Alignment Echo Research Articles

Investigation on gaseous molecular alignment echoes induced by the intense phase-tunable terahertz pulses

Investigation on gaseous molecular alignment echoes induced by the intense phase-tunable terahertz pulses

Feedback Optimization Strategy for Rotational Alignment Echo Spectroscopy

The recent discovery of rotational echoes has contributed to extend the applications of field‐free molecular alignment to short time scales, namely to a temporal region preceding the first alignment revival of the molecule. Most echo measurements require adjusting the position of the echo over time, which in the case of molecular alignment echo unavoidably leads to a change in its amplitude, unless the intensity of the pulse sequence triggering the echo is properly modified. Herein, it is proposed to avoid this drawback by using an optical pulse shaper steered by a learning algorithm. It is demonstrated that a temporal shaping, whose characteristics are optimized to maintain a constant echo amplitude regardless of its creation time, can be generated by controlling the spectral phase and amplitude of the laser pulse which are then used in an open‐loop control system. As a proof of principle, the optimization strategy is applied to the observation of short‐term dissipative dynamics of laser‐aligned molecules exposed to collisions and to the measurement of associated decoherence and population decay time constants.

Creating alignment echoes using a phase-shaped femtosecond laser pulse

In recent years, molecular alignment echoes induced by a pair of time-delayed femtosecond laser pulses have been proposed and have aroused wide research interest. However, we demonstrate that an alignment echo can be alternatively produced by a shaped femtosecond laser pulse with a V-style spectral phase modulation. The full, fractional, and imaginary alignment echoes are formed by the excitation of the tailored two time-delayed sub-pulses. Both the delay time and the ratio of intensity between the two sub-pulses can be easily manipulated by designing the modulation parameters to induce various types of echoes. We further show that the optimal ratio of intensity between the two sub-pulses, which results in the maximal alignment degrees of the full echo, closely correlates with the energy of the sub-pulse. When the pulse energy is relatively low, the maximal alignment degree of the full echo is obtained when the two sub-pulses have equal intensity. The optimal ratio of intensity increases with the excitation energy of the first pump pulse.

Generation of fractional and multiple imaginary rotational alignment echoes

We present a theoretical investigation to understand the connection between the formation of different rotational alignment echoes and the underlying excitation pathways induced by temporally delayed laser pulses. The fractional and multiple imaginary alignment echoes are predicted and demonstrated in the linear polar molecule carbonyl sulfide. We also use a two-dimensional spectrum obtained from higher-order alignment echo signals to identify the underlying quantum coherence. This work deepens our understanding of the alignment echo phenomenon. It provides a way to gain insight into the relationship between the echo signal and the underlying pathway with potential applications in rotational echo spectroscopy.

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."

Investigating Diffusion of Lithium Intercalated in Graphite By a Combination of Multiscale Modeling and NMR

Lithium ion batteries play a key role in the implementation of fully sustainable electrical mobility. Long lifetime, fast recharging and safety are required for the acceptance of any battery powered vehicle. Graphite is still the state of art as negative electrode. Despite decades of investigation into the mechanism of lithium intercalation, the ion mobility and the underlying microscopic processes are still not fully understood, limiting progress in performance and lifetime prediction of a battery. In particular, improvements in fast charging of batteries mandates a deeper understanding of the lower states of charge (SoC), bellow or around 20 %. We propose a combination of advanced NMR experiments, i.e spin alignment echo (SAE), with a theoretical multi scale modelling approach to investigate relevant phenomena such as lithium ion diffusion in graphite. Here, we present a novel multi-level accelerated first-principles kinetic Monte Carlo (1p-kMC) model to assess in detail the mobility at a low SoC, i.e LiC108. In particular, an external potential is applied in order to mimic the driving force causing (dis)charge of the battery.

Echoes in unidirectionally rotating molecules

Abstract We report the experimental observation of molecular unidirectional rotation (UDR) echoes, and analyze their origin and behavior both classically and quantum mechanically. The molecules are excited by two time-delayed polarization-twisted ultrashort laser pulses and the echoes are measured by exploding the molecules and reconstructing their spatial orientation from the detected recoil ions momenta. Unlike alignment echoes which are induced by linearly polarized pulses, here the axial symmetry is broken by the twisted polarization, giving rise to molecular unidirectional rotation. We find that the rotation sense of the echo is governed by the twisting sense of the second pulse even when its intensity is much weaker than the intensity of the first pulse. In our theoretical study, we rely on classical phase space analysis and on three-dimensional quantum simulations of the laser-driven molecular dynamics. Both approaches nicely reproduce the experimental results. Echoes in general, and the unique UDR echoes in particular, provide new tools for studies of relaxation processes in dense molecular gases.

