The influence of ultrashort excitations on the vibrational dynamics in a diatomic molecule

The problem of vibrational wave packet dynamics in the system of two electronic states of a diatomic molecule, where the states are coupled by infinitely short light pulses, is solved. The electronic states were modeled by shifted harmonic oscillators with different frequencies. Exact expressions for the probability densities of the wave packets in the ground and excited states were derived. The spatial, spectral, and temporal characteristics of the wave packets, namely, the range of motion, spatial width, mean energy, spectral width (the mean number of vibrational states in a wave packet), and the autocorrelation function, were calculated as functions of the molecular parameters (the frequency ratio and the distance between the potential minima) and of the delay time between the light pulses. The possibility of controlling the mean energy and spectral width of the wave packets in the ground electronic state by varying the delay time is considered. It was shown that "squeezed" wave packets can be prepared in the ground electronic state if the upper electronic state is shallow.     

Active control of the lifetime of excited resonance states by means of laser pulses

Quantum control of the lifetime of a system in an excited resonance state is investigated theoretically by creating coherent superpositions of overlapping resonances. This control scheme exploits the quantum interference occurring between the overlapping resonances, which can be controlled by varying the width of the laser pulse that creates the superposition state. The scheme is applied to a realistic model of the Br(2)(B)-Ne predissociation decay dynamics through a three-dimensional wave packet method. It is shown that extensive control of the system lifetime is achievable, both enhancing and damping it remarkably. An experimental realization of the control scheme is suggested.     

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.     

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.     

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.     

Ultrafast dynamics of halogens in rare gas solids

We perform time resolved pump-probe spectroscopy on small halogen molecules ClF, Cl2, Br2, and I2 embedded in rare gas solids (RGS). We find that dissociation, angular depolarization, and the decoherence of the molecule is strongly influenced by the cage structure. The well ordered crystalline environment facilitates the modelling of the experimental angular distribution of the molecular axis after the collision with the rare gas cage. The observation of many subsequent vibrational wave packet oscillations allows the construction of anharmonic potentials and indicate a long vibrational coherence time. We control the vibrational wave packet revivals, thereby gaining information about the vibrational decoherence. The coherence times are remarkable larger when compared to the liquid or high pressure gas phase. This fact is attributed to the highly symmetric molecular environment of the RGS. The decoherence and energy relaxation data agree well with a perturbative model for moderate vibrational excitation and follow a classical model in the strong excitation limit. Furthermore, a wave packet interferometry scheme is applied to deduce electronic coherence times. The positions of those cage atoms, excited by the molecular electronic transitions are modulated by long living coherent phonons of the RGS, which we can probe via the molecular charge transfer states.     

Control of nonadiabatic dissociation dynamics with the use of laser-induced wave packet interferences

Based on wave packet interferences induced by a stationary laser field, a simple way of controlling nonadiabatic dissociation dynamics is proposed. We treat a simple two-state model of diatomic molecules. In this model, there exist two dissociative potential energy curves which cross and are strongly coupled at an internuclear distance, and thus dissociations into one channel are predominant. We propose a control scheme to selectively dissociate a molecule into any favorite channel by choosing the laser frequency and intensity appropriately. The semiclassical estimation of desirable laser parameters can be performed easily by regarding the dissociation processes as nonadiabatic transitions between the Floquet states. The agreement between the semiclassical estimation and the quantum wave packet calculation is found to be satisfactory in the high frequency region (> or =1000 cm(-1)) where the Floquet state picture is valid. In the low frequency region (<1000 cm(-1)), on the other hand, there are discrepancies between them due to the invalidity of the Floquet picture and the dissociation probability is sensitive to the laser phase. This control scheme is applied to the predissociation dynamics of NaI, NaI-->Na+I.     

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.     

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.     

Control of Li2 wave packet dynamics by modification of the quantum mechanical amplitude of a single state

Sequences of pulses with different spectra are used to control rotational wave packet dynamics in Li(2) by exploiting quantum interference phenomena. Wave packet superpositions are excited in a two-step resonant Raman process by two different pulses. Interferences between individual states shared by both wave packets can be used to enhance or destroy specific components of a superposition by varying the time delay between the pulses and/or the relative phase within the pulses. Elimination of selected quantum beats is achieved by greater than 94% for each case. A simple, yet effective, method for generating different color phase-locked pairs of laser pulses in a liquid-crystal pulse shaper setup without the need for interferometric stabilization schemes is described. The ability to manipulate single states of a superposition is an important advancement for intuitive control schemes and provides a potential new approach for initialization schemes in the field of quantum information.     

