Active control of the dynamics of atoms and molecules

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Weak-Field Coherent Control of Ultrafast Molecule Making

Coherent control of ultrafast molecule making from colliding reactants is crucial for realizing coherent control of binary photoreactions (CCBP). To handle diverse excitation scenarios, feasibility with both weak and strong fields is essential. We experimentally demonstrate here the weak-field feasibility, achieving it even under thermally hot conditions typical of chemical reactions. The making of KAr complexes from hot pairs of colliding K and Ar atoms via resonance-mediated two-photon excitation is controlled by weak linearly chirped femtosecond pulses. Negative chirps enhance the yield. Our experimental and ab initio theoretical results are in excellent agreement. New routes to CCBP are opened.

Accelerating wavepacket propagation with machine learning

In this work, we discuss the use of a recently introduced machine learning (ML) technique known as Fourier neural operators (FNO) as an efficient alternative to the traditional solution of the time-dependent Schrödinger equation (TDSE). FNOs are ML models which are employed in the approximated solution of partial differential equations. For a wavepacket propagating in an anharmonic potential and for a tunneling system, we show that the FNO approach can accurately and faithfully model wavepacket propagation via the density. Additionally, we demonstrate that FNOs can be a suitable replacement for traditional TDSE solvers in cases where the results of the quantum dynamical simulation are required repeatedly such as in the case of parameter optimization problems (e.g., control). The speed-up from the FNO method allows for its combination with the Markov-chain Monte Carlo approach in applications that involve solving inverse problems such as optimal and coherent laser control of the outcome of dynamical processes.

Simulating Cavity-Modified Electron Transfer Dynamics on NISQ Computers

We present an algorithm based on the quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) method for simulating cavity-modified electron transfer dynamics on noisy intermediate-scale quantum (NISQ) computers. The utility and accuracy of the proposed methodology is demonstrated on a model for the photoinduced intramolecular electron transfer reaction within the carotenoid-porphyrin-C60 molecular triad in tetrahydrofuran (THF) solution. The electron transfer rate is found to increase significantly with increasing coupling strength between the molecular system and the cavity. The rate process is also seen to shift from overdamped monotonic decay to under-damped oscillatory dynamics. The electron transfer rate is seen to be highly sensitive to the cavity frequency, with the emergence of a resonance cavity frequency for which the effect of coupling to the cavity is maximal. Finally, an implementation of the algorithm on the IBM Osaka quantum computer is used to demonstrate how TT-TFD-based electron transfer dynamics can be simulated accurately on NISQ computers.

Quantum Molecular Devices

Miniaturization has been the driving force in contemporary technologies. However, two main obstacles limit further progress: additional reduction in size has reached its quantum limit, and lithography has reached its threshold. Future progress requires tackling three challenges: chemical synthesis of a complete device, active cooling for exploiting quantum characteristics, and quantum coherent control for operation. Chemical synthesis replaces the current top-bottom approach to manufacturing with bottom-up synthesis from elementary building blocks. New ultracold synthetic methods should be developed. An additional challenge is the active cooling of molecules, where the bottleneck is entropy removal. Notably, the current solution, namely, diffusion, is too slow. A coherent approach offers a possible solution; specifically, quantum coherent control is the method of choice for manipulating ultracold matter. Finally, the many degrees of freedom of molecules should be an asset that allows the design and implementation of complex tasks such as sensing communication and computing.

