Quantum control of vibrational excitations in a heteronuclear diatomic molecule

Optimal control theory is applied to obtain infrared laser pulses for selective vibrational excitation in a heteronuclear diatomic molecule. The problem of finding the optimized field is phrased as a maximization of a cost functional which depends on the laser field. A time dependent Gaussian factor is introduced in the field prior to evaluation of the cost functional for better field shape. Conjugate gradient method^21,24 is used for optimization of constructed cost functional. At each instant of time, the optimal electric field is calculated and used for the subsequent quantum dynamics, within the dipole approximation. The results are obtained using both Morse potential as well as potential energy obtained using ab initio calculations.     

Laser control of vibrational excitation in carboxyhemoglobin: a quantum wave packet study

A coherent control algorithm is applied to obtain complex-shaped infrared laser pulses for the selective vibrational excitation of carbon monoxide at the active site of carbonmonoxyhemoglobin, modeled by the six-coordinated iron-porphyrin-imidazole-CO complex. The influence of the distal histidine is taken into account by an additional imidazole molecule. Density-functional theory is employed to calculate a multidimensional ground-state potential energy surface, and the vibrational dynamics as well as the laser interaction is described by quantum wave-packet calculations. At each instant in time, the optimal electric field is calculated and used for the subsequent quantum dynamics. The results presented show that the control scheme is applicable to complex systems and that it yields laser pulses with complex time-frequency structures, which, nevertheless, have a clear physical interpretation.     

Ab initio design of picosecond infrared laser pulses for controlling vibrational-rotational excitation of CO molecules

Optimal control of rovibrational excitations of the CO molecule using picosecond infrared laser pulses is described in the framework of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)]. The potential energy surface of the CO molecule in the presence of an electric field is calculated using coupled cluster theory with a large orbital basis set. The quantum dynamics of the process is treated using a full three dimensional treatment of the molecule in the laser field. The detailed mechanisms leading to efficient control of the selected excitation processes are discussed.     

Design of infrared laser pulses for the deexcitation of highly excited homonuclear diatomic molecules

We explore the possibility of using shaped infrared laser pulses to deexcite a homonuclear diatomic molecule from its highest vibrational state down to its ground vibrational state. The motivation for this study arises from the need to deexcite alkali metal dimers in a similar way so as to stabilize molecular Bose-Einstein condensates. We demonstrate that for the case of the H(2) molecule, where it is possible to evaluate all the necessary high accuracy ab initio data on the interaction of the molecule with an electric field, we are able to successfully design a sequence of infrared laser pulses to accomplish the desired deexcitation process in a highly efficient manner.     

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.     

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.     

Vibrationally selective optimal control of alignment and orientation using infrared laser pulses: application to carbon monoxide

Optimal control methods are used to study molecular alignment and orientation using infrared laser pulses. High order molecule-field interactions are taken into account through the use of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)]. High degrees of alignment and orientation are achieved by optimized infrared laser pulses of duration on the order of one rotational period of the molecule. It is shown that, through the incorporation of a vibrational projection operator into the optimization procedure, it is possible not only to maximize the alignment and orientation but also to bring the whole system into a single prescribed vibrational manifold. Numerical calculations are performed for carbon monoxide using ab initio potential energies computed in the presence of external electric fields.     

Pulse shaping effect on two-photon excitation efficiency of alpha-perylene crystals and perylene in chloroform solution

We demonstrated that the two-photon excitation efficiency of perylene in chloroform solution as well as that of crystalline perylene was dramatically increased by optimizing the shape of intense femtosecond laser pulses of a regenerative amplifier output. The efficiency was three times higher than for an unshaped single femtosecond pulse with the pulse width of shorter than 50 fs. The pulse shape optimized for the solution sample was a pulse train with a repetition frequency of about 340 cm(-1), and the pulse shape optimized for crystalline perylene was very similar. These results supported our previous findings on alpha-perylene crystals using weak femtosecond pulses from a mode-locked laser oscillator [T. Okada et al. J. Chem. Phys. 121, 6385 (2004)]. Furthermore, it was confirmed that the shaped pulse optimized for the liquid sample could also increase the two-photon excitation efficiency of alpha-perylene crystals and vice versa. We concluded that the mechanism for the increase in excitation efficiency of perylene in chloroform was almost the same as that for alpha-perylene crystal, and that the efficiency increased mainly through intramolecular dynamical processes. Processes involving intermolecular interactions and/or energy states delocalized over the crystal cannot play the major role.     

Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.     

Selective preparation of the zeroth-order vibrational states in the HOD molecule by ultrashort infrared laser pulses

An approach for controlling the molecular dynamics competing aginst intramolecular vibrational-energy redistribution and selective preparation of the zeroth-order vibrational states on a picosecond time scale is developed and demonstrated for the HOD molecule. The zeroth-order states of the local OH bond are prepared selectively and demonstrate the coherent oscillatory behaviour after the end of the laser escitation. Coherent in-phase and out-of-phase oscillations are demonstrated by two single zeroth-order states efficiently coupled to each other. Quasi-periodic in-phase and out-of-phase oscillations occur if a single zeroth-order state is coupled to several other zeroth-order states. The frequence of these oscillations depends on the laser field which appears the state. The laser control scheme includes superposition of properly optimized infrared laser pulses of a subpicosecond duration.     

On the selective elimination of intramolecular vibrational redistribution using strong resonant laser fields

A method is proposed for the selective elimination of intramolecular vibrational redistribution (IVR) in polyatomic molecules by using a strong resonant laser excitation. When the Rabi frequency is larger than the frequency spread of an isolated group of molecular eigenstates, IVR processes are totally suppressed, and the molecule simply oscillates between the ground state and the doorway state. The method may have direct implications on laser-selective chemistry.     

The experimental visualisation of molecular structural changes during both photochemical and thermal reactions by real-time vibrational spectroscopy

Have you ever hoped to observe transition states? Chemists have long desired to monitor the deformation of molecular structures via transition states to understand the mechanisms of complicated reactions. Detailed knowledge of transition states helps find strategies to develop novel reaction schemes for introducing new functionalities to chemicals. Molecular structural changes via transition states can be observed by real-time vibrational spectroscopy using sub-5 fs laser pulses. In this paper, I report the direct observation of time-dependent frequency shifts of relevant molecular vibrational modes, which allowed for the clear visualization of ultrafast structural changes in molecules during bond breaking and bond reformation steps. Various mechanisms for photochemical reactions were clarified using sub-5 fs laser pulses. Moreover, a non-thermal vibrational excitation method for efficiently driving chemical reactions in the electronic ground state in solution with the use of broadband visible sub-5 fs laser pulses has been developed. The respective chemical reaction processes were directly observed, including transition states during not only "photochemical" but also "thermal" reactions. Time-resolved spectroscopy with a time resolution of a few femtoseconds enables observation of real-time vibrational amplitudes of complicated molecules and opens up new ways for clarifying reaction mechanisms and developing new chemical transformations.     

Laser adiabatic manipulation of the bond length of diatomic molecules with a single chirped pulse

We propose and test numerically a scheme for controlling the bond distance in a diatomic molecule that requires the use of a single chirped pulse. The laser prepares a superposition state of both nuclear and electronic degrees of freedom, where the main character of the electronic wave function is that of an excited dissociative state. The main limitation of the scheme is the need of ultra broadband pulses, where the bandwidth must be of the order of the dissociation energy to achieve large bond elongations. The scheme can be used to deform the bond during the laser excitation to an arbitrary large and constant value, or to allow slow time-dependent bond elongations. Additionally, the scheme can be used to prepare highly excited vibrational wave packets in the ground potential after the pulse is switched off, at the expense of losing some population that dissociates. These wave packets are initially localized at the outer well of the potential, at energies controllable by the excitation process.     

Quantum control of molecular motion including electronic polarization effects with a two-stage toolkit

A method for incorporating strong electric field polarization effects into optimal control calculations is presented. A Born-Oppenheimer-type separation, referred to as the electric-nuclear Born-Oppenheimer (ENBO) approximation, is introduced in which variations of both the nuclear geometry and the external electric field are assumed to be slow compared with the speed at which the electronic degrees of freedom respond to these changes. This assumption permits the generation of a potential energy surface that depends not only on the relative geometry of the nuclei but also on the electric field strength and on the orientation of the molecule with respect to the electric field. The range of validity of the ENBO approximation is discussed in the paper. A two-stage toolkit implementation is presented to incorporate the polarization effects and reduce the cost of the optimal control dynamics calculations. As an illustration of the method, it is applied to optimal control of vibrational excitation in a hydrogen molecule aligned along the field direction. Ab initio configuration interaction calculations with a large orbital basis set are used to compute the H-H interaction potential in the presence of the electric field. The significant computational cost reduction afforded by the toolkit implementation is demonstrated.     

