Coherent Control of Photofragment Distributions Using Laser Phase Modulation in the Weak-Field Limit

Quantum Control of Resonance Lifetimes in Molecular Photodissociation with Intense Laser Fields

Control of molecular reaction dynamics has been pursued in the last decades. Among these reactions are molecular photodissociation processes governed by resonances. Controlling the lifetime of such resonances imply to control the time duration of the processes. Here, some control schemes that apply moderately intense laser fields are proposed to modify (reducing or increasing) a resonance lifetime. The control strategy applies an intense field as a way to generate a new effective coupling that produces a resonance decay different from the natural one, with a different decay lifetime. In particular, different control schemes are suggested to reduce the lifetime of a long-lived resonance, and to increase the lifetime of a short-lived resonance. A large degree and flexibility of control both in the reduction and in the increase of the resonance lifetime is demonstrated. The experimental applicability of the schemes is discussed. The present schemes thus open the possibility of extensive and universal control of molecular photodissociation processes mediated by resonances.

Population transfer between degenerate continuum states via impulsive stimulated Raman scattering: application to the control of HOD photofragmentation

This work proposes a new scheme for the coherent control of the branching ratio of photodissociation reactions. HOD's photodissociation in the first electronic-excited state illustrates the idea. The scheme involves the induction of quantum interference between the continuum eigenstates of the excited state through interaction with a non-resonant NIR ultrashort laser pulse, subsequent to electronic excitation. A high-level, frequency-dependent excited state polarizability surface of HOD is determined, in order to model the non-resonant coupling between the laser pulse and molecule. The results of this scheme on the control of the branching ratio between OD + H and OH + D are presented, as well as an analysis of the interaction between the ultrashort pulses and the excited-state eigenstates. The understanding of the degenerate nature of these continuum states is shown to be crucial for a correct description of the processes that lead to a change in the reaction's outcome, and is further discussed through an exploration of a model system.

Absolute control over the quantum yield of a photodissociation reaction mediated by nonadiabatic couplings

Control of molecular reaction dynamics with laser pulses has been developed in the last decades. Among the different magnitudes whose control has been actively pursued, the branching ratio between different product channels constitutes the clearest signature of quantum control. In polyatomic molecules, the dynamics in the excited state is quagmired by non-adiabatic couplings, which are not directly affected by the laser, making control over the branching ratio a very demanding challenge. Here we present a control scheme for the CH3I photodissociation in the A band, that modifies the quantum yield of the two fragmentation channels of the process. The scheme relies on the optimized preparation of an initial superposition of vibrational states in the ground potential, which further interfere upon the excitation with a broad pump pulse. This interference can suppress any of the channels, regardless of its dominance, and can be achieved over the whole spectral range of the A band. Furthermore, it can be accomplished without strong fields or direct intervention during the dynamics in the excited states: the whole control is predetermined from the outset. The present work thus opens the possibility of extensive and universal control of the channel branching ratio in complex photodissociation processes.

Unveiling Ultrafast-Weak-Field Coherent Control of Indirect Dissociation Reactions

Coherent control of molecular photodissociation through one-photon transitions has become a topic of interest in physical chemistry. Previous studies have shown that modulating the spectral phase of a single ultrafast laser pulse while keeping its spectral amplitude constant does not affect the dissociation yield of reactions originating from a pure eigenstate of the ground electronic state. Here, we explore the indirect photodissociation reaction of NaI molecules using theoretical and numerical methods. Our findings show that, in contrast to the outcomes achieved with negatively chirped pulses, time-dependent population of the eigenstates of the excited adiabatic potential induced by positively chirped laser pulses, acting as intermediates in the reaction, cannot be periodically restored to that caused by the unchirped pulse. This gives rise to an intriguing phenomenon: the sign of the pulse's chirp rate influences the distribution of dissociation fragments in coordinate and momentum space over extended periods. This work highlights the potential of using spectral-phase modulated pulses to manipulate indirect photodissociation reactions, offering a way to modify the transient photofragment distributions by controlling reaction intermediates.