Wave packet dynamics and control in excited states of molecular nitrogen

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

Application of density matrix Wigner transforms for ultrafast macromolecular and chemical x-ray crystallography

Time-Resolved Serial Femtosecond Crystallography (TR-SFX) conducted at X-ray Free Electron Lasers (XFELs) has become a powerful tool for capturing macromolecular structural movies of light-initiated processes. As the capabilities of XFELs advance, we anticipate that a new range of coherent control and structural Raman measurements will become achievable. Shorter optical and x-ray pulse durations and increasingly more exotic pulse regimes are becoming available at free electron lasers. Moreover, with high repetition enabled by the superconducting technology of European XFEL (EuXFEL) and Linac Coherent Light Source (LCLS-II) , it will be possible to improve the signal-to-noise ratio of the light-induced differences, allowing for the observation of vibronic motion on the sub-Angstrom level. To predict and assign this coherent motion, which is measurable with a structural technique, new theoretical approaches must be developed. In this paper, we present a theoretical density matrix approach to model the various population and coherent dynamics of a system, which considers molecular system parameters and excitation conditions. We emphasize the use of the Wigner transform of the time-dependent density matrix, which provides a phase space representation that can be directly compared to the experimental positional displacements measured in a TR-SFX experiment. Here, we extend the results from simple models to include more realistic schemes that include large relaxation terms. We explore a variety of pulse schemes using multiple model systems using realistic parameters. An open-source software package is provided to perform the density matrix simulation and Wigner transformations. The open-source software allows us to define any arbitrary level schemes as well as any arbitrary electric field in the interaction Hamiltonian.

An Accurate Linearized Semiclassical Approach for Calculating Cavity-Modified Charge Transfer Rate Constants

We show that combining the linearized semiclasscial approximation with Fermi's golden rule (FGR) rate theory gives rise to a general-purpose cost-effective and scalable computational framework that can accurately capture the cavity-induced rate enhancement of charge transfer reactions that occurs when the molecular system is placed inside a microcavity. Both partial linearization with respect to the nuclear and photonic degrees of freedom and full linerization with respect to nuclear, photonic, and electronic degrees of freedom (the latter within the mapping Hamiltonian approach) are shown to be highly accurate, provided that the Wigner transforms of the product (WoP) of operators at the initial time is not replaced by the product of their Wigner transforms. We also show that the partial linearization method yields the quantum-mechanically exact cavity-modified FGR rate constant for a model system in which the donor and acceptor potential energy surfaces are harmonic and identical except for a shift in the equilibrium energy and geometry, if WoP is applied.

Investigation of photoassociation with full-dimensional thermal-random-phase wavefunctions

By taking the femtosecond two-photon photoassociation (PA) of magnesium atoms as an example, we propose a method to calculate the thermally averaged population, which is transferred from the ground X¹Σ_g ⁺ state to the target (1)¹Π_g state, based on the solution of full-dimensional time-dependent Schrödinger equation. In this method, named as method A, we use thermal-random-phase wavefunctions with the random phases expanded in both the vibrational and rotational degrees of freedom to model the thermal ensemble of the initial eigenstates. This method is compared with the other two methods (B and C) at different temperatures. Method B is also based on thermal-random-phase wavefunctions, except that the random-phase expansion is merely used for the vibrational degree of freedom. Method C is based on the independent propagation of every initial eigenstate, instead of the thermal-random-phase wavefunctions. Taking the (1)¹Π_g state as the target state, it is found that although these three methods can present the same population on the (1)¹Π_g state, the computation efficiency of method A increases dramatically with the increase in temperature. With this efficient method A, we find that the PA process at 1000 K can also induce rotational coherence, i.e., the molecular field-free alignment in the excited electronic states.

Coherent Control of Internal Conversion in Strong-Field Molecular Ionization

We demonstrate coherent control over internal conversion during strong-field molecular ionization with shaped, few-cycle laser pulses. The control is driven by interference in different neutral states, which are coupled via non-Born-Oppenheimer terms in the molecular Hamiltonian. Our measurements highlight the preservation of electronic coherence in nonadiabatic transitions between electronic states.

