Quantum unidirectional rotation directly imaged with molecules

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.

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.

Real-time hydrogen molecular dynamics satisfying the nuclear spin statistics of a quantum rotor

Apparent presence of the nuclear-spin species of a hydrogen molecule, para-hydrogen and ortho-hydrogen, associated with the quantum rotation is a manifestation of the nuclear quantum nature of hydrogen, governing not only molecular structures but also physical and chemical properties of hydrogen molecules. It has been a great challenge to observe and calculate real-time dynamics of such molecularized fermions. Here, we developed the non-empirical quantum molecular dynamics method that enables real-time molecular dynamics simulations of hydrogen molecules satisfying the nuclear spin statistics of the quantum rotor. While reproducing the species-dependent quantum rotational energy, population ratio, specific heat, and H-H bond length and frequency, we found that their translational, orientational and vibrational dynamics becomes accelerated with the higher rotational excitation, concluding that the nuclear quantum rotation stemmed from the nuclear spin statistics can induce various kinds of dynamics and reactions intrinsic to each hydrogen species.

Rotational spectroscopy of the argon dimer by time-resolved Coulomb explosion imaging of rotational wave packets

We report time-domain rotational spectroscopy of the argon dimer, Ar₂, by implementing time-resolved Coulomb explosion imaging of rotational wave packets. The rotational wave packets are created in Ar₂ with a linearly polarized, nonresonant, ultrashort laser pulse, and their spatiotemporal evolution is fully characterized by measuring angular distribution of the fragmented Ar⁺ promptly ejected from Ar₂²⁺ generated by the more intense probe pulse. The pump-probe measurements have been carried out up to a delay time of 16 ns. The alignment parameters, derived from the observed images, exhibit periodic oscillation lasting for more than 15 ns. The pure rotational spectrum of Ar₂ is obtained by Fourier transformation of the time traces of the alignment parameters. The frequency resolution in the spectrum is about 90 MHz, the highest ever achieved for Ar₂. The rotational constant and the centrifugal distortion constant are determined with much improved precision than the previous experimental results: B₀ = 1.72713 ± 0.00009 GHz and D₀ = 0.0310 ± 0.0005 MHz. The present B₀ value does not match within the quoted experimental uncertainty with that from the VUV spectroscopy, so far accepted as an experimental reference to assess theories. The present improved constants would stand as new references to calibrate state-of-the-art theoretical investigations and an indispensable experimental source for the construction of an accurate empirical intermolecular potential.

Single and sequential double ionization of NO radical in intense laser fields

We examine the dependences of the single and double ionization probabilities of NO radical on the angle between the NO axis and the laser polarization direction in an intense laser field (790 nm, 100 fs, 1–10 × 1014 W/cm2) and show that the double ionization is enhanced when the NO axis is parallel to the laser polarization direction. We reveal that the angular dependence of the sequential double ionization probability is determined by the shape of the 5σ orbital of NO+ from which the second photoelectron is emitted in the ionization from NO+ to NO2+. We also reveal that the fast oscillation in the probability of the tunnel ionization of NO originating from a coherent superposition of the two spin–orbit components in the electronic ground X2Π state is described well based on the molecular Ammosov-Delone-Krainov (MO-ADK) theory in which the time evolution of the electron density distribution of the 2π orbital is taken into account.

Rotational dynamics and transitions between Λ-type doubling of NO induced by an intense two-color laser field

We numerically investigate the rotational dynamics of NO in the electronic ground X²Π state induced by an intense two-color laser field (10 TW/cm²) as a function of pulse duration (0.3-25 ps). In the short pulse duration of less than 12 ps, rotational Raman excitation is effectively induced and results in molecular orientation. On the contrary, when the pulse duration is longer than 15 ps, the rotational excitation is suppressed. In addition to the rotational excitation, we find that transitions between Λ-type doubling are induced. Significantly, the maximum coherent wave packet between Λ-type doubling in J = 0.5 is generated using the pulse duration of 19.8 ps. The wave packet changes to the eigenstates of Λ = +1 or -1 alternatively, where Λ is the projection of the electronic orbital angular momentum on the N-O axis, which is regarded as the unidirectional rotation of an unpaired 2π electron around the N-O axis in a space-fixed frame as well as in a molecule-fixed frame. The experimental method to observe the alternation of the rotational direction of the electron around the N-O axis is proposed.

