Molecular alignment by trains of short laser pulses

Alignment transport between ultracold polar molecules

We propose an array of ultracold polar molecules as a platform to study alignment transport between molecules. We envision a polar molecule being aligned with an intense off-resonant laser field whose alignment migrates to a nearby molecule due to dipole-dipole interactions. Our results show that the transport of the alignment is due to a complex interplay between electric field-driven excitations and dipole-dipole interactions. All mechanisms for alignment transfer are elucidated and analyzed. Using NaCs as a prototype molecule, we find that the time for alignment transfer is (10 μs), which makes the phenomena readily observable in the lab.

Regular arrangement of dispersed 2D flakes detected by polarization of light

Regular arrangement of dispersed 2D flakes, as the "Wind-Chime" model, has been regarded as possible mechanism of spatial self-phase modulation. But this regular arrangement caused by the laser have not been confirmed, and the relation with the concentration of dispersed 2D flakes is still unclear. Here, the relationship between arrangement caused by electric field and polarized transmittance have been explored at first. Then, the model of flakes rotation to regular arrangement were established, which were proof by the response time by turning on/off electric field. On this basis, by building the polarization-related cross optical switch system, light-induced regular arrangement were observed and proven.

Ultrafast isolated molecule imaging without crystallization

SignificanceExcitation of molecules by an ultrashort laser pulse creates rotational wave packets that lead to transient alignment of the molecules along the laser polarization direction. Here, we show that a train of ultrashort laser pulses can be used to enhance the degree of alignment to a high level such that the diffraction from precisely timed ultrashort electron beams may be used to reconstruct the structure of the isolated molecules with atomic resolution through a coherent diffraction imaging technique. Our results mark a great step toward imaging noncrystallized molecules with atomic resolution and pave the way for creation of three-dimensional "molecular movies" at the femtosecond time scale and atomic spatial scale.

Orientation and Alignment dynamics of polar molecule driven by shaped laser pulses

We review the theoretical status of intense laser induced orientation and alignment-a field of study which lies at the interface of intense laser physics and chemical dynamics and having potential applications such as high harmonic generation, nano-scale processing and control of chemical reactions. The evolution of the rotational wave packet and its dynamics leading to orientation and alignment is the topic of the present discussion. The major part of this article primarily presents an overview of recent theoretical progress in controlling the orientation and alignment dynamics of a molecule by means of shaped laser pulses. The various theoretical approaches that lead to orientation and alignment such as static electrostatic field in combination with laser field(s), combination of orienting and aligning field, combination of aligning fields, combination of orienting fields, application of train of pulses etc. are discussed. It is observed that the train of pulses is quite an efficient tool for increasing the orientation or alignment of a molecule without causing the molecule to ionize. The orientation and alignment both can occur in adiabatic and non-adiabatic conditions with the rotational period of the molecule taken under consideration. The discussion is mostly limited to non-adiabatic rotational excitation (NAREX) i.e. cases in which the pulse duration is shorter than the rotational period of the molecule. We have emphasised on the so called half-cycle pulse (HCP) and square pulse (SQP). The effect of ramped pulses and of collision on the various laser parameters is also studied. We summarize the current discussion by presenting a consistent theoretical approach for describing the action of such pulses on movement of molecules. The impact of a particular pulse shape on the post-pulse dynamics is also calculated and analysed. In addition to this, the roles played by various laser parameters including the laser frequency, the pulse duration and the system temperature etc. are illustrated and discussed. The concept of alignment is extended from one-dimensional alignment to three-dimensional alignment with the proper choice of molecule and the polarised light. We conclude the article by discussing the potential applications of intense laser orientation and alignment.

Laser-induced alignment dynamics of gas phase CS2 dimers

Rotational dynamics of gas phase carbon disulfide (CS₂) dimers were induced by a moderately intense, circularly polarized alignment laser pulse and measured as a function of time by Coulomb explosion imaging with an intense fs probe pulse. For the alignment pulse, two different temporal intensity profiles were used: a truncated pulse with a 150 ps turn-on and a 8 ps turn-off, or a 'kick' pulse with a duration of 1.3 ps. For both types of pulse, rich rotational dynamics with characteristic full and fractional revivals were recorded, showing that the intermolecular carbon-carbon axis periodically aligns along the propagation direction of the laser pulses. The truncated pulse gave the strongest alignment, which we rationalize as being due to a flat relative phase between the components in the rotational wave packet generated. Fourier analysis of the alignment dynamics gave well-spaced peaks which were fit to determine the rotational constant, B, and the centrifugal constant, D_J, for the ground state of the dimer. Our results agree with values from high-resolution IR spectroscopy. Numerical simulations of the alignment accurately reproduced the experimental dynamics when the truncated pulse or a low intensity kick pulse was used, but failed to reproduce the dynamics induced by a high intensity kick pulse. We posit that the discrepancy is due to excitation of the intermolecular torsional motion by the kick pulse.