Universal energy scaling law for optimally excited nonlinear oscillators

We compute the optimal temporal profile for an external driving force F(t) that can maximize the energy absorption of any driven nonlinear oscillator. The technique is based on constraining the maximum amplitude of the force field such that optimal control theory can provide quasianalytical solutions. We illustrate this computational technique for the undamped Duffing oscillator as well as for a driven quantum mechanical two-level system. We find that under optimal force conditions the asymptotic time-dependence of the maximum amplitude growth is given by a power law X(t)∼t^{2/α}, where the (possibly noninteger) exponent is determined by the highest degree of the oscillator's nonlinearity α. As a universal result, this predicts that the maximal energy absorption of any nonlinear oscillator grows (under an optimized force field) quadratically in time. We also find for the two-level system that-even under optimized excitation conditions-the maximally achievable inversion does not monotonically increase with the force amplitude. It is characterized by an interesting sequence of n-cycle thresholds as well as a self-termination of the growth.

Molecular ground-state dissociation in the condensed phase employing plasmonic field enhancement of chirped mid-infrared pulses

Selective bond cleavage via vibrational excitation is the key to active control over molecular reactions. Despite its great potential, the practical implementation in condensed phases have been hampered to date by poor excitation efficiency due to fast vibrational relaxation. Here we demonstrate vibrationally mediated, condensed-phase molecular dissociation by employing intense plasmonic near-fields of temporally-shaped mid-infrared (mid-IR) pulses. Both down-chirping and substantial field enhancement contribute to efficient ladder climbing of the carbonyl stretch vibration of W(CO)6 in n-hexane solution and to the resulting CO dissociation. We observe an absorption band emerging with laser irradiation at the excitation beam area, which indicates that the dissociation is followed by adsorption onto metal surfaces. This successful demonstration proves that the combination of ultrafast optics and nano-plasmonics in the mid-IR range is useful for mode-selective vibrational ladder climbing, paving the way toward controlled ground-state chemistry.

Observation of Floquet Raman Transition in a Driven Solid-State Spin System

We experimentally observe Floquet Raman transitions in the weakly driven solid-state spin system of a nitrogen-vacancy center in diamond. The periodically driven spin system simulates a two-band Wannier-Stark ladder model and allows us to observe coherent spin state transfer arising from a Raman transition mediated by Floquet synthetic levels. It also leads to the prediction of an analog photon-assisted Floquet Raman transition and dynamical localization in a driven two-level quantum system. The demonstrated rich Floquet dynamics offers new capabilities to achieve effective Floquet coherent control of a quantum system with potential applications in various types of quantum technologies based on driven quantum dynamics. In particular, the Floquet Raman system may be used as a quantum simulator for the physics of periodically driven systems.

Self-Organization of Metal Nanoparticles in Light: Electrodynamics-Molecular Dynamics Simulations and Optical Binding Experiments

Light-driven self-organization of metal nanoparticles (NPs) can lead to unique optical matter systems, yet simulation of such self-organization (i.e., optical binding) is a complex computational problem that increases nonlinearly with system size. Here we show that a combined electrodynamics-molecular dynamics simulation technique can simulate the trajectories and predict stable configurations of silver NPs in optical fields. The simulated dynamic equilibrium of a two-NP system matches the probability density of oscillations for two optically bound NPs obtained experimentally. The predicted stable configurations for up to eight NPs are further compared to experimental observations of silver NP clusters formed by optical binding in a Bessel beam. All configurations are confirmed to form in real systems, including pentagonal clusters with five-fold symmetry. Our combined simulations and experiments have revealed a diverse optical matter system formed by anisotropic optical binding interactions, providing a new strategy to discover artificial materials.

Control quantum evolution speed of a single dephasing qubit for arbitrary initial states via periodic dynamical decoupling pulses

We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).

Controlling the Excited-State Dynamics of Nuclear Spin Isomers Using the Dynamic Stark Effect

Stark control of chemical reactions uses intense laser pulses to distort the potential energy surfaces of a molecule, thus opening new chemical pathways. We use the concept of Stark shifts to convert a local minimum into a local maximum of the potential energy surface, triggering constructive and destructive wave-packet interferences, which then induce different dynamics on nuclear spin isomers in the electronically excited state of a quinodimethane derivative. Model quantum-dynamical simulations on reduced dimensionality using optimized ultrashort laser pulses demonstrate a difference of the excited-state dynamics of two sets of nuclear spin isomers, which ultimately can be used to discriminate between these isomers.