Ultrafast collisional dissipation of symmetric-top molecules probed by rotational alignment echoes

We experimentally and theoretically investigate the ultrafast collisional dynamics of a symmetric-top molecule (${\mathrm{C}}_{2}{\mathrm{H}}_{6}$) in pure gas and mixtures with He at high density by employing the rotational alignment echo created by a pair of time-delayed intense laser kicks. The decrease of the amplitude of the echo when increasing the delay between the two laser pulses, reflecting the collisional relaxation of the system, is measured by probing the transient birefringence induced in the medium. The theoretical predictions, carried using purely classical molecular dynamics simulations, reproduce well the observed features, as demonstrated previously for a linear molecule. The analysis shows that the dissipation of the ethane alignment, despite the fact that this species has an extra rotational degree of freedom as compared to a linear molecule, barely involves more complex collisional relaxation channels due to characteristics of the ${\mathrm{C}}_{2}{\mathrm{H}}_{6}\ensuremath{-}{\mathrm{C}}_{2}{\mathrm{H}}_{6}$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{6}\ensuremath{-}\mathrm{He}$ interactions. However, our findings reveal that the dissipative dynamics of a symmetric-top molecule can be properly approached using the recently discovered rotational alignment echoes, which, so far, have been only tested for probing rotational decoherence of simpler (linear) molecules.

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.

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.

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 50bar 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.

Investigation of the Li-ion conduction behavior in the Li10GeP2S12 solid electrolyte by two-dimensional T1-spin alignment echo correlation NMR

Li10GeP2S12 (LGPS) is the fastest known Li-ion conductor to date due to the formation of one-dimensional channels with a very high Li mobility. A knowledge-based optimization of such materials for use, for example, as solid electrolyte in all-solid-state batteries requires, however, a more comprehensive understanding of Li ion conduction that considers mobility in all three dimensions, mobility between crystallites and different phases, as well as their distributions within the material. The spin alignment echo (SAE) nuclear magnetic resonance (NMR) technique is suitable to directly probe slow Li ion hops with correlation times down to about 10−5 s, but distinction between hopping time constants and relaxation processes may be ambiguous. This contribution presents the correlation of the 7Li spin lattice relaxation (SLR) time constants (T1) with the SAE decay time constant τc to distinguish between hopping time constants and signal decay limited by relaxation in the τc distribution. A pulse sequence was employed with two independently varied mixing times. The obtained multidimensional time domain data was processed with an algorithm for discrete Laplace inversion that does not use a non-negativity constraint to deliver 2D SLR–SAE correlation maps. Using the full echo transient, it was also possible to estimate the NMR spectrum of the Li ions responsible for each point in the correlation map. The signal components were assigned to different environments in the LGPS structure.

Toward understanding of ion dynamics in highly conductive lithium ion conductors: Some perspectives by solid state NMR techniques

Solid state lithium ion conductors are promising to replace the organic liquid electrolytes for a safer and long cycle-life lithium battery. However, solid electrolytes are still not fully explored and need extensive basic studies to understand their intrinsic conducting mechanism and interfacial properties between electrodes and electrolytes. In this review, we highlight the latest progresses in the research of lithium ion conductors by using advanced solid state nuclear magnetic resonance(SS NMR) spectroscopy, i.e. Magic angle spinning (MAS) NMR, pulsed-field gradient (PFG) NMR, spin-lattice(SLR) as well as spin-spin relaxation NMR, spin alignment echo (SAE) NMR and two-dimensional exchange (2D EXSY) NMR, and briefly review the application of these solid NMR techniques in LISICON-, NASICON- and Garnet-type lithium ion conductors in the different time/length scales, as well as the measurement in the determination of ion occupancy, ion diffusion pathways, and diffusion coefficients.

Ultraslow Dynamics of a Framework Linker in MIL-53 (Al) as a Sensor for Different Isomers of Xylene

MIL-53 (Al) is an important example of metal–organic frameworks (MOFs) with a flexible framework capable to efficiently separate ortho and para isomers of xylene at moderate temperatures. The MIL-53 MOF contains mobile terephthalate phenylene fragments that can be used as a dynamic probe to investigate the guest–host interactions and the origin of the separation selectivity. Here 2H NMR spin alignment echo technique for the first time was applied to probe ultraslow structural mobility (0.1–1 kHz) in MOFs materials, with particular application to MIL-53(Al) saturated with ortho or para isomers of xylene. A specific influence of different isomers of xylene adsorbed in the MOF pores on the rotation of the phenylenes in MIL-53 for the temperature range with proved separation selectivity (T < 393 K) is shown. It has been established that the rotation of phenylene fragments is sensitive to the type of xylene isomer. The phenylenes’ rotation performs 1 order of magnitude slower in the presence of o-xylene (korth...

Orientation and alignment echoes.