Laser control of reactions of photoswitching functional molecules

Laser control schemes of reactions of photoswitching functional molecules are proposed based on the quantum mechanical wave-packet dynamics and the design of laser parameters. The appropriately designed quadratically chirped laser pulses can achieve nearly complete transitions of wave packet among electronic states. The laser parameters can be optimized by using the Zhu-Nakamura theory of nonadiabatic transition. This method is effective not only for the initial photoexcitation process but also for the pump and dump scheme in the middle of the overall photoswitching process. The effects of momentum of the wave packet crossing a conical intersection on the branching ratio of products have also been clarified. These control schemes mentioned above are successfully applied to the cyclohexadiene/hexatriene photoisomerization (ring-opening) process which is the reaction center of practical photoswitching molecules such as diarylethenes. The overall efficiency of the ring opening can be appreciably increased by using the appropriately designed laser pulses compared to that of the natural photoisomerization without any control schemes.     

Field-free molecular orientation enhanced by two dual-color laser subpulses

In this paper, we theoretically show that the field-free molecular orientation created by a single dual-color laser pulse can be significantly enhanced by separating it into two time-delayed dual-color subpulses. It is indicated that the maximum enhancement of the molecular orientation created by two time-delayed dual-color subpulses can be achieved with their intensity ratio of about 1:2 and by simultaneously applying the second one at the beginning of the rotational wave packet rephasing or the end of the rotational wave packet dephasing induced by the first one. It is also shown that the enhancement or suppression of the molecular orientation can be coherently manipulated by varying the relative phase between the fundamental field and its second harmonic field of the second dual-color subpulse, and its enhancement is obtained around half rotational period.     

Implementation of quantum gate operations in molecules with weak laser fields

We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision.     

Electronic coherences and vibrational wave-packets in single molecules studied with femtosecond phase-controlled spectroscopy

Employing femtosecond pulse-shaping techniques we investigate ultrafast, coherent and incoherent dynamics in single molecules at room temperature. In first experiments single molecules are excited into their purely electronic 0-0 transition by phase-locked double-pulse sequences with pulse durations of 75 fs and 20 nm spectral band width. Their femtosecond kinetics can then be understood in terms of a 2-level system and modelled with the optical Bloch equations. We find that we observe the coherence decay in single molecules, and the purely electronic dephasing times can be retrieved directly in the time domain. In addition, the Rabi-frequencies and thus the transition dipole moments of single molecules are determined from these data. Upon excitation of single molecules into a vibrational level of the electronically excited state also incoherent intra-molecular vibrational relaxation is recorded. Increasing the spectral band width of the excitation pulses to up to 120 nm (resulting in a transform-limited pulse width of 15 fs) coherent superpositions of excited state vibrational modes, i.e. vibrational wave packets, are excited. The wave-packet oscillations in the excited state potential energy surface are followed in time by a phase-controlled pump-probe scheme, which permits to record wave packet interference, and to determine the energies of vibrational modes and their coupling strengths to the electronic transition.     

Limits of the creation of electronic wave packets using time-dependent density functional theory

Explicitly time-dependent density functional theory (TDDFT) has often been suggested as the method of choice for controlling the correlated dynamics of many electron systems. However, it is not yet clear which control tasks can be achieved reliably and how this depends on the functionals used. In this article, we show that the control task of creating a simple wave packet, having a population of 50% in the excited state, can indeed be achieved if a certain condition is fulfilled. This result is in contrast to the observation that a full population inversion is extremely difficult to achieve. In addition, we identify a rule to predict when TDDFT produces the correct wave packet. To illustrate our findings, we study the molecules Li(2)C(2), Li(7)OH, and B(2)N(2)CO using two different functionals as well as time-dependent Hartree-Fock (TDHF). To assess the performance of TDDFT and TDHF, we compare with time-dependent configuration interaction calculations.     