Enhancing the branching ratios in the dissociation channels for O(16)O(16)O(18) molecule by designing optimum laser pulses: A study using stochastic optimization

We propose a strategy of using a stochastic optimization technique, namely, simulated annealing to design optimum laser pulses (both IR and UV) to achieve greater fluxes along the two dissociating channels (O(18) + O(16)O(16) and O(16) + O(16)O(18)) in O(16)O(16)O(18) molecule. We show that the integrated fluxes obtained along the targeted dissociating channel is larger with the optimized pulse than with the unoptimized one. The flux ratios are also more impressive with the optimized pulse than with the unoptimized one. We also look at the evolution contours of the wavefunctions along the two channels with time after the actions of both the IR and UV pulses and compare the profiles for unoptimized (initial) and optimized fields for better understanding the results that we achieve. We also report the pulse parameters obtained as well as the final shapes they take.

Strong field laser control of photochemistry

Strong ultrashort laser pulses have opened new avenues for the manipulation of photochemical processes like photoisomerization or photodissociation. The presence of light intense enough to reshape the potential energy surfaces may steer the dynamics of both electrons and nuclei in new directions. A controlled laser pulse, precisely defined in terms of spectrum, time and intensity, is the essential tool in this type of approach to control chemical dynamics at a microscopic level. In this Perspective we examine the current strategies developed to achieve control of chemical processes with strong laser fields, as well as recent experimental advances that demonstrate that properties like the molecular absorption spectrum, the state lifetimes, the quantum yields and the velocity distributions in photodissociation processes can be controlled by the introduction of carefully designed strong laser fields.

Vibrational ladder climbing in carboxy-hemoglobin: effects of the protein environment

We present simulations on vibrational ladder climbing in carboxy-hemoglobin. Motivated by recent experiments, we study the influence of different realistic pump probe parameters. To allow for a direct comparison with experimental results, transient absorption spectra obtained by a weak probe pulse following the strong, shaped pump pulse are calculated. The influence of the protein fluctuations is taken into account using a recently developed microscopic model. This model consists of a quantum Hamiltonian describing the CO vibration in carboxy-hemoglobin, together with a fluctuating potential, which is obtained by electronic structure calculation based on a large number of protein configurations. Using realistic pulse parameters, vibrational excitations to very high-lying states are possible, in qualitative agreement with experimental observations.

Potential energy surfaces and reaction pathways for light-mediated self-organization of metal nanoparticle clusters

Potential energy surfaces are the central concept in understanding the assembly of molecules; atoms form molecules via covalent bonds with structures defined by the stationary points of the surfaces. Similarly, dispersion interactions give Lennard-Jones potentials that describe atomic clusters and liquids. The formation of molecules and clusters can follow various pathways depending on the initial conditions and the potentials. Here we show that analogous mechanistic effects occur in light-mediated self-organization of metal nanoparticles; atoms are replaced by silver nanoparticles that are arranged by electrodynamic (that is, optical trapping and optical binding) interactions. We demonstrate this concept using simple Gaussian optical fields and the formation of stable clusters with various two-dimensional (2D) and three-dimensional (3D) geometries. The formation of specific clusters is 'path-dependent'; the particle motions follow an electrodynamic potential energy surface. This work paves the way for rational design of photonic clusters with combinations of imposed beam shapes, gradients and optical binding interactions.

