Role of rotational temperature in adiabatic molecular alignment

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.

Alignment Thresholds of Molecules

Molecules have long been known to align in moderately intense, far off-resonance laser fields with a large variety of applications in physics and optics. We illustrate and describe the physical origin of a previously unexplored phenomenon in the adiabatic alignment dynamics of molecules, which is fundamentally interesting and also has an important practical implication. Specifically, the intensity dependence of the degree of adiabatic alignment exhibits a threshold behavior, below which molecules are isotropically distributed rotationally and above which the alignment rapidly reaches a plateau. Furthermore, we show that both the intensity and the temperature dependencies of the alignment of all linear molecules exhibit universal curves and derive analytical forms to describe these dependencies. Finally, we illustrate that the alignment threshold occurs very generally at a lower intensity than the off-resonance ionization threshold, a numerical observation that is readily illustrated analytically. The threshold behavior is attributed to a tunneling mechanism that rapidly switches off at the threshold intensity, where tunneling between the potential wells corresponding to the two orientations of the aligned molecules becomes impossible. The universal threshold behavior of molecular alignment is a simple phenomenon, but one that was not realized before and can be readily tested experimentally.

Picosecond pulse-shaping for strong three-dimensional field-free alignment of generic asymmetric-top molecules

Fixing molecules in space is a crucial step for the imaging of molecular structure and dynamics. Here, we demonstrate three-dimensional (3D) field-free alignment of the prototypical asymmetric top molecule indole using elliptically polarized, shaped, off-resonant laser pulses. A truncated laser pulse is produced using a combination of extreme linear chirping and controlled phase and amplitude shaping using a spatial-light-modulator (SLM) based pulse shaper of a broadband laser pulse. The angular confinement is detected through velocity-map imaging of H⁺ and C²⁺ fragments resulting from strong-field ionization and Coulomb explosion of the aligned molecules by intense femtosecond laser pulses. The achieved three-dimensional alignment is characterized by comparing the result of ion-velocity-map measurements for different alignment directions and for different times during and after the alignment laser pulse to accurate computational results. The achieved strong three-dimensional field-free alignment of [Formula: see text] demonstrates the feasibility of both, strong three-dimensional alignment of generic complex molecules and its quantitative characterization.

Laser-Induced Coulomb Explosion Imaging of Aligned Molecules and Molecular Dimers

We discuss how Coulomb explosion imaging (CEI), triggered by intense femtosecond laser pulses and combined with laser-induced alignment and covariance analysis of the angular distributions of the recoiling fragment ions, provides new opportunities for imaging the structures of molecules and molecular complexes. First, focusing on gas phase molecules, we show how the periodic torsional motion of halogenated biphenyl molecules can be measured in real time by timed CEI, and how CEI of one-dimensionally aligned difluoroiodobenzene molecules can uniquely identify four structural isomers. Next, focusing on molecular complexes formed inside He nanodroplets, we show that the conformations of noncovalently bound dimers or trimers, aligned in one or three dimensions, can be determined by CEI. Results presented for homodimers of CS₂, OCS, and bromobenzene pave the way for femtosecond time-resolved structure imaging of molecules undergoing bimolecular interactions and ultimately chemical reactions. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

High density molecular jets of complex neutral organic molecules with Tesla valves

Supersonic jets of gas-phase atoms and small molecules have enabled a variety of ultrafast and ultracold chemical studies. However, extension to larger, more complex neutral molecules proves challenging for two reasons: (i) Complex molecules, such as cis-stilbene, exist in a liquid or solid phase at room temperature and ambient pressure and (ii) a unidirectional flow of high-density gaseous beams of such molecules to the interaction region is required. No delivery system currently exists that can deliver dense enough molecular jets of neutral complex molecules without ionizing or exciting the target for use in gas-phase structural dynamics studies. Here, we present a novel delivery system utilizing Tesla valves, which generates more than an order-of-magnitude denser gaseous beam of molecules compared to a bubbler without Tesla valves at the interaction region by ensuring a fast unidirectional flow of the gaseous sample. We present combined experimental and flow simulations of the Tesla valve setup. Our results open new possibilities of studying large complex neutral molecules in the gas-phase with low vapor pressures in future ultrafast and ultracold studies.

Quantum-assisted diamagnetic deflection of molecules

We measure the diamagnetic deflection of anthracene and adamantane in a long-baseline matter-wave interferometer.

Spatially Separating the Conformers of a Dipeptide

Atomic-resolution-imaging approaches for single molecules, such as coherent X-ray diffraction at free-electron lasers, require the delivery of high-density beams of identical molecules. However, even very cold beams of biomolecules typically have multiple conformational states populated. We demonstrate the production of very cold (T_rot ≈2.3 K) molecular beams of intact dipeptide molecules, which were then spatially separated into the individual populated conformational states. This is achieved using the combination of supersonic expansion laser-desorption vaporization with electrostatic deflection in strong inhomogeneous fields. This represents the first demonstration of a conformer-separated and rotationally cold molecular beam of a peptide, which enables the investigation of conformer-specific chemistry using inherently non-conformer-specific techniques. It furthermore represents a milestone toward the direct structural imaging of individual biological molecules with atomic resolution by ultrafast diffractive-imaging methods.