Locally optimized control pulses with nonlinear interactions

The local control theory has been extended to deal with nonlinear interactions, such as polarizability interaction, as well as a combination of dipole and polarizability interactions. We explain herein how to implement the developed pulse-design algorithm in a standard computer code that numerically integrates the Liouville equation and/or the Schrödinger equation without incurring additional high computational cost. Through a case study of the rotational dynamics control of crystalline orbital molecules, the effectiveness of the locally optimized control pulses is demonstrated by adopting four types of control objectives, namely, two types of state-selective excitation, alignment, and orientation control.

Molecular movie of ultrafast coherent rotational dynamics of OCS

Recording molecular movies on ultrafast timescales has been a longstanding goal for unravelling detailed information about molecular dynamics. Here we present the direct experimental recording of very-high-resolution and -fidelity molecular movies over more than one-and-a-half periods of the laser-induced rotational dynamics of carbonylsulfide (OCS) molecules. Utilising the combination of single quantum-state selection and an optimised two-pulse sequence to create a tailored rotational wavepacket, an unprecedented degree of field-free alignment, 〈cos2θ2D〉 = 0.96 (〈cos2θ〉 = 0.94) is achieved, exceeding the theoretical limit for single-pulse alignment. The very rich experimentally observed quantum dynamics is fully recovered by the angular probability distribution obtained from solutions of the time-dependent Schrödinger equation with parameters refined against the experiment. The populations and phases of rotational states in the retrieved time-dependent three-dimensional wavepacket rationalises the observed very high degree of alignment.

All-optical field-free three-dimensional orientation of asymmetric-top molecules

Orientation and alignment of molecules by ultrashort laser pulses is crucial for a variety of applications and has long been of interest in physics and chemistry, with the special emphasis on stereodynamics in chemical reactions and molecular orbitals imaging. As compared to the laser-induced molecular alignment, which has been extensively studied and demonstrated, achieving molecular orientation is a much more challenging task, especially in the case of asymmetric-top molecules. Here, we report the experimental demonstration of all-optical field-free three-dimensional orientation of asymmetric-top molecules by means of phase-locked cross-polarized two-color laser pulse. This approach is based on nonlinear optical mixing process caused by the off-diagonal elements of the molecular hyperpolarizability tensor. It is demonstrated on SO2 molecules and is applicable to a variety of complex nonlinear molecules.

Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨𝖼𝗈𝗌𝟤 θ⟩ directly from ⟨𝖼𝗈𝗌𝟤 θ2D⟩ by Fourier analysis

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos²θ⟩, directly from its two-dimensional counterpart, ⟨cos²θ_2D⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos²θ_2D⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos²θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos²θ_2D⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos²θ⟩ is obtained and, finally, ⟨cos²θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos²θ⟩ trace from a measured ⟨cos²θ_2D⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos²θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I₂ molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos²θ_2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos²θ_2D⟩ and ⟨cos²θ⟩ in general.

Optimal control of orientation and entanglement for two dipole–dipole coupled quantum planar rotors

Optimal control simulations are performed for orientation and entanglement of two dipole–dipole coupled identical quantum rotors.

Laser-Controlled Torsions: Four-Dimensional Theory and the Validity of Reduced Dimensionality Models

A multitude of possible applications along with unique coherence, chirality, and symmetry properties makes the control of molecular torsion with moderately strong, nonresonant laser pulses a fascinating subject. A description of combined rotation and torsion requires at least four angular degrees of freedom, which is challenging for the majority of systems. Lower-dimensional models have been proposed but also questioned. Here, we develop a four-dimensional model for the coupled rotational-torsional motions of molecules consisting of two identical moieties. By comparing four-dimensional calculations with a two-dimensional model, we define conditions under which the lower-dimensional model is valid. In particular, we point to the crucial role of coordinate dependence of the polarizability tensor. Our results do not agree with those of previous four-dimensional calculations but support the conclusions of recent experiments.