Infrared multiphoton excitation of small molecules

The collisionless infrared excitation by short CO₂ laser pulses of the molecules SO₂, OCS, NO₂, NH₃ and DN₃ is compared with that of larger molecules. The average number of photons absorbed per molecule and the fraction of molecules dissociated depends predominantly on the laser intensity, while for larger molecules with higher densities of vibrational states the excitation is primarily determined by the laser fluence.     

Accuracy of gates in a quantum computer based on vibrational eigenstates

A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.     

Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory

Optimal control theory is used to tailor laser pulses which enhance a femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) spectrum in a certain frequency range. For this aim the optimal control theory has to be applied to a target state distributed in time. Explicit control mechanisms are given for shaping either the Stokes or the probe pulse in the four-wave mixing process. A simple molecule for which highly accurate potential energy surfaces are available, namely molecular iodine, is used to test the procedure. This approach of controlling vibrational motion and delivering higher intensities to certain frequency ranges might also be important for the improvement of CARS microscopy.     

Ultrafast S1 to S0 internal conversion dynamics for dimethylnitramine through a conical intersection

Electronically nonadiabatic processes such as ultrafast internal conversion (IC) from an upper electronic state (S(1)) to the ground electronic state (S(0)) though a conical intersection (CI), can play an essential role in the initial steps of the decomposition of energetic materials. Such nonradiative processes following electronic excitation can quench emission and store the excitation energy in the vibrational degrees of freedom of the ground electronic state. This excess vibrational energy in the ground electronic state can dissociate most of the chemical bonds of the molecule and can generate stable, small molecule products. The present study determines ultrafast IC dynamics of a model nitramine energetic material, dimethylnitramine (DMNA). Femtosecond (fs) pump-probe spectroscopy, for which a pump pulse at 271 nm and a probe pulse at 405.6 nm are used, is employed to elucidate the IC dynamics of this molecule from its S(1) excited state. A very short lifetime of the S(1) excited state (～50 ± 16 fs) is determined for DMNA. Complete active space self-consistent field (CASSCF) calculations show that an (S(1)/S(0))(CI) CI is responsible for this ultrafast decay from S(1) to S(0). This decay occurs through a reaction coordinate involving an out-of-plane bending mode of the DMNA NO(2) moiety. The 271 nm excitation of DMNA is not sufficient to dissociate the molecule on the S(1) potential energy surface (PES) through an adiabatic NO(2) elimination pathway.     

Design of an infrared laser pulse to control the multiphoton dissociation of the Fe-CO bond in CO-heme compounds

Optimal control theory is used to design a laser pulse for the multiphoton dissociation of the Fe-CO bond in the CO-heme compounds. The study uses a hexacoordinated iron-porphyrin-imidazole-CO complex in its ground electronic state as a model for CO liganded to the heme group. The potential energy and dipole moment surfaces for the interaction of the CO ligand with the heme group are calculated using density functional theory. Optimal control theory, combined with a time-dependent quantum dynamical treatment of the laser-molecule interaction, is then used to design a laser pulse capable of efficiently dissociating the CO-heme complex model. The genetic algorithm method is used within the mathematical framework of optimal control theory to perform the optimization process. This method provides good control over the parameters of the laser pulse, allowing optimized pulses with simple time and frequency structures to be designed. The dependence of photodissociation yield on the choice of initial vibrational state and of initial laser field parameters is also investigated. The current work uses a reduced dimensionality model in which only the Fe-C and C-O stretching coordinates are explicitly taken into account in the time-dependent quantum dynamical calculations. The limitations arising from this are discussed in Sec. IV.     

Minimizing broadband excitation under dissipative conditions

Optimal control theory is employed for the task of minimizing the excited-state population of a dye molecule in solution. The spectrum of the excitation pulse is contained completely in the absorption band of the molecule. Only phase control is studied which is equivalent to optimizing the transmission of the pulse through the medium. The molecular model explicitly includes two electronic states and a single vibrational mode. The other degrees of freedom are classified as bath modes. The surrogate Hamiltonian method is employed to incorporate these bath degrees of freedom. Their influence can be classified as electronic dephasing and vibrational relaxation. In accordance with experimental results, minimal excitation is associated with a negatively chirped pulses. Optimal pulses with more complex transient structure are found to be superior to linearly chirped pulses. The difference is enhanced when the fluence is increased. The improvement degrades when dissipative effects become more dominant.