Impact of Early Coherences on the Control of Ultrafast Photodissociation Reactions

By coherent control, the yield of photodissociation reactions can be maximized, starting in a suitable superposition of vibrational states. In ultrafast processes, the interfering pathways are born from the early vibrational coherences in the ground electronic potential. We interpret their effect from a purely classical picture, in which the correlation between the initial position and momentum helps to synchronize the vibrational dynamics at the Franck-Condon window when the pulse is at its maximum intensity. In the quantum domain, we show that this localization in time and space is mediated by dynamic squeezing of the wave packet.

Unveiling Coherent Control of Halomethane Dissociation Induced by a Single Strong Ultraviolet Pulse

We present a theoretical investigation into the coherent control of photodissociation reactions in halomethanes, specifically focusing on CH2BrCl by manipulating the spectral phase of a single femtosecond laser pulse. We examine the photodissociation of CH2BrCl under an ultrashort pulse with a quadratic spectral phase and reveal the sensitivity of both the total dissociation probability and the resulting radical products (Br+CH2Cl and Cl+CH2Br) to chirp rates. To gain insights into the underlying mechanism, we calculate the population distributions of excited vibrational states in the ground electronic state, demonstrating the occurrence of resonance Raman scattering (RRS) in the strong-field limit regime. By utilizing chirped pulses, we show that this RRS phenomenon can be suppressed and even eliminated through quantum destructive interference. This highlights the high sensitivity of photodissociation into Cl+CH2Br to the spectral phase, showcasing a phenomenon that goes beyond the traditional one-photon photodissociation of isolated molecules in the weak-field limit regime. These findings emphasize the importance of coherent control in the exploration and utilization of photodissociation in polyatomic molecules, paving the way for new advancements in chemical physics and femtochemistry.

Photodissociation of the methyl radical: the role of nonadiabatic couplings in enhancing the variety of dissociation mechanisms

The nonadiabatic photodissociation dynamics of the CH₃ (and CD₃) radical from the 3p_z and 3s Rydberg states is investigated by applying a one-dimensional (1D) wave packet model that uses recently calculated ab initio 1D electronic potential-energy curves and nonadiabatic couplings. Calculated predissociation lifetimes are found to be too long as compared to the experimental ones. The 1D dynamical model, however, is able to predict qualitatively and explain the fragmentation mechanisms that produce the hydrogen-fragment translational energy distributions (TED) measured experimentally for the ground vibrational resonance of the 3p_z and 3s Rydberg states (CH₃(v = 0, 3p_z) and CH₃(v = 0, 3s)). The CH₃(v = 0, 3p_z) TED found experimentally displays a rather large energy spreading, while the experimental CH₃(v = 0, 3s) TED is remarkably more localized in energy. The present model also predicts a widely spread CH₃(v = 0, 3p_z) TED, produced by a complex dissociation mechanism which involves predissociation to one dissociative valence state through a nonadiabatic coupling, as well as transfer of population to a second valence state through three conical intersections. Also in agreement with experiment, the model predicts a rather localized CH₃(v = 0, 3s) TED because the conical intersections no longer operate in this photodissociation process, and predissociation occurs only into a single valence state. Another complex dissociation mechanism is predicted by the model for initial CH₃(v > 0, 3s) and CD₃(v > 0, 3s) resonances. In this case the mechanism is gradually activated, as vibrational excitation increases, by the interplay between the two nonadiabatic couplings connecting the 3s and 3p_x,y Rydberg states with the dissociative ²A₁ valence state, and produces complex TEDs with signals from several resonances of both 3s and 3p_x,y. Thus the present 1D quantum model reveals a rich photodissociation dynamics of methyl, where a variety of complex fragmentation mechanisms is favored by the presence of different nonadiabatic couplings between the electronic states involved.

On Weak-Field (One-Photon) Coherent Control of Photoisomerization

Photochemistry induced by phase-coherent laser light is an intriguing topic. The possibility of weak-field (one-photon) phase-only control of photoisomerization is controversial. Experimental studies on the weak-field coherent control of cis-trans isomerization have led to conflicting results. Here we address this issue by quantum dynamical calculations, focusing on a mechanism where different "phase-shaped" wave packets are quickly stabilized ("dumped") in the trans configuration because of prompt energy dissipation. We systematically investigate different relaxation rates with the system-bath dynamics described within the time-dependent Hartree approximation leading to a friction-type force. We find evidence for phase control of trans-isomer yields (about 5%) in this model with pure energy dissipation given sufficiently strong dampening.