Simultaneous manipulation and observation of multiple ro-vibrational eigenstates in solid para-hydrogen

We have experimentally performed the coherent control of delocalized ro-vibrational wave packets (RVWs) of solid para-hydrogen (p-H₂) by the wave packet interferometry (WPI) combined with coherent anti-Stokes Raman scattering (CARS). RVWs of solid p-H₂ are delocalized in the crystal, and the wave function with wave vector k ∼ 0 is selectively excited via the stimulated Raman process. We have excited the RVW twice by a pair of femtosecond laser pulses with delay controlled by a stabilized Michelson interferometer. Using a broad-band laser pulse, multiple ro-vibrational states can be excited simultaneously. We have observed the time-dependent Ramsey fringe spectra as a function of the inter-pulse delay by a spectrally resolved CARS technique using a narrow-band probe pulse, resolving the different intermediate states. Due to the different fringe oscillation periods among those intermediate states, we can manipulate their amplitude ratio by tuning the inter-pulse delay on the sub-femtosecond time scale. The state-selective manipulation and detection of the CARS signal combined with the WPI is a general and efficient protocol for the control of the interference of multiple quantum states in various quantum systems.

Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field

We examine the rotational states of a pair of polar (2)Σ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules ΔJi = 0, ± 1, ΔNi = 2n (n = 0, ±1, ±2,…), and ΔMi = 0, ± 1 imposed by the electric dipole-dipole operator. Here Ji, Ni and Mi are the total, rotational and projection angular momentum quantum numbers of molecules i = 1, 2 in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the pair of coupled rotors.

Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials

The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.

Selective excitation and control of the molecular orientation by a phase shaped laser pulse

Selective excitation and control of the molecular orientation is realized by a dual-color phase-shaped laser pulse.

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.

Observation of nondispersing classical-like molecular rotation

Using the technique of an optical centrifuge, we produce rotational wave packets which evolve in time along either classical-like or non-classical trajectories.

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Example of concerted electronic (right) and nuclear (left) fluxes: isomerization of B₄.

Dynamic stark control of torsional motion by a pair of laser pulses

The torsional motion of a molecule composed of two substituted benzene rings, linked by a single bond, is coherently controlled by a pair of strong (3×10^{13}  W cm^{-2}), nonresonant (800 nm) 200-fs-long laser pulses-both linearly polarized perpendicular to the single-bond axis. If the second pulse is sent at the time when the two benzene rings rotate toward (away from) each other the amplitude of the torsion is strongly enhanced (reduced). The torsional motion persists for more than 150 ps corresponding to approximately 120 torsional oscillations. Our calculations show that the key to control is the strong transient modification of the natural torsional potential by the laser-induced dynamic Stark effect.

Multipulse three-dimensional alignment of asymmetric top molecules

We show, by computation and experiment, that a sequence of nonresonant and impulsive laser pulses with different ellipticities can effectively align asymmetric top molecules in three dimensions under field-free conditions. By solving the Schrödinger equation for the evolution of the rotational wave packet, we show that the 3D alignment of 3,5 difluoroiodobenzene molecules improves with each successive pulse. Experimentally, a sequence of three pulses is used to demonstrate these results, which extend the multipulse schemes used for 1D alignment to full 3D control of rotational motion.

Optics of a gas of coherently spinning molecules

We consider the optical properties of a gas of molecules that are brought to fast unidirectional spinning by a pulsed laser field. It is shown that a circularly polarized probe light passing through the medium inverts its polarization handedness and experiences a frequency shift controllable by the sense and the rate of molecular rotation. Our analysis is supported by two recent experiments on the laser-induced rotational Doppler effect in molecular gases and provides a good qualitative and quantitative description of the experimental observations.

Reactive scattering dynamics of rotational wavepackets: a case study using the model H+H2 and F+H2 reactions with aligned and anti-aligned H2

We propose a method to steer the outcome of reactive atom-diatom scattering, using rotational wavepackets excited by strong non-resonant laser pulses. Full close-coupled quantum mechanical scattering calculations of the D+H2 and F+H2 reactions are presented, where the H2 molecule exists as a coherent superposition of rotational states. The nuclear spin selective control over the molecular bond axis alignment afforded by the creation of rotational wavepackets is applied to reactive scattering systems, enabling a nuclear spin selective influence to be exerted over the reactive dynamics. The extension of the conventional eigenstate-to-eigenstate scattering problem to the case in which the initial state is composed of a coherent superposition of rotational states is detailed, and a selection of example calculations are discussed, along with their mechanistic implications. The feasibility of the corresponding experiments is considered, and a suitable simple two pulse laser scheme is shown to strongly differentiate the reactivities of o-H2 and p-H2.

