Selective Orientation of Chiral Molecules by Laser Fields with Twisted Polarization

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.

Scoring molecular wires subject to an ultrafast laser pulse for molecular electronic devices

A nonionizing ultrafast laser pulse of 20-fs duration with a peak amplitude electric-field ±E = 200 × 10^-4 a.u. was simulated. It was applied to the ethene molecule to consider its effect on the electron dynamics, both during the application of the laser pulse and for up to 100 fs after the pulse was switched off. Four laser pulse frequencies ω = 0.2692, 0.2808, 0.2830, and 0.2900 a.u. were chosen to correspond to excitation energies mid-way between the (S₁ ,S₂ ), (S₂ ,S₃ ), (S₃ ,S₄ ) and (S₄ ,S₅ ) electronic states, respectively. Scalar quantum theory of atoms in molecules (QTAIM) was used to quantify the shifts of the C1C2 bond critical points (BCPs). Depending on the frequencies ω selected, the C1C2 BCP shifts were up to 5.8 times higher after the pulse was switched off compared with a static E-field with the same magnitude. Next generation QTAIM (NG-QTAIM) was used to visualize and quantify the directional chemical character. In particular, polarization effects and bond strengths, in the form of bond-rigidity vs. bond-flexibility, were found, for some laser pulse frequencies, to increase after the laser pulse was switched off. Our analysis demonstrates that NG-QTAIM, in partnership with ultrafast laser irradiation, is useful as a tool in the emerging field of ultrafast electron dynamics, which will be essential for the design, and control of molecular electronic devices.

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.

Ultrafast chirality: the road to efficient chiral measurements

Today we are witnessing the electric-dipole revolution in chiral measurements. Here we reflect on its lessons and outcomes, such as the perspective on chiral measurements using the complementary principles of "chiral reagent" and "chiral observer", the hierarchy of scalar, vectorial and tensorial enantio-sensitive observables, the new properties of the chiro-optical response in the ultrafast and non-linear domains, and the geometrical magnetism associated with the chiral response in photoionization. The electric-dipole revolution is a landmark event. It has opened routes to extremely efficient enantio-discrimination with a family of new methods. These methods are governed by the same principles but work in vastly different regimes - from microwaves to optical light; they address all molecular degrees of freedom - electronic, vibrational and rotational, and use flexible detection schemes, i.e. detecting photons or electrons, making them applicable to different chiral phases, from gases to liquids to amorphous solids. The electric-dipole revolution has also enabled enantio-sensitive manipulation of chiral molecules with light. This manipulation includes exciting and controlling ultrafast helical currents in vibronic states of chiral molecules, enantio-sensitive control of populations in electronic, vibronic and rotational molecular states, and opens the way to efficient enantio-separation and enantio-sensitive trapping of chiral molecules. The word "perspective" has two meanings: an "outlook" and a "point of view". In this perspective article, we have tried to cover both meanings.

Optimization of the double-laser-pulse scheme for enantioselective orientation of chiral molecules

We present a comprehensive study of enantioselective orientation of chiral molecules excited by a pair of delayed cross-polarized femtosecond laser pulses. We show that by optimizing the pulses' parameters, a significant (~ 10%) degree of enantioselective orientation can be achieved at zero and at five kelvin rotational temperatures. This study suggests a set of reasonable experimental conditions for inducing and measuring strong enantioselective orientation. The strong enantioselective orientation and the wide availability of the femtosecond laser systems required for the proposed experiments may open new avenues for discriminating and separating molecular enantiomers.

Upper bound for permanent orientation of symmetric-top molecule induced by linearly polarized electric fields

Many symmetric top molecules are among the most important polyatomic molecules. The orientation of a polyatomic molecule is a challenging task, which is at the heart of its quantum control and crucial for many subsequent applications in various fields. Most recent studies focus on the temporary orientation achieved via the quantum revivals. In this study, we reveal the underlying mechanism behind the observed permanent orientation and discuss strategies for a higher degree of permanent orientation. By a careful analysis of symmetry and unitary, it is possible to estimate an upper bound of [Formula: see text] for a molecule in its thermal equilibrium states using a linear field. We show that this bound can be reached for an oblate symmetric-top molecule in the high temperature limit. To demonstrate different possible schemes, we take CHCl3 as an example. Simply with designed microwave fields, one can permanently orient CHCl3 with a degree of ⟨cos  θ⟩ ≈ 0.045. We show that this value can be significantly increased by adding one or more pump pulses.