Influence of molecular orientation on the photodissociation process of LiH molecules

Regulation of photodissociation dynamics of oriented LiH molecules in different dissociation channels is proposed based on time dependent quantum wave packet theory. The enhancement of molecular orientation on the photodissociation of LiH is obvious with our theoretical scheme. The results show that the molecular orientation in the ground state has a great effect on the angular distributions of wave packets. By using the proper laser pulses and controlling the polarization direction of the laser pulses, the enhancement of the photodissociation could be realized. After the molecular orientation, an optimal dissociation channel is observed with an improved dissociation probability. Compared with the results without molecular orientation, the maximal dissociation probability is increased by 8.1% in the indirect dissociation channel and 30.7% in the direct dissociation channel. The enhancement effect is more obvious in the direct dissociation channel, which provides a possible method to manipulate the dissociation of LiH molecules experimentally. Additionally, the photodissociation process of LiH also relies on the electric intensity and delay time of two pump pulses.     

Femtosecond spectroscopy of the (2)1Σ u + double minimum state of Na2: time domain and frequency spectroscopy

Femtosecond time resolved pump-probe experiments studying wave packet dynamics in the (2)¹Σ _u ⁺ double minimum state of Na₂ are reported. The experiments were performed in a molecular beam with ion Time of Flight (TOF) detection. By Fast Fourier Transformation (FFT) of the observed time domain data the energy spacings of the coherently coupled vibrational levels in the (2)¹Σ _u ⁺ potential are obtained with an accuracy of 0.02 cm^?1, although an ultrafast laser source with its inherent spectral width was used in the experiment. The wavelengths of the pump and probe laser pulses are chosen such that in this two color experiment we can control ionisation versus ionisation induced fragmentation. In order to study the influence of the potential barrier on a vibrational wave packet motion we performed simulations based on time dependent quantum calculations.     

Geometric phase effects in the coherent control of the branching ratio of photodissociation products of phenol

Optimal control simulation is used to examine the control mechanisms in the photodissociation of phenol within a two-dimensional, three-electronic-state model with two conical intersections. This model has two channels for H-atom elimination, which correspond to the (2)pi and (2)sigma states of the phenoxyl radical. The optimal pulse that enhances (2)sigma dissociation initially generates a wave packet on the S(1) potential-energy surface of phenol. This wave packet is bifurcated at the S(2)-S(1) conical intersection into two components with opposite phases because of the geometric phase effect. The destructive interference caused by the geometric phase effect reduces the population around the S(1)-S(0) conical intersection, which in turn suppresses nonadiabatic transitions and thus enhances dissociation to the (2)sigma limit. The optimal pulse that enhances S(0) dissociation, on the other hand, creates a wave packet on the S(2) potential-energy surface of phenol via an intensity borrowing mechanism, thus avoiding geometric phase effects at the S(2)-S(1) conical intersection. This wave packet hits the S(1)-S(0) conical intersection directly, resulting in preferred dissociation to the (2)pi limit. The optimal pulse that initially prepares the wave packet on the S(1) potential-energy surface (PES) has a higher carrier frequency than the pulse that prepares the wave packet on the S(2) PES. This counterintuitive effect is explained by the energy-level structure and the S(2)-S(1) vibronic coupling mechanism.     

A semiclassical study of wave packet dynamics in anharmonic potentials

Classical and semiclassical methods are developed to calculate and invert the wave packet motion measured in pump-probe experiments. With classical propagation of the Wigner distribution of the initial wave packet created by the pump pulse, we predict the approximate probe signal with slightly displaced recurrence peaks, and derive a set of first-order canonical perturbation expressions to relate the temporal features of the signal to the characteristics of the potential surface. A reduced dynamics scheme based on the Gaussian assumption leads to the correct center of mass motion but does not describe the evolution of the shape of the wave packet accurately. To incorporate the quantum interference into classical trajectories, we propose a final-value representation semiclassical method, specifically designed for the purpose of computing pump-probe signals, and demonstrate its efficiency and accuracy with a Morse oscillator and two kinetically coupled Morse oscillators. For the case of one-color pump probe, a simple phase-space quantization scheme is devised to reproduce the temporal profile at the left-turning point without actual wave packet propagation, revealing a quantum mechanical perspective of the nearly classical pump-probe signal.