Commensurate two-quantum coherences induced by time-delayed THz fields

The interaction of carbonyl sulfide dipolar gas molecules with two time-delayed, single-cycle THz pulses is shown both experimentally and theoretically to induce two-quantum rotational coherences that are significantly enhanced with respect to those induced by one THz pulse, depending on the relative delay of the pulses. The underlying phenomenon is quite general in that it can occur even after a single THz pulse if more than one molecular species is present, since the free induction decay emitted by one species (demonstrated here by atmospheric water vapor) can provide the second field interaction for the other.

Quantum resonances in selective rotational excitation of molecules with a sequence of ultrashort laser pulses

We experimentally investigate the effect of quantum resonance in the rotational excitation of the simplest quantum rotor--a diatomic molecule. Using the techniques of high-resolution femtosecond pulse shaping and rotational state-resolved detection, we measure directly the amount of energy absorbed by molecules interacting with a periodic train of laser pulses, and study their dependence on the train period. We show that the energy transfer is significantly enhanced at quantum resonance, and use this effect to demonstrate selective rotational excitation of two nitrogen isotopologs, (14)N(2) and (15)N(2). Moreover, by tuning the period of the pulse train in the vicinity of a fractional quantum resonance, we achieve selective rotational excitation of para- and ortho-isomers of (15)N(2).

Field-free molecular alignment control by phase-shaped femtosecond laser pulse

In this paper, we theoretically show that the field-free molecular alignment can be controlled by shaping the femtosecond laser pulse with a periodic phase step modulation, involving the maximum degree and temporal structure of the molecular alignment. We show that the molecular alignment can be completely suppressed or reconstructed as that by the transform-limited laser pulse, the temporal structure of the alignment transient can be controlled with a desired shape, and the molecular alignment and antialignment for any temporal structure can be switched. Furthermore, we also show that both the degree and direction of the molecular alignment at a fix time delay can be continuously modulated.

Control of molecular rotation with a chiral train of ultrashort pulses

Trains of ultrashort laser pulses separated by the time of rotational revival (typically, tens of picoseconds) have been exploited for creating ensembles of aligned molecules. In this work we introduce a chiral pulse train--a sequence of linearly polarized pulses with the polarization direction rotating from pulse to pulse by a controllable angle. The chirality of such a train, expressed through the period and direction of its polarization rotation, is used as a new control parameter for achieving selectivity and directionality of laser-induced rotational excitation. The method employs chiral trains with a large number of pulses separated on the time scale much shorter than the rotational revival (a few hundred femtosecond), enabling the use of conventional pulse shapers.

Field-free molecular orientation enhanced by two dual-color laser subpulses

In this paper, we theoretically show that the field-free molecular orientation created by a single dual-color laser pulse can be significantly enhanced by separating it into two time-delayed dual-color subpulses. It is indicated that the maximum enhancement of the molecular orientation created by two time-delayed dual-color subpulses can be achieved with their intensity ratio of about 1:2 and by simultaneously applying the second one at the beginning of the rotational wave packet rephasing or the end of the rotational wave packet dephasing induced by the first one. It is also shown that the enhancement or suppression of the molecular orientation can be coherently manipulated by varying the relative phase between the fundamental field and its second harmonic field of the second dual-color subpulse, and its enhancement is obtained around half rotational period.

Intense dynamic bullets in a periodic lattice

Femtosecond filamentation inside a periodic lattice in air is numerically shown to form intense dynamic bullets. The long propagation distance of the bullet structure is primarily attributed to the effect of the lattice that regulates the competition between linear and nonlinear spatiotemporal effects in the region of normal dispersion.

Laser-induced alignment and anti-alignment of rotationally excited molecules

We numerically investigate the post-pulse alignment of rotationally excited diatomic molecules upon nonresonant interaction with a linearly polarized laser pulse. In addition to the simulations, we develop a simple model which qualitatively describes the shape and amplitude of post-pulse alignment induced by a laser pulse of moderate power density. In our treatment we take into account that molecules in rotationally excited states can interact with a laser pulse not only by absorbing energy but also by stimulated emission. The extent to which these processes are present in the interaction depends, on the one hand, on the directionality of the molecular angular momentum (given by the M quantum number), and on the other hand on the ratio of transition frequencies and pulse duration (determined by the J number). A rotational wave packet created by a strong pulse from an initially pure state contains a broad range of rotational levels, over which the character of the interaction can change from non-adiabatic to adiabatic. Depending on the laser pulse duration and amplitude, the transition from the non-adiabatic to the adiabatic limit proceeds through a region with dominant rotational heating, or alignment, for short pulses and a large region with rotational cooling, and correspondingly preferred anti-alignment, for longer pulses.