Rotational-vibrational resonance states

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational-vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments. In a number of chemical applications, most prominently in spectroscopy and reaction dynamics, consideration of rotational-vibrational resonance states is becoming more and more common. There are different first-principles techniques to compute and rationalize rotational-vibrational resonance states: one can perform scattering calculations or one can arrive at rovibrational resonances using variational or variational-like techniques based on methods developed for determining bound eigenstates. The latter approaches can be based either on the Hermitian (L², square integrable) or non-Hermitian (non-L²) formalisms of quantum mechanics. This Perspective reviews the basic concepts related to and the relevance of shape and Feshbach-type rotational-vibrational resonance states, discusses theoretical methods and computational tools allowing their efficient determination, and shows numerical examples from the authors' previous studies on the identification and characterization of rotational-vibrational resonances of polyatomic molecular systems.

Interference of a resonance state with itself: a route to control its dynamical behaviour

It is demonstrated both numerically and mathematically that the dynamical behavior of an isolated resonance state, which comprises the resonance decay lifetime and the asymptotic fragment state distribution produced upon resonance decay, can be extensively controlled by means of quantum interference induced by a laser field in the weak-field regime. The control scheme applied is designed to induce interference between amplitudes excited at two different energies of the resonance line shape, namely the resonance energy and an additional energy. This scheme exploits the resonance property of possessing a nonzero energy width, which makes it possible that a resonance state may interfere with itself, and thus allows interference between the amplitudes excited at the two energies of the resonance width. The application of this scheme opens the possibility of a universal control of both the duration and the fragment product distribution outcome of any resonance-mediated molecular process.

Delaying the Decay of a Superposition of Resonance States

A weak-field coherent control scheme is applied in order to enhance the decay lifetime of a superposition of overlapping resonance states. The scheme uses a pump laser field consisting of two pulses delayed in time, each of them exciting a different energy at which several resonances of the Ne-Br₂(B) complex overlap. Simultaneous excitation of these two energies induces interference between the overlapping resonances, which causes an enhancement of the lifetime of the superposition created. By variation of the delay time between the pulses, the mechanism of resonance interference can be controlled and optimized to achieve a maximum lifetime enhancement. The optimal delay time between pulses leading to maximum superposition lifetime can be quantitatively predicted with a simple law. The effect of the interference mechanism on the lifetime enhancement is investigated. It is found that interference induces a transfer of amplitude between the different resonances back and forth, which delays significantly the natural resonance decay, increasing the global lifetime of the superposition. Due to the simplicity of the control scheme, a wide applicability is envisioned.

Weak-field coherent control of photodissociation in polyatomic molecules

A coherent control scheme is suggested to modify the output of photodissociation in a polyatomic system. The performance of the scheme is illustrated by applying it to the ultrafast photodissociation of CH₃I in the A-band. The control scheme uses a pump laser weak field that combines two pulses of a few femtoseconds delayed in time. By varying the time delay between the pulses, the shape of the laser field spectral profile is modulated, which causes a change in the initial relative populations excited by the pump laser to the different electronic states involved in the photodissociation. Such a change in the relative populations produces different photodissociation outputs, which is the basis of the control achieved. The degree of control obtained over different photodissociation observables, like the branching ratio between the two dissociation channels of CH₃I yielding I(²P_3/2) and I*(²P_1/2) and the fragment angular distributions associated with each channel, is investigated. These magnitudes are found to oscillate strongly with the time delay, with the branching ratio changing by factors between two and three. Substantial variations of the angular distributions also indicate that the scheme provides a high degree of control. Experimental application of the scheme to general polyatomic photodissociation processes should be straightforward.

