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.     

Optimal control theory with continuously distributed target states: An application to NaK

Laser pulse control of molecular dynamics is studied theoretically by using optimal control theory. The control theory is extended to target states which are distributed in time as well as in a space of parameters which are responsible for a change of individual molecular properties. This generalized treatment of a control task is first applied to wave packet formation in randomly oriented diatomic systems. Concentrating on an ensemble of NaK molecules which are not aligned the control yield decreases drastically when compared with an aligned ensemble. Second, we demonstrate for NaK the maximization of the probe pulse transient absorption in a pump–probe scheme with an optimized pump pulse. These computations suggest an overall optical control scheme, whereby a flexible technique is suggested to form particular wave packets in the excited state potential energy surface. In particular, it is shown that considerable wave packet localization at the turning points of the first-excited Σ-state potential energy surfaces of NaK may be achieved. The dependency of the control yield on the probe pulse parameters is also discussed.     

Quantum model simulations of symmetry breaking and control of bond selective dissociation of FHF- using IR+UV laser pulses

Symmetry breaking and control of bond selective dissociation can be achieved by means of ultrashort few-cycle-infrared (IR) and ultraviolet (UV) laser pulses. The mechanism is demonstrated for the oriented model system, FHF-, by nuclear wave packets which are propagated on two-dimensional potential energy surfaces calculated at the QCISD/d-aug-cc-pVTZ level of theory. The IR laser pulse is optimized to drive the wave packet coherently along alternate bonds. Next, a well-timed ultrashort UV laser pulse excites the wave packet, via photodetachment of the negative bihalide anion, to the bond selective domain of the neutral surface close to the transition state. The excited wave packet is then biased to evolve along the pre-excited bond toward the target product channel, rather than bifurcating in equal amounts. Comparison of the vibrational frequencies obtained within our model with harmonic and experimental frequencies indicates substantial anharmonicities and mode couplings which impose restrictions on the mechanism in the domain of ultrashort laser fields. Extended applications of the method to randomly oriented or to asymmetric systems XHY- are also discussed, implying the control of product directionality and competing bond-breaking.     

Optical control of excited-state vibrational coherences of a molecule in solution: The influence of the excitation pulse spectrum and phase in LD690

Spectral and phase shaping of femtosecond laser pulses is used to selectively excite vibrational wave packets on the ground (S0) and excited (S1) electronic states in the laser dye LD690. The transient absorption signals observed following excitation near the peak of the ground-state absorption spectrum are characterized by a dominant 586 cm(-1) vibrational mode. This vibration is assigned to a wave packet on the S0 potential energy surface. When the excitation pulse is tuned to the blue wing of the absorption spectrum, a lower frequency 568 cm(-1) vibration dominates the response. This lower frequency mode is assigned to a vibrational wave packet on the S1 electronic state. The spectrum and phase of the excitation pulse also influence both the dephasing of the vibrational wave packet and the amplitude profiles of the oscillations as a function of probe wavelength. Excitation by blue-tuned, positively chirped pulses slows the apparent dephasing of the vibrational coherences compared with a transform-limited pulse having the same spectrum. Blue-tuned negatively chirped excitation pulses suppress the observation of coherent oscillations in the ground state.     

Wave packet theory of dynamic stimulated Raman spectra in femtosecond pump-probe spectroscopy

The quantum theory for stimulated Raman spectroscopy from a moving wave packet using the third-order density matrix and polarization is derived. The theory applies, in particular, to the new technique of femtosecond broadband stimulated Raman spectroscopy (FSRS). In the general case, a femtosecond actinic pump pulse first prepares a moving wave packet on an excited state surface which is then interrogated with a coupled pair of picosecond Raman pump pulse and a femtosecond Raman probe pulse and the Raman gain in the direction of the probe pulse is measured. It is shown that the third-order polarization in the time domain, whose Fourier transform governs the Raman gain, is given simply by the overlap of a first-order wave packet created by the Raman pump on the upper electronic state with a second-order wave packet on the initial electronic state that is created by the coupling of the Raman pump and probe fields acting on the molecule. Calculations are performed on model potentials to illustrate and interpret the FSRS spectra.     

Laser control of electronic transitions of wave packet by using quadratically chirped pulses

An effective scheme is proposed for the laser control of wave packet dynamics. It is demonstrated that by using specially designed quadratically chirped pulses, fast and nearly complete excitation of wave packet can be achieved without significant distortion of its shape. The parameters of the laser pulse can be estimated analytically from the Zhu-Nakamura theory of nonadiabatic transition. If the wave packet is not too narrow or not too broad, then the scheme is expected to be utilizable for multidimensional systems. The scheme is applicable to various processes such as simple electronic excitation, pump-dump, and selective bond breaking, and it is actually numerically demonstrated to work well by taking diatomic and triatomic molecules (LiH, NaK, H(2)O) as examples.     

