Orientation and alignment echoes

The Manifestations of "l-Doubling" in Gas-Phase Rotational Dynamics

The "l-Doubling" phenomenon emanates from the coupling between molecular rotations and perpendicular vibrations (bending modes) in polyatomic molecules. This elusive phenomenon has been largely discarded in laser-induced molecular alignment. Here we explore and unveil the ramifications of l-Doubling on the coherent rotational dynamics of linear triatomic molecules at ambient temperatures and above. The observed l-Doubling dynamics may be wrongly considered as collisional decay throughout the first few hundreds of picoseconds past excitation, highlighting the importance of correct assimilation of l-Doubling in current research of dissipative rotational dynamics and in coherent rotational dynamics in general.

Unveiling Nonsecular Collisional Dissipation of Molecular Alignment

We conducted a joint theoretical and experimental study to investigate the collisional dissipation of molecular alignment. By comparing experimental measurements to the quantum simulations, the nonsecular effect in the collision dissipation of molecular alignment was unveiled from the gas-density-dependent decay rates of the molecular alignment revival signals. Different from the conventional perspective that the nonsecular collisional effect rapidly fades within the initial few picoseconds following laser excitation, our simulations of the time-dependent decoherence process demonstrated that this effect can last for tens of picoseconds in the low-pressure regime. This extended timescale allows for the distinct identification of the nonsecular effect from molecular alignment signals. Our findings present the pioneering evidence that nonsecular molecular collisional dissipation can endure over an extended temporal span, challenging established concepts and strengthening our understanding of molecular dynamics within dissipative environments.

Intermolecular interactions probed by rotational dynamics in gas-phase clusters

The rotational dynamics of a molecule is sensitive to neighboring atoms or molecules, which can be used to probe the intermolecular interactions in the gas phase. Here, we real-time track the laser-driven rotational dynamics of a single N2 molecule affected by neighboring Ar atoms using coincident Coulomb explosion imaging. We find that the alignment trace of N-N axis decays fast and only persists for a few picoseconds when an Ar atom is nearby. We show that the decay rate depends on the rotational geometry of whether the Ar atom stays in or out of the rotational plane of the N2 molecule. Additionally, the vibration of the van der Waals bond is found to be excited through coupling with the rotational N-N axis. The observations are well reproduced by solving the time-dependent Schrödinger equation after taking the interaction potential between the N2 and Ar into consideration. Our results demonstrate that environmental effects on a molecular level can be probed by directly visualizing the rotational dynamics.

Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Quantum control of field-free molecular orientation

Generating field-free (non-stationary) orientation of molecules in space has been a longstanding goal in the field of quantum control of molecular rotation, which has significant applications in physical chemistry, chemical physics, strong-field physics, and quantum information science. In this Perspective, we review and examine several representative control schemes developed in recent years and implemented in theoretical and experimental areas for generating field-free orientation of molecules. By conducting numerical simulations of different control schemes on the same molecular system, we demonstrate that quantum coherent control, specifically targeting a limited number of the lowest-lying rotational levels to achieve an optimal superposition, can result in a high degree of orientation. To this end, we provide an overview of our latest developed analytical method, which enables the precise design of terahertz field parameters through resonant excitation. This design approach facilitates the attainment of desired field-free orientations by optimizing the amplitudes and phases of rotational wave functions for the selected rotational levels. Finally, we outlook the significance of such progress in multiple frontier research fields, highlighting its potential applications in ultracold physics, quantum computation, quantum simulation, and quantum metrology.

Nonadiabatic Laser-Induced Alignment Dynamics of Molecules on a Surface

We demonstrate that a sodium dimer, Na_{2}(1^{3}Σ_{u}^{+}), residing on the surface of a helium nanodroplet, can be set into rotation by a nonresonant 1.0 ps infrared laser pulse. The time-dependent degree of alignment measured, exhibits a periodic, gradually decreasing structure that deviates qualitatively from that expected for gas-phase dimers. Comparison to alignment dynamics calculated from the time-dependent rotational Schrödinger equation shows that the deviation is due to the alignment dependent interaction between the dimer and the droplet surface. This interaction confines the dimer to the tangential plane of the droplet surface at the point where it resides and is the reason that the observed alignment dynamics is also well described by a 2D quantum rotor model.

