Generalized Theory for the Timescale of Molecular Electronic Decoherence in the Condensed Phase

Using Machine Learning to Understand the Causes of Quantum Decoherence in Solution-Phase Bond-Breaking Reactions

Decoherence is a fundamental phenomenon that occurs when an entangled quantum state interacts with its environment, leading to collapse of the wave function. The inevitability of decoherence provides one of the most intrinsic limits of quantum computing. However, there has been little study of the precise chemical motions from the environment that cause decoherence. Here, we use quantum molecular dynamics simulations to explore the photodissociation of Na2+ in liquid Ar, in which solvent fluctuations induce decoherence and thus determine the products of chemical bond breaking. We use machine learning to characterize the solute-solvent environment as a high-dimensional feature space that allows us to predict when and onto which photofragment the bonding electron will localize. We find that reaching a requisite photofragment separation and experiencing out-of-phase solvent collisions underlie decoherence during chemical bond breaking. Our work highlights the utility of machine learning for interpreting complex solution-phase chemical processes as well as identifies the molecular underpinnings of decoherence.

Mapping electronic decoherence pathways in molecules

Establishing the fundamental chemical principles that govern molecular electronic quantum decoherence has remained an outstanding challenge. Fundamental questions such as how solvent and intramolecular vibrations or chemical functionalization contribute to the decoherence remain unanswered and are beyond the reach of state-of-the-art theoretical and experimental approaches. Here we address this challenge by developing a strategy to isolate electronic decoherence pathways for molecular chromophores immersed in condensed phase environments that enables elucidating how electronic quantum coherence is lost. For this, we first identify resonance Raman spectroscopy as a general experimental method to reconstruct molecular spectral densities with full chemical complexity at room temperature, in solvent, and for fluorescent and non-fluorescent molecules. We then show how to quantitatively capture the decoherence dynamics from the spectral density and identify decoherence pathways by decomposing the overall coherence loss into contributions due to individual molecular vibrations and solvent modes. We illustrate the utility of the strategy by analyzing the electronic decoherence pathways of the DNA base thymine in water. Its electronic coherences decay in [Formula: see text]30 fs. The early-time decoherence is determined by intramolecular vibrations while the overall decay by solvent. Chemical substitution of thymine modulates the decoherence with hydrogen-bond interactions of the thymine ring with water leading to the fastest decoherence. Increasing temperature leads to faster decoherence as it enhances the importance of solvent contributions but leaves the early-time decoherence dynamics intact. The developed strategy opens key opportunities to establish the connection between molecular structure and quantum decoherence as needed to develop chemical strategies to rationally modulate it.

Stark control of electrons across the molecule-semiconductor interface

Controlling matter at the level of electrons using ultrafast laser sources represents an important challenge for science and technology. Recently, we introduced a general laser control scheme (the Stark control of electrons at interfaces or SCELI) based on the Stark effect that uses the subcycle structure of light to manipulate electron dynamics at semiconductor interfaces [A. Garzón-Ramírez and I. Franco, Phys. Rev. B 98, 121305 (2018)]. Here, we demonstrate that SCELI is also of general applicability in molecule-semiconductor interfaces. We do so by following the quantum dynamics induced by non-resonant few-cycle laser pulses of intermediate intensity (non-perturbative but non-ionizing) across model molecule-semiconductor interfaces of varying level alignments. We show that SCELI induces interfacial charge transfer regardless of the energy level alignment of the interface and even in situations where charge exchange is forbidden via resonant photoexcitation. We further show that the SCELI rate of charge transfer is faster than those offered by resonant photoexcitation routes as it is controlled by the subcycle structure of light. The results underscore the general applicability of SCELI to manipulate electron dynamics at interfaces on ultrafast timescales.

Tuning and Enhancing Quantum Coherence Time Scales in Molecules via Light-Matter Hybridization

Protecting quantum coherences in matter from the detrimental effects introduced by its environment is essential to employ molecules and materials in quantum technologies and develop enhanced spectroscopies. Here, we show how dressing molecular chromophores with quantum light in the context of optical cavities can be used to generate quantum superposition states with tunable coherence time scales that are longer than those of the bare molecule, even at room temperature and for molecules immersed in solvent. For this, we develop a theory of decoherence rates for molecular polaritonic states and demonstrate that quantum superpositions that involve such hybrid light-matter states can survive for times that are orders of magnitude longer than those of the bare molecule while remaining optically controllable. Further, by studying these tunable coherence enhancements in the presence of lossy cavities, we demonstrate that they can be enacted using present-day optical cavities. The analysis offers a viable strategy to engineer and increase quantum coherence lifetimes in molecules.