Time‐dependent wave packet approach to Rabi oscillation in strong laser field

The phenomenon of Rabi oscillation is obtained in the investigation of the NO multiphoton ionization (MPI) in femtosecond laser fields. The “split operator‐Fourier transform” method of wave packet propagation is used in the representation of Rabi oscillation of population in each electronic state of NO molecule. The origin of Rabi oscillation and the effect on multiphoton ionization is analyzed. The high‐frequency oscillation riding on the top of Rabi oscillation is attributed to the nonrotating wave component in strong laser fields. Also illustrated is that through adjusting the pump‐probe delay time and the laser intensity appropriately the control of the ionization yield can be realized. This idea may be important for the laser control of chemical reaction. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 95: 30–36, 2003     

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.     

Ultrafast control of the internuclear distance with parabolic chirped pulses

Recently, control over the bond length of a diatomic molecule with the use of parabolic chirped pulses was predicted on the basis of numerical calculations [Chang; et al. Phys. Rev. A 2010, 82, 063414]. To achieve the required bond elongation, a laser scheme was proposed that implies population inversion and vibrational trapping in a dissociative state. In this work we identify two regimes where the scheme works, called the strong and the weak adiabatic regimes. We define appropriate parameters to identify the thresholds where the different regimes operate. The strong adiabatic regime is characterized by a quasi-static process that requires longer pulses. The molecule is stabilized at a bond distance and at a time directly controlled by the pulse in a time-symmetrical way. In this work we analyze the degree of control over the period and elongation of the bond as a function of the pulse bandwidth. The weak adiabatic regime implies dynamic deformation of the bond, which allows for larger bond stretch and the use of shorter pulses. The dynamics is anharmonic and not time-symmetrical and the final state is a wave packet in the ground potential. We show how the vibrational energy of the wave packet can be controlled by changing the pulse duration.     

Multiphoton association reaction He + H+ → HeH+ steered by ultra‐short laser pulse

The multiphoton association reaction He + H⁺ → HeH⁺ in the electronic ground state is investigated using the time‐dependent quantum wave packet method. It is shown that the collision pairs He + H⁺ in continuum state transfer into ν = 0 state and then produce stable molecules HeH⁺ through emission of two or three photons. The multiphoton transition takes place via intermediate states, and the transfer probability is determined by the collision energy and the intermediate states. The populations of the intermediate states and ν = 0 state can be controlled by the laser duration. The three‐photon transition is more efficient than the two‐photon transition for producing the molecule HeH⁺ in ν = 0 state. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ultrafast photofragmentation dynamics of molecular iodine driven with timed XUV and near-infrared light pulses

Photofragmentation dynamics of molecular iodine was studied as a response to the joint illumination with femtosecond 800 nm near-infrared and 13 nm extreme ultraviolet (XUV) pulses delivered by the free-electron laser facility FLASH. The interaction of the molecular target with two light pulses of different wavelengths but comparable pulse energy elucidates a complex intertwined electronic and nuclear dynamics. To follow distinct pathways out of a multitude of reaction channels, the recoil of created ionic fragments is analyzed. The delayed XUV pulse provides a way of following molecular photodissociation of I(2) with a characteristic time-constant of (55 ± 10) fs after the laser-induced formation of antibonding states. A preceding XUV pulse, on the other hand, preferably creates a 4d(-1) inner-shell vacancy followed by the fast Auger cascade with a revealed characteristic time constant τ(A2)=(23±11) fs for the second Auger decay transition. Some fraction of molecular cationic states undergoes subsequent Coulomb explosion, and the evolution of the launched molecular wave packet on the repulsive Coulomb potential was accessed by the laser-induced postionization. A further unexpected photofragmentation channel, which relies on the collective action of XUV and laser fields, is attributed to a laser-promoted charge transfer transition in the exploding molecule.     

Molecular wave packet interferometry and quantum entanglement

We study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phase-locked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical molecule-electromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.     

Laser pulse control of exciton dynamics in a biological chromophore complex

Femtosecond laser pulse control of exciton dynamics in a biological chromophore complex is studied theoretically. The computations use the optimal control theory specified to open quantum systems and formulated in the framework of the rotating wave approximation. Based on the laser pulse induced formation of an excitonic wave packet the possibility to localize excitation energy at a certain chromophore within a photosynthetic antenna system (FMO complex of green bacteria) is investigated. Details of exciton dynamics driven by a polarization shaped pulse are discussed.     

