Rovibrational Wave Packet Research Articles

Air-Laser-Based Standoff Coherent Raman Spectrometer

Among currently available optical spectroscopic methods, Raman spectroscopy has versatile application to investigation of dynamical processes of molecules leading to chemical changes in the gas and liquid phases. However, it is still a challenge to realize an ideal standoff coherent Raman spectrometer with which both high temporal resolution and high-frequency resolution can be achieved, so that one can remotely probe chemical species in real time with high temporal resolution while monitoring the populations in their respective rovibronic levels in the frequency domain with sufficiently high spectral resolution. In the present study, we construct an air-laser-based Raman spectrometer, in which near-infrared femtosecond (fs) laser pulses at 800 nm and cavity-free picosecond N 2 + air-laser pulses at 391 nm generated by the filamentation induced by the fs laser pulses are simultaneously used, enabling us to generate a hybrid ps/fs laser source at a desired standoff position for standoff surveillance of chemical and biochemical species. With this prototype Raman spectrometer, we demonstrate that the temporal evolution of the electronic, vibrational, and rotational states of N 2 + and the coupling processes of the rovibrational wave packet of N 2 molecules can be probed.

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.

Two-color vibrational, femtosecond, fully resonant electronically enhanced CARS (FREE-CARS) of gas-phase nitric oxide.

A resonantly enhanced, two-color, femtosecond time-resolved coherent anti-Stokes Raman scattering (CARS) approach is demonstrated and used to explore the nature of the frequency- and time-dependent signals produced by gas-phase nitric oxide (NO). Through careful selection of the input pulse wavelengths, this fully resonant electronically enhanced CARS (FREE-CARS) scheme allows rovibronic-state-resolved observation of time-dependent rovibrational wavepackets propagating on the vibrationally excited ground-state potential energy surface of this diatomic species. Despite the use of broadband, ultrafast time-resolved input pulses, high spectral resolution of gas-phase rovibronic transitions is observed in the FREE-CARS signal, dictated by the electronic dephasing timescales of these states. Analysis and computational simulation of the time-dependent spectra observed as a function of pump-Stokes and Stokes-probe delays provide insight into the rotationally resolved wavepacket motion observed on the excited-state and vibrationally excited ground-state potential energy surfaces of NO, respectively.

Mutual influence of rotations and vibrations of a strongly ‘kicked’ diatomic heteronuclear molecule

The interaction of a diatomic heteronuclear molecule with strong ultrashort electromagnetic pulses is investigated by direct numerical integration of the nonstationary Schroedinger equation. The direct action of the pulse on the nuclear subsystem of a molecule is considered and both rotational and vibrational degrees of freedom are taken into account. The strong mutual influence of rotational and vibrational dynamics on each other is found and the possibility to provide an efficient rotational excitation and molecular orientation is established. In the case of the ‘δ-pulse’ action, an analytical approach is developed to describe the ro-vibrational behaviour of the molecule in the after-pulse regime. The features of the field-induced coherent ro-vibrational wave packet are analyzed and the polarization signal at teraherz frequencies is found.

Theoretical studies of femtosecond photoionization for the Na<sub>2</sub> molecule

Multiphoton ionization of the Na2 molecule by a single phase shaped fem- tosecond laser pulse has been theoretically studied using time-dependent quantum wave packet method including the effect of molecular rotation. We analyze the tempo- ral development of the population and further discuss the molecular motion by map- ping the rovibrational wave packet propagation in the excited state. The calculated results show a strong dependence of the kinetic energy-resolved photoelectron spectra on the laser chirp directions and the pulse duration. PACS: 33.80.Rv

Ultrafast X-ray diffraction in liquid, solution and gas: present status and future prospects

In recent years, the time-resolved X-ray diffraction technique has been established as an excellent tool for studying reaction dynamics and protein structural transitions with the aid of 100 ps X-ray pulses generated from third-generation synchrotrons. The forthcoming advent of the X-ray free-electron laser (XFEL) will bring a substantial improvement in pulse duration, photon flux and coherence of X-ray pulses, making time-resolved X-ray diffraction even more powerful. This technical breakthrough is envisioned to revolutionize the field of reaction dynamics associated with time-resolved diffraction methods. Examples of candidates for the first femtosecond X-ray diffraction experiments using highly coherent sub-100 fs pulses generated from XFELs are presented in this paper. They include the chemical reactions of small molecules in the gas and solution phases, solvation dynamics and protein structural transitions. In these potential experiments, ultrafast reaction dynamics and motions of coherent rovibrational wave packets will be monitored in real time. In addition, high photon flux and coherence of XFEL-generated X-ray pulses give the prospect of single-molecule diffraction experiments.