Rational Pulse Design for Enantiomer-Selective Microwave Three-Wave Mixing

Microwave three-wave mixing allows for enantiomer-selective excitation of randomly oriented chiral molecules into rotational states with different energy. The random orientation of molecules is reflected in the degeneracy of the rotational spectrum with respect to the orientational quantum number M and reduces, if not accounted for, enantiomer-selectivity. Here, we show how to design pulse sequences with maximal enantiomer-selectivity from an analysis of the M-dependence of the Rabi frequencies associated with rotational transitions induced by resonant microwave drives. We compare different excitations schemes for rotational transitions and show that maximal enantiomer-selectivity at a given rotational temperature is achieved for synchronized three-wave mixing with circularly polarized fields.

Time-varying orbital angular momentum in tight focusing of ultrafast pulses

The orbital angular momentum (OAM) of light has important applications in a variety of fields, including optical communication, quantum information, super-resolution microscopic imaging, particle trapping, and others. However, the temporal properties of OAM in ultrafast pulses and in the evolution process of spin-orbit coupling has yet to be revealed. In this work, we theoretically studied the spatiotemporal property of time-varying OAM in the tightly focused field of ultrafast light pulses. The focusing of an incident light pulse composed of two time-delayed femtosecond sub-pulses with the same OAM but orthogonal spin states is investigated, and the ultrafast dynamicsa time delay of OAM variation during the focusing process driven by the spin-orbit coupling is visualized. Temporal properties of three typical examples, including formation, increase, and transformation of topological charge are investigated to reveal the non-uniform evolutions of phase singularities, local topological charges, self-torques, and time-varying OAM per photon. This work could deepen the understanding of spin-orbit coupling in time domain and promote many promising applications such as ultrafast OAM modulation, laser micromachining, high harmonic generation, and manipulation of molecules and nanostructures.

Selective rotational control in mixtures of molecular super-rotors

We demonstrate experimentally a method of all-optical selective rotational control in gas mixtures. Using an optical centrifuge-an intense laser pulse whose linear polarization rotates at an accelerated rate, we simultaneously excite two different molecular species to two different rotational frequencies of choice. The new level of control is achieved by shaping the centrifuge spectrum according to the rotational spectra of the centrifuged molecules. The shaped optical centrifuge releases one molecular species earlier than the other, therefore separating their target rotational frequencies and corresponding rotational states. The technique is applicable to molecules with non-overlapping rotational spectra in the frequency range of interest and will expand the utility of rotational control in the studies of the effects of molecular rotation on collisions and chemical reactions.

Observation of Mechanical Faraday Effect in Gaseous Media

We report the experimental observation of the rotation of the linear polarization of light propagating in a gas of fast-spinning molecules (molecular superrotors). In the observed effect, related to Fermi's prediction of "polarization drag" by a rotating medium, the vector of linear polarization tilts in the direction of molecular rotation. We use an optical centrifuge to bring the molecules in a gas sample to ultrafast unidirectional rotation and measure the polarization drag angles of the order of 10^{-4}  rad (with an experimental uncertainty about 10^{-6}  rad) over the propagation distance of the order of 1 mm in a number of gases under ambient conditions. We demonstrate an all-optical control of the drag magnitude and direction and investigate the robustness of the mechanical Faraday effect with respect to molecular collisions.

Detecting handedness of spatially oriented molecules by Coulomb explosion imaging

We present a new technique for detecting chirality in the gas phase: Chiral molecules are spatially aligned in three dimensions by a moderately strong elliptically polarized laser field. The momentum distributions of the charged fragments, produced by laser-induced Coulomb explosion, show distinct three-dimensional orientation of the enantiomers when the laser polarization ellipse is rotated by a non-right angle with respect to the norm vector of the detector plane. The resulting velocity-map-image asymmetry is directly connected to the enantiomeric excess and to the absolute handedness of molecules. We demonstrated our scheme computationally for camphor (C₁₀H₁₆O), with its methyl groups as marker fragments, using quantum-mechanical simulations geared toward experimentally feasible conditions. Computed sensitivity to enantiomeric excess is comparable to other modern chiroptical approaches. The present method can be readily optimized for any chiral molecule with an anisotropic polarizability tensor by adjusting the polarization state and intensity profile of the laser field.

Laser control of molecular rotation: Expanding the utility of an optical centrifuge

Since its invention in 1999, the optical centrifuge has become a powerful tool for controlling molecular rotation and studying molecular dynamics and molecular properties at extreme levels of rotational excitation. This technique has been applied to a variety of molecular species, from simple linear molecules to symmetric and asymmetric tops, to molecular ions and chiral enantiomers. Properties of isolated ultrafast rotating molecules, the so-called molecular superrotors, have been investigated, as well as their collisions with one another and the interaction with external fields. The ability of an optical centrifuge to spin a particular molecule of interest depends on both the molecular structure and the parameters of the centrifuge laser pulse. An interplay between these two factors dictates the utility of an optical centrifuge in any specific application. Here, we discuss the strategy of assessing and adjusting the properties of the centrifuge to those of the molecular rotors and describe two practical examples of optical centrifuges with very different characteristics, implemented experimentally in our laboratory.