A unified theory of weak-field coherent control of the behavior of a resonance state

A unified weak-field control scheme to modify the two properties that determine the whole behavior of a resonance state, namely the lifetime and the asymptotic fragment distribution produced upon resonance decay, is proposed. Control is exerted through quantum interference induced between overlapping resonances of the system, by exciting two different energies at which the resonances overlap. The scheme applies a laser field consisting of a first pulse that excites the energy of the resonance to be controlled, and two additional pulses that excite another different energy to induce interference, with a delay time with respect to the first pulse. Each of the two additional pulses is used to control one of the two resonance properties, by adjusting its corresponding delay time: with a relatively short delay time the second pulse controls the resonance lifetime, while with a very long delay time the third pulse modifies the asymptotic fragment distribution produced. The efficiency of the control of each resonance property is found to be strongly dependent on the choice of the second interfering energy, which allows for a more flexible control optimization by choosing a different energy for each property. The theory underlying the interference mechanism of the control scheme is developed and presented, and is applied to analyze and explain the results obtained. The present scheme thus appears to be a useful tool for controlling resonance-mediated molecular processes.

Weak-Field Coherent Control of Molecular Photofragment State Distributions

It is known that the long-time energy-resolved photofragment state distribution produced upon photodissociation of a molecule cannot be modified in the weak-field limit for a fixed pump pulse spectral profile. This work, however, demonstrates both computationally and mathematically that the above limitation can be circumvented in practice when the molecule presents overlapping resonances. It is shown that when two or more energies where the resonances overlap are excited by different laser pulses delayed in time, interference is induced between the product fragment states associated with the different energies populated. The occurrence of interference is found to be independent of the delay time between the pulses exciting the different energies. Thus, as demonstrated, this finding makes it possible to modify the fragment distribution at a given energy, as far in time and as many times as desired.

Control of photodissociation of the NaI molecule via pulse chirping

A dynamic pump control scheme is proposed to manipulate the predissociation process of NaI molecules in different reaction channels. A linearly chirped pulse is used to excite the NaI molecule, and a time-delayed infrared pulse is employed to modify the molecular potentials in the coupling zone. The predissociation branching ratio of the product from two channels can be controlled by tuning the chirp rate with a proper range of delay times. Furthermore, an additional ultrafast photoionization step is adopted to monitor the wave packet evolution and probe the possible modifications of the electronic potential under the influence of a chirped pump field to reveal the physical mechanism behind the control. Aulter-Townes splitting is observed at a proper chirp rate, and the dressed-state population can be controlled via pulse chirping.

Optimal and robust control of quantum state transfer by shaping the spectral phase of ultrafast laser pulses

Achieving fast and efficient quantum state transfer is a fundamental task in physics, chemistry and quantum information science. However, the successful implementation of the perfect quantum state transfer also requires robustness under practically inevitable perturbative defects. Here, we demonstrate how an optimal and robust quantum state transfer can be achieved by shaping the spectral phase of an ultrafast laser pulse in the framework of frequency domain quantum optimal control theory. Our numerical simulations of the single dibenzoterrylene molecule as well as in atomic rubidium show that optimal and robust quantum state transfer via spectral phase modulated laser pulses can be achieved by incorporating a filtering function of the frequency into the optimization algorithm, which in turn has potential applications for ultrafast robust control of photochemical reactions.

Unravelling the mechanisms of interference between overlapping resonances

The enhancement of the resonance lifetime that occurs upon interference of two overlapping resonances excited coherently by two pulses with delayed time has been investigated as a function of the pulse temporal width and the delay time between the pulses. A general law predicting quantitatively the optimal delay time that maximizes the lifetime enhancement of the two resonances has been established in terms of the pulse width and of the lifetimes of both resonances when they are excited isolatedly. The specific form of the law and all the results found can be closely related to the characteristic features of the mechanism of interference between the overlapping resonances, providing a detailed understanding on how the mechanism operates. The proposed law is envisioned as a useful tool to design experimental strategies to control the resonance lifetime.

The structure of a resonance state

The existence of a structure in a resonance state is systematically investigated. A resonance structure is defined as the energy dependence across the resonance width of the fragment state distributions produced upon resonance decay. Different types of resonances, both isolated and overlapping ones, have been explored for this purpose. It is found that isolated resonances do not present an appreciable energy dependence on the product state distributions. On the contrary, overlapping resonances exhibit a clear structure regarding the fragment distributions, which becomes increasingly more pronounced as the intensity of the overlap between the resonances increases. Such an energy dependence of the product distributions arises from the quantum interference between the amplitudes of the overlapping resonances, as demonstrated formally here by the equations derived from the condition of resonance overlap. The application of the present effect to the control of the fragment state distributions produced in a wide variety of molecular processes governed by resonance states is envisioned.