Quantum modeling, beyond secularity, of the collisional dissipation of molecular alignment using the energy-corrected sudden approximation

We propose a Markovian quantum model for the time dependence of the pressure-induced decoherence of rotational wave packets of gas-phase molecules beyond the secular approximation. It is based on a collisional relaxation matrix constructed using the energy-corrected sudden approximation, which improves the previously proposed infinite order sudden one by taking the molecule rotation during collisions into account. The model is tested by comparisons with time-domain measurements of the pressure-induced decays of molecular-axis alignment features (revivals and echoes) for HCl and CO2 gases, pure and diluted in He. For the Markovian systems HCl-He and CO2-He, the comparisons between computed and measured data demonstrate the robustness of our approach, even when the secular approximation largely breaks down. In contrast, significant differences are obtained in the cases of pure HCl and CO2, for which the model underestimates the decay rate of the alignment at short times. This result is attributed to the non-Markovianity of HCl-HCl and CO2-CO2 interactions and the important contribution of those collisions that are ongoing at the time when the system is excited by the aligning laser pulse.

Visualizing ultrafast weak-field-induced rotational revivals of air molecules at room temperature

The ability to observe quantum coherence and interference is crucial for understanding quantum effects in nonlinear optical spectroscopy and is of fundamental interest in quantum mechanics. Here, we present an experimental study combined with theoretical analysis and numerical simulations to identify the underlying process behind the rotational revivals induced by a pair of time-delayed ultrafast femtosecond laser pulses for air molecules under ambient conditions. Our time-resolved two-dimensional alignment measurements confirm that one-step non-resonant Raman transitions from initial states of mixed molecules play a dominant role, showing a signature of weak-field-induced rotational revivals. Furthermore, we demonstrate that such rotational revival spectra can simultaneously measure the entire pure rotational Raman spectra and observe the quantum interference between two transition pathways from a given initial state. This work provides a powerful tool to observe, control, and identify the rotational dynamics of mixed molecular samples under weak-field excitations.

Molecular orientation echoes via concerted terahertz and near-IR excitations

A new and efficient method for orientation echo spectroscopy is presented and realized experimentally. The excitation scheme utilizes concerted rotational excitations by both ultrashort terahertz and near-IR pulses and its all-optical detection is enabled by the molecular orientation-induced second harmonic method [J. Phys. Chem. A126, 3732 (2022)10.1021/acs.jpca.2c03237]. This method provides practical means for orientation echo spectroscopy of gas phase molecules and highlights the intriguing underlying physics of coherent rotational dynamics induced by judiciously-orchestrated interactions with both resonant (terahertz) and nonresonant (NIR) fields.

Rotationally-Resolved Two-Dimensional Infrared Spectroscopy of CO2(g): Rotational Wavepackets and Angular Momentum Transfer

Angular momentum transfer and wavepacket dynamics of CO₂(g) were measured on the picosecond time scale using polarization-resolved two-dimensional infrared (2D-IR) spectroscopy. The dynamics of rotational levels up to J_max ≈ 50 are observed simultaneously at room temperature. Rotational wavepackets launched by the pump pulses cause oscillations in the intensity of individual peaks and beating patterns in the 2D-IR spectra. The structure of the rotationally resolved 2D-IR spectrum is explained using nonlinear response function theory. Spectral diffusion of the rotationally resolved 2D-IR peaks reveals information about angular momentum transfer. We demonstrate the ability to directly measure inelastic angular momentum dynamics simultaneously across the ∼50 thermally excited rotational levels over several hundred picoseconds.