We present one of the simplest classical systems featuring the echo phenomenon-a collection of randomly oriented free rotors with dispersed rotational velocities. Following excitation by a pair of time-delayed impulsive kicks, the mean orientation or alignment of the ensemble exhibits multiple echoes and fractional echoes. We elucidate the mechanism of the echo formation by the kick-induced filamentation of phase space, and provide the first experimental demonstration of classical alignment echoes in a thermal gas of CO_{2} molecules excited by a pair of femtosecond laser pulses.

Investigation of the effect of a variety of pulse errors on spin I = 1 quadrupolar alignment echo spectroscopy

We report on an analysis of a well known three-pulse sequence for generating and detecting spin I = 1 quadrupolar order when various pulse errors are taken into account. In the situation of a single quadrupolar frequency, such as the case found in a single crystal, we studied the potential leakage of single and/or double quantum coherence when a pulse flip error, finite pulse width effect, RF transient or a resonance offset is present. Our analysis demonstrates that the four-step phase cycling scheme studied is robust in suppressing unwanted double and single quantum coherence as well as Zeeman order that arise from the experimental artifacts, allowing for an unbiased measurement of the quadrupolar alignment relaxation time, T 1 Q . This work also reports on distortions in quadrupolar alignment echo spectra in the presence of experimental artifacts in the situation of a powdered sample, by simulation. Using our simulation tool, it is demonstrated that the spectral distortions associated with the pulse artifacts may be minimized, to some extent, by optimally choosing the time between the first two pulses. We highlight experimental results acquired on perdeuterated hexamethylbenzene and polyethylene that demonstrate the efficacy of the phase cycling scheme for suppressing unwanted quantum coherence when measuring T 1 Q . It is suggested that one employ two separate pulse sequences when measuring T 1 Q to properly analyze the short time behavior of quadrupolar alignment relaxation data.

Alignment Echo of Spin-3/29Be Nuclei: Detection of Ultraslow Motion

It is demonstrated that the alignment echo of9Be is quite useful for detecting ultraslow atomic motions in the metallic glass Zr46.75Ti8.25Cu7.5Ni10Be27.5. The time scale of detectable atomic motion is betweenT2= 1.5 ms andT1of a few seconds. Similar to previous works of2H NMR, the Jeener–Broekaert sequence is used to create quadrupolar order for spin-32nuclei upon nonselective excitations. Since the chemical and Knight shift distributions are not negligible for9Be, the proper choice of the dephasing time between the first and the second pulses is essential for achieving pure quadrupolar order. It is demonstrated experimentally that slow atomic motions contribute significantly to the decay of the alignment echo near the glass transition temperature.

Probing Slow Atomic Motions in Metallic Glasses using NMR

AbstractWe report a nuclear magnetic resonance (NMR) study of slow atomic motions in Zr-Ti-Cu- Ni-Be bulk metallic glasses. The employed 9Be spin alignment echo technique is able to probe Be motions with jump rate below 0.1 Hz. It was found that the Be motion is spatially homogeneous. The jump rate follows a perfect Arrhenius temperature dependence. The measured activation enthalpy of 1.2 eV is nearly identical to that obtained by Be diffusivity measurement using elastic backscattering (EBS); this indicates that energy barriers are the same for short and long range Be motions. The present work provides direct experimental evidences that exclude vacancy-assisted and interstitial diffusion mechanisms for Be motions in these systems. The result is interpreted in terms of the spread-out free volume fluctuation mechanism.

Deuteron nuclear magnetic resonance study of high-pressure effects on the molecular dynamics in amorphous polyethylene

The effect of high pressure up to 2500 bar on the chain motion in amorphous chain-deuterated polyethylene is studied in a wide range of temperature (203–393 K) using the deuteron nuclear magnetic resonance ( 2H n.m.r.) quadrupole echo and spin alignment echo technique. Quadrupole echo spectra simulated on the basis of Flory's rotational isomeric state model appear to reproduce the experimental spectra quite well. The comparison yields information on the time-scale of the motion. The temperature dependence of the mean correlation time shows an Arrhenius behaviour in the temperature range from 223 to 383 K. The activation energy at ambient pressure is 11.3 kJ mol −1, which is slightly lower than the value of the barrier between the trans and gauche conformations (13.2 kJ mol −1). The effect of increasing the pressure by 1 kbar corresponds roughly to lowering the temperature by 15 K.

2H n.m.r. study of high pressure effects on the molecular dynamics in polystyrene: 1. Main chain motion

The effect of high pressure on the main chain motion near the glass transition temperature ( T g) in amorphous chain-deuterated polystyrene is studied using deuteron n.m.r. spin alignment echo and quadrupole echo spectra. Comparison with simulated spectra yields information on the time-scale and the type of motion. In the vicinity of T g the main chain performs ultra-slow small angle diffusive motion. The temperature dependence of the mean correlation time shows a strongly non-Arrhenius behaviour, typical for the so-called α-process. The width of the correlation time distribution rapidly increases on approaching T g. The effect of pressure on the motion is found to be much weaker than could be expected from equation-of-state data.