Rovibrational Wave-Packet Dispersion during Femtosecond Laser Filamentation in Air

An impulsive, femtosecond filament-based Raman technique producing high quality Raman spectra over a broad spectral range (1554.7-4155 cm(-1)) is presented. The temperature of gas phase molecules can be measured by temporally resolving the dispersion of impulsively excited vibrational wave packets. Application to laser-induced filamentation in air reveals that the initial rovibrational temperature is 300 K for both N2 and O2. The temperature-dependent wave-packet dynamics are interpreted using an analytic anharmonic oscillator model. The wave packets reveal a 1/e dispersion time of 3.9 ps for N2 and 2.8 ps for O2. Pulse self-compression of temporal features to 8 fs within the filament is directly measured by impulsive vibrational excitation of H2.

Pulse shaping and its characterization of mid-infrared femtosecond pulses: Toward coherent control of molecules in the ground electronic states

We have examined a technique of complex shaping of mid-infrared femtosecond laser pulses towards accurate and precise control of rovibrational wave packets of molecules in the ground electronic state. A Germanium acousto-optics modulator was used as a device for the pulse shaping. In order to characterize the shaped pulses precisely, sum-frequency cross-correlation frequency-resolved optical gating was introduced for the analysis of both amplitude and phase of the electric fields. The mid-infrared pulses were shaped and characterized with a frequency resolution better than 4.5 cm −1. Such a resolution is supposed to be sufficient for the realization of quantum gate operations with high fidelity, which is one of the most challenging applications of rovibrational wave packet manipulation of molecules. In order to demonstrate the precision of our method of shaping and its characterization, we have generated shaped pulses that will realize Hadamard and NOT quantum gates with rovibrational states of a CO molecule.

Manipulation of ro-vibronic wave packet composition using chirped ultrafast laser pulses

Linearly chirped femtosecond laser pulses are used to excite ro-vibrational wave packets in lithium dimers from a single well-prepared launch state. Two-photon resonant Raman transitions excite a manifold of rotational states in a coherent superposition. Excitation with positively chirped laser pulses is shown to enhance a quantum beat involving states with lower rotational quantum numbers, whereas negatively chirped pulses enhance a quantum beat between states with higher rotational quantum numbers, thus steering the rotational coherences to higher or lower rotational states. Time-dependent perturbation theory calculations verify the magnitudes and directions of the enhancement as a function of the applied chirp. The quantitative calculations and experimental results demonstrate that excitation with chirped pulses is an effective method for enhancing specific rotational coherences involving higher or lower rotational states.

Rovibrational wave-packet manipulation using shaped midinfrared femtosecond pulses

We have calculated the propagation of rovibrational wave-packet in the $^{1}\ensuremath{\Sigma}$ state of $\mathrm{CO}$ and the $^{2}\ensuremath{\Pi}$ state of $\mathrm{NO}$ manipulated by shaped midinfrared femtosecond laser pulses. The rotational states of the molecules were fully taken into account in the calculation and the effects of the rotational states in the vibrational wave-packet evolution were examined in detail. As a result, it is found that rotational excitations associated with the vibrational excitation affect the wave-packet propagation drastically, which suggests that the rotational states should not be ignored when vibrational states of molecules are used as the target state for coherent control and qubits for quantum computation. For the experimental detection of the amplitude and phase information on the rovibrational wave-packets, the time profiles of the transition intensities from the rovibrational wave-packet to an electronically excited state were calculated. It is shown that both ionization and laser induced fluorescence signals contain information necessary for the analysis of the phase and relative amplitude of the rovibrational wave-packets.

Femtosecond pulse shaping in the mid-infrared generated by difference-frequency mixing: a simulation and experiment

We have examined phase- and amplitude-modulated femtosecond laser pulses in the mid-infrared (MIR) region (3-10 μm) generated by difference-frequency mixing both theoretically and experimentally. Transfer of the pulse shape from near infrared to MIR by a difference-frequency process was evaluated in detail for various spectra, linear chirps, phases, and optical delays of two pulses before the different frequency was compared and with experimentally obtained MIR shapes. In the experiment, the signal pulse of an optical parametric amplifier was shaped with an acousto-optic programmable dispersive filter and mixed in an AgGaS2 crystal with the idler pulse that was temporally stretched by passing it through a dispersion block to generate a shaped MIR pulse. The agreement between the theory and experiment was reasonable despite the complicated experimental procedure. It was demonstrated that the resultant MIR pulse shape could be completely different from the pulse shape before the difference-frequency generation. However, it is possible to reproduce any shape of MIR pulses by predicting the pulse shape using the present theoretical framework. This will allow us to manipulate rovibrational wave packets of real molecules for practical applications.

Nonlinear Wave-Packet Interferometry and Molecular State Reconstruction in a Vibrating and Rotating Diatomic Molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.

Molecular orientation via a dynamically induced pulse-train: wave packet dynamics of NaI in a static electric field.

We regard the rovibrational wave packet dynamics of NaI in a static electric field after femtosecond excitation to its first electronically excited state. The following quasibound nuclear wave packet motion is accompanied by a bonding situation changing from covalent to ionic. At times when the charge separation is present, i.e., when the bond-length is large, a strong dipole moment exists and rotational excitation takes place. Upon bond contraction, the then covalently bound molecule does not experience the external field. This scenario repeats itself periodically. Thus, the vibrational dynamics causes a situation which is comparable to the interaction of the molecule with a train of pulses where the pulse separation is determined by the vibrational period.