Preparation and resolution of molecular states by coherent sequences of phase-locked ultrashort laser pulses

We study the application of nonlinear wave packet interferometry to the preparation and resolution of the overlaps of nonstationary nuclear wave functions evolving in an excited electronic state of a diatomic molecule. It is shown that possible experiments with two phase-locked ultrashort pulsepairs can be used to determine a specific vibrational wave packet state in terms of coherent states of the ground electronic state. We apply this scheme to an idealized molecule with harmonic potential energy surfaces and to the X <-- B transition states of the iodine molecule. Our results indicate that this scheme is very promising as a potential tool to quantum control.     

Radiative excitation of the harmonic oscillator with applications to stereomutation in chiral molecules

We present theoretical considerations and quantitative numerical simulations of the coherent radiative excitation of chiral molecules exhibiting a double well potential in the electronic ground state (with stable enantiomers) and a harmonic oscillator potential with achiral minimum geometry in the excited electronic state following a scheme proposed in [33]. The one-dimensional short time dynamics is presented on the femtosecond time scale. We demonstrate the phenomena of quasiexponential, radiationless decay of the survival probability in the excited electronic state by simple harmonic oscillator wave packet motion, as well as coherent periodic chiral stereomutation. The differences and similarities of the excited state harmonic oscillator dynamics with two quite different ground state potentials are discussed. A designed pulse sequence allows for chemically efficient laser controlled stereomutation with high enantiomeric specificity. The results are discussed in relation to Friedrich Hund's early work on stereomutation by tunneling and in relation to our current understanding of chiral molecules including dynamical chirality and anharmonic vibrational dynamics on the femtosecond time scale and the violation of parity and other fundamental symmetries.     

Coherent spin control of matrix isolated molecules by IR+UV laser pulses: quantum simulations for ClF in Ar

Two coherent sequential IR+UV laser pulses may be used to generate two time-dependent nuclear wave functions in electronic excited triplet and singlet states via single (UV) and two photon (IR+UV) excitation pathways, exploiting spin-orbit coupling and vibrational pre-excitation, respectively. These wave functions evolve from different Franck-Condon domains until they overlap in a domain of bond stretching with efficient intersystem crossing. Here, the coherence of the laser pulses is turned into optimal interferences of the wave packets, yielding the total wave packet at the target place, time, and with dominant target spin. The time resolution of spin control is few femtoseconds. The mechanism is demonstrated by means of quantum model simulations for ClF in an Ar matrix.     

Quantum control of a molecular system in an intense field via the selective population of dressed states

We theoretically investigate the physical mechanism of quantum control on a K(2) molecule with an ultrafast strong laser pulse by solving the time-dependent Schr?dinger equation exactly using a wave packet approach. The structures of the triple splitting in the 3-photon ionization spectra of a K(2) molecule are presented to analyze the information of a selective population of dressed states. In this work, it is found that the tunability of the dressed states energies is achieved by regulating the laser intensity and the high selectivity of the dressed state population is attained by altering the envelope and wavelength of the intense laser pulse.     

Vibrational dynamics of excited electronic states of molecular iodine

Femtosecond degenerate four-wave-mixing spectroscopy following an initial pump laser pulse was used to observe the wave packet dynamics in excited electronic states of gas phase iodine. The focus of the investigation was on the ion pair states belonging to the first tier dissociating into the two ions I-(1S) + I+(3P2). By a proper choice of the wavelengths of the initial pump and degenerate four-wave-mixing pulses, we were able to observe the vibrational dynamics of the B (3)Pi(u) (+) state of molecular iodine as well as the ion pair states accessible from there by a one-photon transition. The method proves to be a valuable tool for exploring higher lying states that cannot be directly accessed from the ground state due to selection rule exclusion or unfavorable Franck-Condon overlap.     

Stationary molecular wave packets at nonequilibrium nuclear configurations

We study different schemes that allow laser controlled adiabatic manipulation of the bond in diatomic molecules by using sequences of nonresonant time-delayed chirped pulses. The schemes rely on adiabatic passage of the vibrational wave packet by laser-induced potential shaping from the ground electronic state to a laser-stabilized dissociative electronic state by two-photon absorption. The degree of control that is possible over the position (bond length) and width (bond spread) of the vibrational wave packet is compared for the different schemes. The dynamics is analyzed detailing the role of the different control knobs and the conditions that allow or break the adiabatic passage.     

Adiabatic squeezing of molecular wave packets by laser pulses

Strong pulse sequences can be used to control the position and width of the molecular wave packet. In this paper we propose a new scheme to maximally compress the wave packet in a quasistatic way by freezing it at a peculiar adiabatic potential shaped by two laser pulses. The dynamic principles of the scheme and the characteristic effect of the different control parameters are presented and analyzed. We use two different molecular models, electronic potentials modeled by harmonic oscillators, with the same force constants, and the Na(2) dimer, to show the typical yield that can be obtained in compressing the initial (minimum width) molecular wave function.