Velocity map imaging with non-uniform detection: Quantitative molecular axis alignment measurements via Coulomb explosion imaging

We present a method for inverting charged particle velocity map images which incorporates a non-uniform detection function. This method is applied to the specific case of extracting molecular axis alignment from Coulomb explosion imaging probes in which the probe itself has a dependence on molecular orientation which often removes cylindrical symmetry from the experiment and prevents the use of standard inversion techniques for the recovery of the molecular axis distribution. By incorporating the known detection function, it is possible to remove the angular bias of the Coulomb explosion probe process and invert the image to allow quantitative measurement of the degree of molecular axis alignment.

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.

A Reaction Accelerator: Mid-infrared Strong Field Dissociation Yields Mode-Selective Chemistry

Mode-selective chemistry has been a dream of chemists since the advent of the laser in the 1970s. Despite intense effort, this goal has remained elusive due to efficient energy randomization in polyatomic molecules. Using ab initio molecular dynamics calculations, we show that the interaction of molecules with intense, ultrashort mid-infrared laser pulses can accelerate and promote reactions that are energetically and entropically disfavored, owing to efficient kinetic energy pumping into the corresponding vibrational mode(s) by the laser field. In a test case of formyl chloride ion photodissociation, the reactions are ultimately complete under field-free conditions within 500 fs after the laser pulse, which effectively overcomes competition from intramolecular vibrational energy redistribution (IVR). The approach is quite general and experimentally accessible using currently available technology.

Characterising and optimising impulsive molecular alignment in mixed gas samples

Laser induced impulsive molecular alignment has been fully characterized in linear molecules by matching numerical simulations and experimental data of the corresponding rotational wavepacket in the frequency domain. A rigorous procedure for an accurate matching between simulation and experimental data is presented for the first time, making this a versatile technique for experiments where the molecular axis distribution is not directly accessible. Seeding small molecules in Ar as a carrier gas has then been employed to assist cooling and we systematically retrieve the molecule's rotational temperature and alignment distribution for different mixing ratios. For a total backing pressure of 2 bar it was found that seeding 10% N(2) in Ar results in the best cooling. Compared to pure N(2) the rotational temperature was reduced from 24 ± 2 K down to 9 ± 2 K. This leads to an improvement of the peak alignment distribution from <cos(2)θ> = 0.60 to <cos(2)θ> = 0.71. For the same mixing ratio CO(2) was cooled from 34 ± 3 K to 9 ± 1 K improving the alignment distribution from 0.48 to 0.64. In O(2) a cooling from 58 ± 2 K to 37 ± 4 K was observed, corresponding to an alignment distribution improvement from 0.49 to 0.58. The results demonstrate the wide applicability of the characterisation procedure and of seeded supersonic beams to optimise impulsive alignment of small molecules.

State- and conformer-selected beams of aligned and oriented molecules for ultrafast diffraction studies

The manipulation of the motion of neutral molecules with electric or magnetic fields has seen tremendous progress over the last decade. Recently, these techniques have been extended to the manipulation of large and complex molecules. In this article we introduce experimental approaches to the manipulation of large molecules, i.e., the deflection, focusing and deceleration using electric fields. We detail how these methods can be exploited to spatially separate quantum states and how to select individual conformers of complex molecules. We briefly describe mixed-field orientation experiments made possible by the quantum-state selection. Moreover, we provide an outlook on ultrafast diffraction experiments using these highly controlled samples.

A short pulse (7 micros FWHM) and high repetition rate (dc-5 kHz) cantilever piezovalve for pulsed atomic and molecular beams

In this paper we report on the design and operation of a novel piezovalve for the production of short pulsed atomic or molecular beams. The high speed valve operates on the principle of a cantilever piezo. The only moving part, besides the cantilever piezo itself, is a very small O-ring that forms the vacuum seal. The valve can operate continuous (dc) and in pulsed mode with the same drive electronics. Pulsed operation has been tested at repetition frequencies up to 5 kHz. The static deflection of the cantilever, as mounted in the valve body, was measured as a function of driving field strength with a confocal microscope. The deflection and high speed dynamical response of the cantilever can be easily changed and optimized for a particular nozzle diameter or repetition rate by a simple adjustment of the free cantilever length. Pulsed molecular beams with a full width at half maximum pulse width as low as 7 micros have been measured at a position 10 cm downstream of the nozzle exit. This represents a gas pulse with a length of only 10 mm making it well matched to for instance experiments using laser beams. Such a short pulse with 6 bar backing pressure behind a 150 microm nozzle releases about 10(16) particles/pulse and the beam brightness was estimated to be 4x10(22) particles/(s str). The short pulses of the cantilever piezovalve result in a much reduced gas load in the vacuum system. We demonstrate operation of the pulsed valve with skimmer in a single vacuum chamber pumped by a 520 l/s turbomolecular pump maintaining a pressure of 5x10(-6) Torr, which is an excellent vacuum to have the strong and cold skimmed molecular beam interact with laser beams only 10 cm downstream of the nozzle to do velocity map slice imaging with a microchannel-plate imaging detector in a single chamber. The piezovalve produces cold and narrow (Delta v/v=2%-3%) velocity distributions of molecules seeded in helium or neon at modest backing pressures of only 6 bar. The low gas load of the cantilever valve makes it possible to design very compact single chamber molecular beam machines with high quality cold and intense supersonic beams. The high speed cantilever piezovalve may find broad applicability in experiments where short and strong gas pulses are needed with only modest pumping, the effective use of (expensive) samples, or the production of cold atomic and molecular beams.