Anti-alignment driven dynamics in the excited states of molecules under strong fields

We develop two novel models of the H2+ molecule and its isotopes from which we assess quantum-mechanically and semi-classically whether the molecule anti-aligns with the field in the first excited electronic state. The results from both models allow us to predict anti-alignment dynamics even for the HD+ isotope, which possesses a permanent dipole moment. The molecule dissociates at angles perpendicular to the field polarization in both the excited and the ground electronic state, as the population is exchanged through a conical intersection. The quantum mechanical dispersion of the initial state is sufficient to cause full dissociation. We conclude that the stabilization of these molecules in the excited state through bond-hardening under a strong field is highly unlikely.

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.

Femtosecond Resolving Photodissociation Dynamics of the SO2 Molecule

We experimentally investigate the ultrafast photodissociation dynamics of the SO₂ molecule induced by intense ultrashort laser pulses in a pump-probe scheme. Different three-body fragmentation pathways are discriminated using the time-dependent kinetic energy release spectrum with femtosecond time resolution. A nontrivial three-body fragmentation pathway, denoted as the bonding pathway, is unraveled, in which an intermediate fast rotating O₂ molecule is formed before complete fragmentation. The ultrafast chemical bond rearrangement after electron release is tracked in real time. The bonding pathway generally exists in the three-body fragmentation processes induced by strong laser fields of different wavelengths, which is observed in infrared, ultraviolet, and mixed two-color cases. Our findings are significant for understanding the photon-induced ultrafast processes of the SO₂ molecule in atmospheric chemistry.

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.

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.

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.

Real-Time Observation of Molecular Spinning with Angular High-Harmonic Spectroscopy

We demonstrate an angular high-harmonic spectroscopy method to probe the spinning dynamics of a molecular rotation wave packet in real time. With the excitation of two time-delayed, polarization-skewed pump pulses, the molecular ensemble is impulsively kicked to rotate unidirectionally, which is subsequently irradiated by another delayed probe pulse for high-order harmonic generation (HHG). The spatiotemporal evolution of the molecular rotation wave packet is visualized from the time-dependent angular distributions of the HHG yields and frequency shift measured at various polarization directions and time delays of the probe pulse. The observed frequency shift in HHG is demonstrated to arise from the nonadiabatic effect induced by molecular spinning. Different from the previous spectroscopic and Coulomb explosion imaging techniques, the angular high-harmonic spectroscopy method can reveal additionally the electronic structure and multiple orbitals of the sampled molecule. All the experimental findings are well reproduced by numerical simulations. Further extension of this method would provide a powerful tool for probing complex polyatomic molecules with HHG spectroscopy.

Selective Orientation of Chiral Molecules by Laser Fields with Twisted Polarization

We explore a pure optical method for enantioselective orientation of chiral molecules by means of laser fields with twisted polarization. Several field implementations are considered, including a pair of delayed, cross-polarized laser pulses, an optical centrifuge, and polarization-shaped pulses. We show that these schemes lead to out-of-phase time-dependent dipole signals for different enantiomers, and we also predict a substantial permanent molecular orientation persisting long after the laser fields are over. The underlying classical orientation mechanism common to all of these fields is discussed, and its operation is demonstrated for a range of chiral molecules of various complexity: hydrogen thioperoxide (HSOH), propylene oxide (CH₃CHCH₂O), and ethyl oxirane (CH₃CH₂CHCH₂O). The presented results demonstrate generality, versatility, and robustness of this optical method for manipulating molecular enantiomers in the gas phase.