Field-Induced Diastereomers for Chiral Separation

A novel approach for the state-specific enantiomeric enrichment and the spatial separation of enantiomers is presented. Our scheme utilizes techniques from strong-field laser physics-specifically an optical centrifuge in conjunction with a static electric field-to create a chiral field with defined handedness. Molecular enantiomers experience unique rotational excitation dynamics, and this can be exploited to spatially separate the enantiomers using electrostatic deflection. Notably, the rotational-state-specific enantiomeric enhancement and its handedness are fully controllable. To explain these effects, the conceptual framework of field-induced diastereomers of a chiral molecule is introduced and computationally demonstrated through robust quantum-mechanical simulations on the prototypical chiral molecule propylene oxide (C_{3}H_{6}O), for which ensembles with an enantiomeric excess of up to 30% were obtained.

Controlled Enantioselective Orientation of Chiral Molecules with an Optical Centrifuge

We report on the first experimental demonstration of enantioselective rotational control of chiral molecules with a laser field. In our experiments, two enantiomers of propylene oxide are brought to accelerated unidirectional rotation by means of an optical centrifuge. Using Coulomb explosion imaging, we show that the centrifuged molecules acquire preferential orientation perpendicular to the plane of rotation, and that the direction of this orientation depends on the relative handedness of the enantiomer and the rotating centrifuge field. The observed effect is in agreement with theoretical predictions and is reproduced in numerical simulations of the centrifuge excitation followed by Coulomb explosion of the centrifuged molecules. The demonstrated technique opens new avenues in optical enantioselective control of chiral molecules with a plethora of potential applications in differentiation, separation, and purification of chiral mixtures.

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.

Polarization-based tachometer for measuring spinning rotors

We report on the polarization analysis of shortpulse ultraviolet radiation produced by third-harmonic generation in a gas of coherently spinning molecules. A pulse of twisted linear polarization imprints a unidirectional rotational motion to the molecules leading to an orientation of their rotational angular momenta. A second pulse, time-delayed with respect to the first one, circularly polarized in the plane of rotation of the molecules, acts as a driving field for third-harmonic generation. The angular momentum and energy conservation applied to this process foresees the generation of two Doppler-shifted circularly-polarized harmonics of opposite handedness. Our analysis reveals that spinning molecules enable the generation of a well polarized third-harmonic radiation exhibiting a high degree of ellipticity. Tracking the orientation of the latter allows a time-capture of the molecular axis direction from which the average angular velocity of the rotating molecules is inferred. This method provides a user-friendly polarization-based tachometer for measurement of the rotational speed of spinning nonlinear rotors.

Climbing the Rotational Ladder to Chirality

Molecular chirality is conventionally understood as space-inversion-symmetry breaking in the equilibrium structure of molecules. Less well known is that achiral molecules can be made chiral through extreme rotational excitation. Here, we theoretically demonstrate a clear strategy for generating rotationally induced chirality: An optical centrifuge rotationally excites the phosphine molecule (PH_{3}) into chiral cluster states that correspond to clockwise (R enantiomer) or anticlockwise (L enantiomer) rotation about axes almost coinciding with single P─H bonds. The application of a strong dc electric field during the centrifuge pulse favors the production of one rotating enantiomeric form over the other, creating dynamically chiral molecules with permanently oriented rotational angular momentum. This essential step toward characterizing rotationally induced chirality promises a fresh perspective on chirality as a fundamental aspect of nature.

Coherent Control of the Rotation Axis of Molecular Superrotors

The control of ultrafast molecular rotational motion has benefited from the development of innovative techniques in strong-field laser physics. Here, we theoretically demonstrate a novel type of coherent control by inducing rotation of an asymmetric-top molecule about two different molecular axes. An optical centrifuge is applied to the hydrogen sulfide (H₂S) molecule to create a molecular superrotor, an object performing ultrafast rotation about a well-defined axis. Using two distinct pulse envelopes for the optical centrifuge, we show that H₂S can be excited along separate pathways of rotational states. This leads to stable rotation about two entirely different molecular axes while ensuring rotation is about the propagation direction of the centrifuge, i.e., the laboratory-fixed Z-axis. The presented scheme to control the angular momentum alignment of a molecule will, for instance, be useful in studies of molecule-molecule or molecule-surface scattering, especially due to the large amounts of energy associated with superrotors, which can even be controlled by changing the duration of the optical centrifuge pulse.