Photoexcitation of adsorbates on metal surfaces: one-step or three-step

In this essay we discuss the light-matter interactions at molecule-covered metal surfaces that initiate surface photochemistry. The hot-electron mechanism for surface photochemistry, whereby the absorption of light by a metal surface creates an electron-hole pair, and the hot electron scatters through an unoccupied resonance of adsorbate to initiate nuclear dynamics leading to photochemistry, has become widely accepted. Yet, ultrafast spectroscopic measurements of molecule-surface electronic structure and photoexcitation dynamics provide scant support for the hot electron mechanism. Instead, in most cases the adsorbate resonances are excited through photoinduced substrate-to-adsorbate charge transfer. Based on recent studies of the role of coherence in adsorbate photoexcitation, as measured by the optical phase and momentum resolved two-photon photoemission measurements, we examine critically the hot electron mechanism, and propose an alternative description based on direct charge transfer of electrons from the substrate to adsorbate. The advantage of this more quantum mechanically rigorous description is that it informs how material properties of the substrate and adsorbate, as well as their interaction, influence the frequency dependent probability of photoexcitation and ultimately how light can be used to probe and control surface femtochemistry.

Generating molecular rovibrational coherence by two-photon femtosecond photoassociation of thermally hot atoms

The formation of diatomic molecules with rotational and vibrational coherence is demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, colliding in their electronic ground state, are excited into coherent superpositions of bound rovibrational levels in an electronically excited state. The rovibrational coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV fluorescence. A comprehensive theoretical model based on ab initio calculations rationalizes the generation of coherence by Franck-Condon filtering of collision energies and partial waves, quantifying it in terms of an increase in quantum purity of the thermal ensemble. Our results open the way to coherent control of a binary reaction.

Weak-field multiphoton femtosecond coherent control in the single-cycle regime

Weak-field coherent phase control of atomic non-resonant multiphoton excitation induced by shaped femtosecond pulses is studied theoretically in the single-cycle regime. The carrier-envelope phase (CEP) of the pulse, which in the multi-cycle regime does not play any control role, is shown here to be a new effective control parameter that its effect is highly sensitive to the spectral position of the ultrabroad spectrum. Rationally chosen position of the ultrabroadband spectrum coherently induces several groups of multiphoton transitions from the ground state to the excited state of the system: transitions involving only absorbed photons as well as Raman transitions involving both absorbed and emitted photons. The intra-group interference is controlled by the relative spectral phase of the different frequency components of the pulse, while the inter-group interference is controlled jointly by the CEP and the relative spectral phase. Specifically, non-resonant two- and three-photon excitation is studied in a simple model system within the perturbative frequency-domain framework. The developed intuition is then applied to weak-field multiphoton excitation of atomic cesium (Cs), where the simplified model is verified by non-perturbative numerical solution of the time-dependent Schrödinger equation. We expect this work to serve as a basis for a new line of femtosecond coherent control experiments.

Exploring the role of phase modulation on photoluminescence yield

We report an investigation to elucidate the mechanisms of control in phase-sensitive experiments in two molecular systems. A first inspection of optimization procedures yields the same experimental result: increase in the emission efficiency upon excitation by a phase modulated pulse in a two-photon transition. More detailed studies, which include power dependence, spectral response, one and two color pump-probe and pump-pump experiments show that while for one chromophore phase modulation leads to spectral matching between the two-photon cross section and the second order power spectrum for the other it provides a tool to manipulate the wavepacket dynamics in the excited state.

Coherent Control of Quantum Dynamics with Sequences of Unitary Phase-Kick Pulses

Coherent-optical-control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways and manipulate dynamical processes. These active control methods are closely related to dynamical decoupling techniques, popularized in the field of quantum information. Inspired by nuclear magnetic resonance spectroscopy, dynamical decoupling methods apply sequences of unitary operations to modify the interference phenomena responsible for the system dynamics thus also belonging to the general class of coherent-control techniques. This article reviews related developments in the fields of coherent optical control and dynamical decoupling, emphasizing the control of tunneling and decoherence in general model systems. Considering recent experimental breakthroughs in the demonstration of active control of a variety of systems, we anticipate that the reviewed coherent-control scenarios and dynamical-decoupling methods should raise significant experimental interest.