mixing spectroscopy with temporally well-separated pulses of arbitrary strength. The expressions for the signals in the strong-pulse doorway-window representation are derived in the framework of the nonperturbative theory of N-wave-mixing spectroscopy. The strong-pulse doorway-window representation is complementary to the equation-of-motion phase-matching approach. The latter fully accounts for pulse-overlap effects in signals induced by weak pulses but is computationally more expensive. The performance of the doorway-window approximation for temporally well-separated strong pulses is illustrated for an electronic two-level system with an underdamped Condon-active vibrational mode.

Wave packet interferometry with attosecond precision and picometric structure

Wave packet (WP) interferometry is applied to the vibrational WPs of the iodine molecule. Interference fringes of quantum waves weave highly regular space-time images called "quantum carpets." The structure of the carpet has picometre and femtosecond resolutions, and changes drastically depending on the amplitudes and phases of the vibrational eigenstates composing the WP. In this review, we focus on the situation where quantum carpets are created by two counter-propagating nuclear vibrational WPs. Such WPs can be prepared with either a single or double femtosecond (fs) laser pulse. In the single pulse scheme, the relevant situation appears around the half revival time. Similar situations can be generated with a pair of fs laser pulses whose relative phase is stabilized on the attosecond time scale. In the latter case we can design the quantum carpet by controlling the timing between the phase-locked pulses. We demonstrate this carpet design and visualize the designed carpets by the fs pump-probe measurements, tuning the probe wavelength to resolve the WP density-distribution along the internuclear axis with ~3 pm spatial resolution and ~100 fs temporal resolution.

Using wave-packet interferometry to monitor the external vibrational control of electronic excitation transfer

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)].

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Nuclear interference in the Coulomb explosion of H2+ in short vuv laser fields

We report ab initio calculations of H2+ three-photon ionization by vuv/fs 10(12) W/cm(2) laser pulses including electronic and vibrational degrees of freedom in the Born-Oppenheimer approximation. The initial nuclear wave packet of H2+(1ssigma(g)) is assumed to be equal to the H2 vibrational ground state. For pulse durations longer than 10 fs, we find an unexpected modulation in the kinetic energy spectra of the correlated fragments (H++H+). It is shown that the structures in the spectra originate from the interference between a direct and a sequential dissociation channel. While the first channel is open even for relatively short pulses, the sequential one only opens for pulse durations longer than 10 fs. In the latter case we show that interference between the two components results in a modulated kinetic energy release spectrum in the dissociation channel 3dsigma(g), which is reflected in the ionization spectrum.

Actively tailored spatiotemporal images of quantum interference on the picometer and femtosecond scales

Interference fringes of quantum waves weave highly regular space-time images, which could be seen in various wave systems such as wave packets in atoms and molecules, Bose-Einstein condensates, and fermions in a box potential. We have experimentally designed and visualized spatiotemporal images of dynamical quantum interferences of two counterpropagating nuclear wave packets in the iodine molecule; the wave packets are generated with a pair of femtosecond laser pulses whose relative phase is locked within the attosecond time scale. The design of the image has picometer and femtosecond resolutions, and changes drastically as we change the relative phase of the laser pulses, providing a direct spatiotemporal control of quantum interferences.

Development of ultrahigh-precision coherent control and its applications

Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.