Field-free molecular alignment for studies using x-ray pulses from a synchrotron radiation source

A short, intense laser pulse may be employed to create a spatially aligned molecular sample that persists after the laser pulse is over. We theoretically investigate whether this impulsive molecular alignment technique may be exploited for experiments using x-ray pulses from a third-generation synchrotron radiation facility. Using a linear rigid rotor model, the alignment dynamics of model molecular systems with systematically increasing size is calculated utilizing both a quantum density matrix formalism and a classical ensemble method. For each system, the alignment dynamics obtained for a 95 ps laser is compared with that obtained for a 10 ps laser pulse. The average degree of alignment after the laser pulse, as calculated quantum mechanically, increases with the size of the molecule. This effect is quantitatively reproduced by the classical calculations. The average degree of impulsive alignment is high enough to induce a pronounced linear dichroism in resonant x-ray absorption using the intense 100 ps x-ray pulses currently available. However, for structural studies based on elastic x-ray scattering, bright x-ray pulses with a duration of 1 ps or shorter will be required in order to make full use of impulsive molecular alignment.

Rapidly pulsed helium droplet source

A pulsed valve connected to a closed-cycle cryostat was optimized for producing helium droplets. The pulsed droplet beam appeared with a bimodal size distribution. The leading part of the pulse consists of droplets suitable for doping with molecules. The average size of this part can be varied between 10(4) and 10(6) helium atoms, and the width of the distribution is smaller as compared to a continuous-flow droplet source. The system has been tested in a single pulse mode and at repetition rates of up to 500 Hz with almost constant intensity. The droplet density was found to be increased by more than an order of magnitude as compared to a continuous-flow droplet source.

Manipulating the torsion of molecules by strong laser pulses

We demonstrate that strong laser pulses can induce torsional motion in a molecule consisting of a pair of phenyl rings. A nanosecond laser pulse spatially aligns the carbon-carbon bond axis, connecting the two phenyl rings, allowing a perpendicularly polarized, intense femtosecond pulse to initiate torsional motion accompanied by an overall rotation about the fixed axis. We monitor the induced motion by femtosecond time-resolved Coulomb explosion imaging. Our theoretical analysis accounts for and generalizes the experimental findings.

Laser-induced alignment and orientation of quantum-state-selected large molecules

A strong inhomogeneous static electric field is used to spatially disperse a supersonic beam of polar molecules, according to their quantum state. We show that the molecules residing in the lowest-lying rotational states can be selected and used as targets for further experiments. As an illustration, we demonstrate an unprecedented degree of laser-induced one-dimensional alignment (cos;(2)theta_(2D)=0.97) and strong orientation of state-selected iodobenzene molecules. This method should enable experiments on pure samples of polar molecules in their rotational ground state, offering new opportunities in molecular science.

Broadband terahertz lasing in aligned molecules

No broadband amplifying medium has been demonstrated yet for terahertz radiation. We present simulations showing that laser-aligned molecules can amplify broadband terahertz radiation, allowing high-energy amplification of few-cycle pulses at terahertz frequencies.

Multiphoton electron angular distributions from laser-aligned CS2 molecules

Laser-aligned carbondisulfide (CS2) molecules are singly ionized by multiphoton absorption from intense, linearly polarized 25 fs laser pulses. The angular distribution of the photoelectrons exhibits a significant dependence on the angle between the polarizations of the aligning and ionizing laser fields. The widely used strong-field approximation predicts angular distributions in qualitative agreement with the experimental data but fails at a quantitative level.

Holding and spinning molecules in space

We illustrate, experimentally and theoretically, a laser-based method to control the rotations of polyatomic molecules in 3D space. A linearly polarized nanosecond pulse strongly aligns the most polarizable axis of an asymmetric top molecule along its polarization axis while an orthogonally polarized, femtosecond pulse sets the molecules into controlled rotation about the aligned axis. As a result, strong three-dimensional (3D) alignment occurs shortly after the femtosecond pulse and is repeated periodically, reflecting coherent revolution about the molecular axis. Our method opens new directions for research in orientationally confined complex molecules.