Rotational echo spectroscopy for accurate measurement of molecular alignment

We measure the molecular alignment induced in gas using molecular rotational echo spectroscopy. Our results show that the echo intensity and the time interval between the local extremas of the echo responses depend sensitively on the pump intensities and the initial molecular rotational temperature, respectively. This allows us to accurately extract these experimental parameters from the echo signals and then further determine the molecular alignment in experiments. The accuracy of our method has been verified by comparing the simulation with the extracted parameters from the molecular alignment experiment performed with a femtosecond pump pulse.

Impulsively Excited Gravitational Quantum States: Echoes and Time-Resolved Spectroscopy

We theoretically study an impulsively excited quantum bouncer (QB)-a particle bouncing off a surface in the presence of gravity. A pair of time-delayed pulsed excitations is shown to induce a wave-packet echo effect-a partial rephasing of the QB wave function appearing at twice the delay between pulses. In addition, an appropriately chosen observable [here, the population of the ground gravitational quantum state (GQS)] recorded as a function of the delay is shown to contain the transition frequencies between the GQSs, their populations, and partial phase information about the wave-packet quantum amplitudes. The wave-packet echo effect is a promising candidate method for precision studies of GQSs of ultracold neutrons, atoms, and antiatoms confined in closed gravitational traps.

Transient mid-IR nonlinear refraction in air

We use the polarization-sensitive, time-resolved Beam-Deflection technique to measure the nonlinear refraction of air, exciting in both the near and mid-IR and probing in the mid-IR. This gives us the first measurements for air using both excitation and probe in the mid-IR, and we find no dispersion of the bound-electronic nonlinear refractive index, n_2,el(λ_p;λ_e), assuming, as has been shown earlier, that the nuclear rotational nonlinear refraction is nearly dispersionless. From these data, we can model the pulsewidth dependence of the effective nonlinear refractive index, n_2,eff, i.e., as would be measured by a single beam. Interestingly, n_2,eff is maximized for a pulsewidth of approximately 0.5 ps. The position of this maximum is nearly independent of pressure while its magnitude decreases with increasing pressure and temperature. From the measurements and modeling, we predict the nonlinear refraction in the atmosphere at different altitudes.

Tracing the Coherent Manipulation of Rotational Dynamics by Shaped Femtosecond Pulse-Induced Two-Dimensional Rotational Coherent Spectrum

The temporal delayed orthogonal pulse pairs generated by the phase shaping technique are used to study the coherent control of the rotational wave packet dynamics in air. By continuously changing the intrapulse delay of the pump pulse, we measured the corresponding revival signals and obtained a two-dimensional rotational coherent spectrum (2D RCS). An additive property of the rotational dynamics is observed from the revival signals. Moreover, combining with the coherent control model, we find that the 2D RCS can be used to demonstrate the control over the underlying Raman rotational excitation. A beat frequency-dependent oscillation of each rotational transition is obtained. The transition process is revealed from the Fourier transformation about the pump delay. The scheme of this work can be used for further control and detection of the rotational wave packet and can be extended to other molecular dynamic researches.

Multilevel quantum interference in the formation of high-order fractional molecular alignment echoes

We theoretically investigate the formation of the high-order fractional alignment echo in OCS molecule and systematically study the dependence of echo intensity on the intensities and time delay of the two excitation pulses. Our simulations reveal an intricate dependence of the intensity of high-order fractional alignment echo on the laser conditions. Based on the analysis with rotational density matrix, this intricate dependence is further demonstrated to arise from the interference of multiple quantum pathways that involve multilevel rotational transitions. Our result provides a comprehensive multilevel picture of the quantum dynamics of high-order fractional alignment echo in molecular ensembles, which will facilitate the development of "rotational echo spectroscopy."

Rotational Coherence Spectroscopy of Molecules in Helium Nanodroplets: Reconciling the Time and the Frequency Domains

Alignment of OCS, CS_{2}, and I_{2} molecules embedded in helium nanodroplets is measured as a function of time following rotational excitation by a nonresonant, comparatively weak ps laser pulse. The distinct peaks in the power spectra, obtained by Fourier analysis, are used to determine the rotational, B, and centrifugal distortion, D, constants. For OCS, B and D match the values known from IR spectroscopy. For CS_{2} and I_{2}, they are the first experimental results reported. The alignment dynamics calculated from the gas-phase rotational Schrödinger equation, using the experimental in-droplet B and D values, agree in detail with the measurement for all three molecules. The rotational spectroscopy technique for molecules in helium droplets introduced here should apply to a range of molecules and complexes.