Visualizing rotational wave functions of electronically excited nitric oxide molecules by using an ion imaging technique

Here we report the dissociative ionization imaging of electronically excited nitric oxide (NO) molecules to visualize rotational wave functions in the electronic excited state (A ²Σ⁺). The NO molecules were excited to a single rotational energy eigenstate in the first electronic excited state by a resonant nanosecond ultraviolet pulse. The molecules were then irradiated by a strong, circularly polarized femtosecond imaging pulse. Spatial distribution of the ejected N⁺ and O⁺ fragment ions from the dissociative NO²⁺ was recorded as a direct measure of the molecular axis distribution using a high-resolution slice ion imaging apparatus. The circularly polarized probe pulse realizes the isotropic ionization and thus undistorted shapes of the functions can be visualized. Due to the higher ionization efficiency of the excited molecules relative to the ground state ones, signals from the excited NO were enhanced. We can, therefore, extract shapes of the square of rotational wave functions in the electronic excited state although the unexcited ground state molecules are the majority in an ensemble. The observed images show s-function-like and p-function-like shapes depending on the excitation wavelengths. These shapes well reflect the rotational (angular momentum) character of the prepared states. The present approach directly leads to the evaluation method of the molecular axis alignment in photo-excited ensembles, and it could also lead to a visualization method for excited state molecular dynamics.

Rotated echoes of molecular alignment: fractional, high order and imaginary

We report experimental observations of rotated echoes of alignment induced by a pair of time-delayed and polarization-skewed femtosecond laser pulses interacting with an ensemble of molecular rotors. Rotated fractional echoes, rotated high order echoes and rotated imaginary echoes are directly visualized by using the technique of coincident Coulomb explosion imaging. We show that the echo phenomenon not only exhibits temporal recurrences but also spatial rotations determined by the polarization of the time-delayed second pulse. The dynamics of echo formation is well described by the laser-induced filamentation in rotational phase space. The quantum-mechanical simulation shows good agreements with the experimental results.

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

We present a method for visualizing laser-induced, ultrafast molecular rotational wave packet dynamics. We have developed a new 2-dimensional Coulomb explosion imaging setup in which a hitherto-impractical camera angle is realized. In our imaging technique, diatomic molecules are irradiated with a circularly polarized strong laser pulse. The ejected atomic ions are accelerated perpendicularly to the laser propagation. The ions lying in the laser polarization plane are selected through the use of a mechanical slit and imaged with a high-throughput, 2-dimensional detector installed parallel to the polarization plane. Because a circularly polarized (isotropic) Coulomb exploding pulse is used, the observed angular distribution of the ejected ions directly corresponds to the squared rotational wave function at the time of the pulse irradiation. To create a real-time movie of molecular rotation, the present imaging technique is combined with a femtosecond pump-probe optical setup in which the pump pulses create unidirectionally rotating molecular ensembles. Due to the high image throughput of our detection system, the pump-probe experimental condition can be easily optimized by monitoring a real-time snapshot. As a result, the quality of the observed movie is sufficiently high for visualizing the detailed wave nature of motion. We also note that the present technique can be implemented in existing standard ion imaging setups, offering a new camera angle or viewpoint for the molecular systems without the need for extensive modification.

Polarization shaping of high-order harmonics in laser-aligned molecules

The present work reports on the generation of short-pulse coherent extreme ultraviolet radiation of controlled polarization. The proposed strategy is based on high-order harmonics generated in pre-aligned molecules. Field-free molecular alignment produced by a short linearly-polarized infrared laser pulse is used to break the isotropy of a gas medium. Driving the aligned molecules by a circularly-polarized infrared pulse allows to transfer the anisotropy of the medium to the polarization of the generated harmonic light. The ellipticity of the latter is controlled by adjusting the angular distribution of the molecules at the time they interact with the driving pulse. Extreme ultraviolet radiation produced with high degree of ellipticity (close to circular) is demonstrated.