Identifying Strong-Field Effects in Indirect Photofragmentation Reactions

Exploring molecular breakup processes induced by light-matter interactions has both fundamental and practical implications. However, it remains a challenge to elucidate the underlying reaction mechanism in the strong field regime, where the potentials of the reactant are modified dramatically. Here we perform a theoretical analysis combined with a time-dependent wavepacket calculation to show how a strong ultrafast laser field affects the photofragment products. As an example, we examine the photochemical reaction of breaking up the molecule NaI into the neutral atoms Na and I, which due to inherent nonadiabatic couplings are indirectly formed in a stepwise fashion via the reaction intermediate NaI*. By analyzing the angular dependencies of fragment distributions, we are able to identify the reaction intermediate NaI* from the weak to the strong field-induced nonadiabatic regimes. Furthermore, the energy levels of NaI* can be extracted from the quantum interference patterns of the transient photofragment momentum distribution.

Weak-field laser phase modulation coherent control of asymptotic photofragment distributions

Coherent control of the asymptotic photofragment state-resolved distributions by means of laser phase modulation in the weak-field limit is demonstrated computationally for a polyatomic molecule. The control scheme proposed applies a pump laser field consisting of two pulses delayed in time. Phase modulation of the spectral bandwidth profile of the laser field is achieved by varying the time delay between the pulses. The underlying equations show that such a phase modulation is effective in order to produce control effects on the asymptotic, long-time limit photofragment distributions only when the bandwidths of the two pulses overlap in a frequency range. The frequency overlap of the pulses gives rise to an interference term which is responsible for the modulation of the spectral profile shape. The magnitude of the range of spectral overlap between the pulses becomes an additional control parameter. The control scheme is illustrated computationally for the asymptotic photofragment state distributions produced from different scenarios of the Ne-Br2 predissociation. An experimental application of the control scheme is found to be straightforward.

Communication: Control of the fragment state distributions produced upon decay of an isolated resonance state

Control of the fragment state distributions produced upon decay of a resonance state is achieved by using a weak laser field consisting of two pulses with a varying time delay between them. It is shown that specific product fragment states can be significantly favored or quenched. The efficiency and flexibility of the control method are found to increase with increasing resonance width. The control scheme is completely independent of the specific system to which it is applied, which makes its applicability universal.

Unravelling the role of quantum interference in the weak-field laser phase modulation control of photofragment distributions

The role played by quantum interference in the laser phase modulation coherent control of photofragment distributions in the weak-field regime is investigated in detail in this work. The specific application involves realistic wave packet calculations of the transient vibrational populations of the Br2(B,vf) fragment produced upon predissociation of the Ne-Br2(B) complex, which is excited to a superposition of overlapping resonance states using different fixed bandwidth pulses where the linear chirps are varied. The postpulse transient phase modulation effects observed on fragment populations for a long time window are explained in terms of the mechanism of interference between overlapping resonances. A detailed description of how the interference mechanism affects the magnitude and the time window of the phase control effects is also provided. In the light of the results, the conditions to maximize phase modulation control on fragment distributions are discussed.

Quantum interference control of an isolated resonance lifetime in the weak-field limit

Resonance states play an important role in a large variety of physical and chemical processes. Thus, controlling the resonance behavior, and particularly a key property like the resonance lifetime, opens up the possibility of controlling those resonance mediated processes. While such a resonance control is possible by applying strong-field approaches, the development of flexible weak-field control schemes that do not alter significantly the system dynamics still remains a challenge. In this work, one such control scheme within the weak-field regime is proposed for the first time in order to modify the lifetime of an isolated resonance state. The basis of the scheme suggested is quantum interference between two pathways induced by laser fields, that pump wave packet amplitude to the target resonance under control. The simulations reported here show that the scheme allows for both enhancement and quenching of the resonance survival lifetime, being particularly flexible to achieve large lifetime enhancements. Control effects on the resonance lifetime take place only while the pulse is operating. In addition, the conditions required to generate the two interfering quantum pathways are found to be rather easy to meet for general systems, which makes the experimental implementation straightforward and implies the wide applicability of the control scheme.