Direct imaging of direction-controlled molecular rotational wave packets created by a polarization-skewed double-pulse

High-precision, time-resolved Coulomb explosion imaging of rotational wave packets in nitrogen molecules created with a pair of time-delayed, polarization-skewed femtosecond laser pulses is presented, providing insight into the creation process and dynamics of direction-controlled wave packets. To initiate unidirectional rotation, the interval of the double-pulse was set so that the second, polarization-tilted pulse hit the molecules at the time when molecules were aligned or antialigned along the polarization vector of the first pulse. During the revival period of the rotational wave packet, pulse intervals around both the full and half revival times were used. The observed molecular wave packet movies clearly show the signatures of quantum rotation, such as angular localization (alignment), dispersion, and revival phenomena, during the unidirectional motion. The patterns are quite different depending on the pulse interval even when the angular distribution at the second pulse irradiation is similar. The observed interval-dependence of the dynamics was analyzed on the basis of the real-time images, with the aid of numerical simulations, and the creation process of the packets was discussed. We show that the observed image patterns can be essentially rationalized in terms of rotational period and alignment parameter. Because the double-pulse scheme is the most fundamental in the creation of direction-controlled rotational wave packets, this study will lead to more sophisticated control and characterization of directional molecular motions.

Observing collisions beyond the secular approximation limit

Quantum coherence plays an essential role in diverse natural phenomena and technological applications. The unavoidable coupling of the quantum system to an uncontrolled environment incurs dissipation that is often described using the secular approximation. Here we probe the limit of this approximation in the rotational relaxation of molecules due to thermal collisions by using the laser-kicked molecular rotor as a model system. Specifically, rotational coherences in N₂O gas (diluted in He) are created by two successive nonresonant short and intense laser pulses and probed by studying the change of amplitude of the rotational alignment echo with the gas density. By interrogating the system at the early stage of its collisional relaxation, we observe a significant variation of the dissipative influence of collisions with the time of appearance of the echo, featuring a decoherence process that is well reproduced by the nonsecular quantum master equation for modeling molecular collisions.

Ultrafast molecular relaxation can be probed with short laser pulses. Here the authors study collisional behavior of a N₂O and He mixture beyond secular approximation by aligning them using laser pulses and probing their rotational echoes.

All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation

An all-optical measurement of high-order fractional molecular echoes is demonstrated by using high-order harmonic generation (HHG). Excited by a pair of time-delayed short laser pulses, the signatures of full and high order fractional (1/2 and 1/3) alignment echoes are observed in the HHG signals measured from CO ₂ molecules at various time delays of the probe pulse. By increasing the time delay of the pump pulses, much higher order fractional (1/4) alignment echo is also observed in N ₂O molecules. With an analytic model based on the impulsive approximation, the spatiotemporal dynamics of the echo process are retrieved from the experiment. Compared to the typical molecular alignment revivals, high-order fractional molecular echoes are demonstrated to dephase more rapidly, which will open a new route towards the ultrashort-time measurement. The proposed HHG method paves an efficient way for accessing the high-order fractional echoes in molecules.

The link between coherence echoes and mode locking

We investigate the appearance of sharp pulses in the mean field of Kuramoto-type globally-coupled phase oscillator systems. In systems with exactly equidistant natural frequencies, self-organized periodic pulsations of the mean field, called mode locking, have been described recently as a new collective dynamics below the synchronization threshold. We show here that mode locking can appear also for frequency combs with modes of finite width, where the natural frequencies are randomly chosen from equidistant frequency intervals. In contrast to that, so-called coherence echoes, which manifest themselves also as pulses in the mean field, have been found in systems with completely disordered natural frequencies as a result of two consecutive stimulations applied to the system. We show that such echo pulses can be explained by a stimulation induced mode locking of a subpopulation representing a frequency comb. Moreover, we find that the presence of a second harmonic in the interaction function, which can lead to the global stability of the mode-locking regime for equidistant natural frequencies, can enhance the echo phenomenon significantly. The nonmonotonic behavior of echo amplitudes can be explained as a result of the linear dispersion within the self-organized mode-locked frequency comb. Finally, we investigate the effect of small periodic stimulations on oscillator systems with disordered natural frequencies and show how the global coupling can support the stimulated pulsation by increasing the width of locking plateaus.