Effect of rotations on the generation of coherent internal molecular motion

AbstractWe discuss the quantum dynamics of the excitation of a diatomic molecule in the presence of external force fields and the general role of orientation on the manipulation of molecular structure. We review the dynamics of the HF molecule in the presence of a static electric field during and after coherent infrared radiation. The time‐dependent dynamics is induced by infrared multiphoton excitation and the time evolution of the rovibrational wave packet is calculated in configuration space. The coherent motion of rotational wave packets obtained from orientation in a static field is compared with the motion of rotational coherent states. Values are given for static field strengths needed to orient molecules such that their internal dynamics can be described by simplified, purely vibrational models. The results are discussed in comparison with the orientation of adsorbed molecules on metal surfaces. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Generation of semiclassical and delocalized vibrational wave packet motion of HF molecules oriented in an external static electric field

The quantum dynamics of the HF molecule is investigated in the presence of a static electric field and coherent infrared radiation. The time dependent dynamics is induced by infrared multiphoton excitation and the time evolution of the rovibrational wave packet is calculated in configuration space. Results are given for static field strengths needed to orient molecules such that their internal dynamics can be described by simplified, purely vibrational models. For highly oriented HF molecules, time intervals of approximate duration of 70 fs occur repeatedly during and after the excitation in which the reduced vibrational wave packet motion is nearly semiclassical (“semiclassical windows”). The occurrence of these time intervals can be made more regular after the excitation, if the pulse duration is chosen adequately.

Quantum control of alignment and orientation of molecules by optimized laser pulses

We present a method for designing laser pulses to control the alignment and orientation of polar molecules. Expressions for the optimal laser pulse are derived using optimal control theory within the semiclassical molecule–radiation field interactions. The optimization method is applied to the alignment and orientation of carbon monoxide to demonstrate its effectiveness. The results obtained by using this method is compared with those obtained using the analytical pulse-control method of Dion et al. (Chem. Phys. Lett. 302 (1999) 215). The control mechanism is explained in terms of the rovibrational wave packets created by optimized pulses.

Rotational and vibrational wave packet motion during the infrared multiphoton excitation of HF

The time dependent quantum dynamics of molecular rotations and vibrations during coherent infrared multiphoton excitation are investigated by calculation of the time evolution of the wave packet in the rotational and vibrational configuration space. Results are presented for the rovibrational motion of HF using recent potential energy and dipole moment functions developed elsewhere by ab initio calculations. Several initial conditions are studied, from the single rovibrational ground state to a superposition of states with different J quantum numbers corresponding to highly oriented molecules. A careful examination of the rovibrational wave packet motion allows for a simple interpretation of the rotational motion and the effects of different initial conditions on the intramolecular kinetics. It is found that, depending on the degree of orientation, the HF molecule undergoes very fast deorientation, faster than its “classical” rotational period, thus perturbing the generation of a semiclassical vibrational motion during the excitation process.

Time-resolved photoelectron angular distributions as a map of rotational motion

Abstract We discuss the application of photoelectron angular distributions as a probe of time-evolving rovibrational wavepackets. A physical picture is drawn of the mechanism through which rotation–vibration coupling mechanisms are reflected in the time-dependent photoionisation asymmetry parameters. The effects of complicating features that may obscure the interpretation of time-resolved photoelectron spectroscopies, including the field intensity and the inherent complexity of ionisation processes are examined.

Phase control of wavepacket dynamics using shaped femtosecond pulses

Coherent vibrational and rotational dynamics of the Li2 molecule is controlled by varying the relative phases, φn, of the rovibrational wavepacket components, ∣n〉 e-i(ωnt+φn). The coherent superposition is created by excitation of a set of ten rovibronic E 1Σg+(νE=12–16, JE=17, 19) states from an intermediate state, A 1Σu+(νA=14, JA=18), using ultrashort optical pulses with well defined spectral amplitudes and phases encoded into the pulse by a liquid crystal spatial light modulator. The wavepacket is probed by time-dependent photoionization and the quantum interference signal is measured as a total ionization yield. The phases of the wavepacket components are optimized to produce partial localization of the wavepacket at a given time t, in specific regions of three-dimensional space defined by the radial and angular coordinates. As a result, the ionization yield, I(t), is maximized or minimized at a time t. The degree of control achieved in the experiment (Imax-Imin)/Imax=64(±12%). The experimental data are interpreted in terms of time-dependent radial and angular probability distributions, calculated for different initial conditions that are determined by the phase relationships in the excitation pulse.

Erratum: “Manipulation of rovibrational wave packet composition in the Li2 E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses” [J. Chem. Phys. 107, 4172 (1997)

Erratum: “Manipulation of rovibrational wave packet composition in the Li2 E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses” [J. Chem. Phys. <b>107</b>, 4172 (1997)