Rotational Echoes as a Tool for Investigating Ultrafast Collisional Dynamics of Molecules

We show that recently discovered rotational echoes of molecules provide an efficient tool for studying collisional molecular dynamics in high-pressure gases. Our study demonstrates that rotational echoes enable the observation of extremely fast collisional dissipation, at timescales of the order of a few picoseconds, and possibly shorter. The decay of the rotational alignment echoes in CO_{2} gas and CO_{2}-He mixture up to 50 bar was studied experimentally, delivering collision rates that are in good agreement with the theoretical expectations. The suggested measurement protocol may be used in other high-density media, and potentially in liquids.

Echo Spectroscopy in Multilevel Quantum-Mechanical Rotors

We study the dynamics of rotational echoes in gas phase molecular ensembles and their dependence on the delay and intensity of the excitation pulses. We explore the unique dynamics of alignment echoes that arise from the multilevel nature of the molecular rotors and impose severe difficulties in utilizing echo responses for rotational spectroscopy. We show experimentally and theoretically that judicious control of both the delay and intensity of the second pulse enables multilevel "rotational echo spectroscopy." The proposed methodology paves the way to rotational spectroscopy in high-density gas samples.

Rotational Echoes: Rephasing of Centrifugal Distortion in Laser-Induced Molecular Alignment

We study and demonstrate the rephasing property of the echo response in a multilevel rotational system of iodomethane via long time-resolved optical birefringence measurements. The strong centrifugal distortion of iodomethane is utilized as a dephasing mechanism imprinted on the echo signal and is shown to rephase throughout its evolution. The dependence of the echo signal amplitude on the driving pulses' intensities is theoretically and experimentally explored. The analogy to Hahn's spin echoes is discussed, and a quantum-mechanical version of Hahn's track runners is provided for the case of multilevel rotational system.

Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase

Ultrafast 2D spectroscopy uses correlated multiple light-matter interactions for retrieving dynamic features that may otherwise be hidden under the linear spectrum; its extension to the terahertz regime of the electromagnetic spectrum, where a rich variety of material degrees of freedom reside, remains an experimental challenge. We report a demonstration of ultrafast 2D terahertz spectroscopy of gas-phase molecular rotors at room temperature. Using time-delayed terahertz pulse pairs, we observe photon echoes and other nonlinear signals resulting from molecular dipole orientation induced by multiple terahertz field-dipole interactions. The nonlinear time domain orientation signals are mapped into the frequency domain in 2D rotational spectra that reveal J-state-resolved nonlinear rotational dynamics. The approach enables direct observation of correlated rotational transitions and may reveal rotational coupling and relaxation pathways in the ground electronic and vibrational state.

Staircase patterns of nuclear fluxes during coherent tunneling in excited doublets of symmetric double well potentials

Step-by-step flux for one-by-one transfers of the lobes of the density, from the reactant (left) to the product (right) in the excited tunneling doublet.

Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases

A polarization-resolved beam deflection technique is used to separate the bound-electronic and molecular rotational components of nonlinear refractive transients of molecular gases. Coherent rotational revivals from N(2), O(2), and two isotopologues of carbon disulfide (CS(2)), are identified in gaseous mixtures. Dephasing rates, rotational and centrifugal distortion constants of each species are measured. Polarization at the magic angle allows unambiguous measurement of the bound-electronic nonlinear refractive index of air and second hyperpolarizability of CS(2). Agreement between gas and liquid phase second hyperpolarizability measurements is found using the Lorentz-Lorenz local field correction.