Coherent and incoherent contributions to molecular electron transport

We numerically isolate the limits of validity of the Landauer approximation to describe charge transport along molecular junctions in condensed phase environments. To do so, we contrast Landauer with exact time-dependent non-equilibrium Green’s function quantum transport computations in a two-site molecular junction subject to exponentially correlated noise. Under resonant transport conditions, we find Landauer accuracy to critically depend on intramolecular interactions. By contrast, under nonresonant conditions, the emergence of incoherent transport routes that go beyond Landauer depends on charging and discharging processes at the electrode–molecule interface. In both cases, decreasing the rate of charge exchange between the electrodes and molecule and increasing the interaction strength with the thermal environment cause Landauer to become less accurate. The results are interpreted from a time-dependent perspective where the noise prevents the junction from achieving steady-state and from a fully quantum perspective where the environment introduces dephasing in the dynamics. Using these results, we analyze why the Landauer approach is so useful to understand experiments, isolate regimes where it fails, and propose schemes to chemically manipulate the degree of transport coherence.

Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules

Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

Momentum-Space Decoherence of Distinguishable and Identical Particles in the Caldeira-Leggett Formalism

In this work, momentum-space decoherence using minimum and nonminimum-uncertainty-product (stretched) Gaussian wave packets in the framework of Caldeira-Leggett formalism and under the presence of a linear potential is studied. As a dimensionless measure of decoherence, purity, a quantity appearing in the definition of the linear entropy, is studied taking into account the role of the stretching parameter. Special emphasis is on the open dynamics of the well-known cat states and bosons and fermions compared to distinguishable particles. For the cat state, while the stretching parameter speeds up the decoherence, the external linear potential strength does not affect the decoherence time; only the interference pattern is shifted. Furthermore, the interference pattern is not observed for minimum-uncertainty-product-Gaussian wave packets in the momentum space. Concerning bosons and fermions, the question we have addressed is how the symmetry of the wave functions of indistinguishable particles is manifested in the decoherence process, which is understood here as the loss of being indistinguishable due to the gradual emergence of classical statistics with time. We have observed that the initial bunching and anti-bunching character of bosons and fermions, respectively, in the momentum space are not preserved as a function of the environmental parameters, temperature, and damping constant. However, fermionic distributions are slightly broader than the distinguishable ones and these similar to the bosonic distributions. This general behavior could be interpreted as a residual reminder of the symmetry of the wave functions in the momentum space for this open dynamics.

Nonadiabatic Dynamics with Coupled Trajectories

In this paper, we discuss coupled-trajectory schemes for molecular-dynamics simulations of excited-state processes. New coupled-trajectory strategies to capture decoherence effects, revival of coherence and nonadiabatic interferences in long-time dynamics are proposed, and compared to independent-trajectory schemes. The working framework is provided by the exact factorization of the electron-nuclear wave function, and it exploits ideas emanating from various surface-hopping schemes. The new coupled-trajectory algorithms are tested on a one-dimensional two-state system using different model parameters which allow one to induce different dynamics. The benchmark is provided by the numerically exact solution of the time-dependent Schrödinger equation.

Intermittent decoherence blockade in a chiral ring environment

It has long been recognized that emission of radiation from atoms is not an intrinsic property of individual atoms themselves, but it is largely affected by the characteristics of the photonic environment and by the collective interaction among the atoms. A general belief is that preventing full decay and/or decoherence requires the existence of dark states, i.e., dressed light-atom states that do not decay despite the dissipative environment. Here, we show that, contrary to such a common wisdom, decoherence suppression can be intermittently achieved on a limited time scale, without the need for any dark state, when the atom is coupled to a chiral ring environment, leading to a highly non-exponential staircase decay. This effect, that we refer to as intermittent decoherence blockade, arises from periodic destructive interference between light emitted in the present and light emitted in the past, i.e., from delayed coherent quantum feedback.

Survival of quantum features in the dynamics of a dissipative quantum system and their effect on the state purity

Destruction of the quantum mechanical features of matter by decoherence restricts the applicability of quantum technologies. The limited information of the quantum features (such as coherence) in the basis-dependent observations urges the use of a basis-independent quantity for a better understanding. In this context, the state purity of a quantum system (composed of quantized pigments immersed in a noisy protein environment) is studied with a numerically exact hierarchical equations of motion approach over the wide range of the parameter domain (with the main focus on the nonzero-energy gradient). It is noted that the state purity does not necessarily reflect any significant information about the persistence of quantum features (in the dissipative environment), even when the quantum coherence survives at the steady state in both the localized and the eigenstate basis.

Exploring the effects of quantum decoherence on the excited-state dynamics of molecular systems

Fewest-switches surface hopping (FSSH) is employed in order to investigate the nonadiabatic excited-state dynamics of thiophene and related compounds and hence to establish a connection between the electronic system, the critical points in configuration space and the deactivation dynamics. The potential-energy surfaces of the studied molecules were calculated with complete active space self-consistent field and time-dependent density-functional theory. They are analyzed thoroughly to locate and optimize minimum-energy conical intersections, which are essential to the dynamics of the system. The influence of decoherence on the dynamics is examined by employing different decoherence schemes. We find that irrespective of the employed decoherence algorithm, the population dynamics of thiophene give results which are sound with the expectations grounded on the analysis of the potential-energy surface. A more detailed look at single trajectories as well as on the excited-state lifetimes, however, reveals a substantial dependence on how decoherence is accounted for. In order to connect these findings, we describe how ensemble averaging cures some of the overcoherence problems of uncorrected FSSH. Eventually, we identify carbon–sulfur bond cleavage as a common feature accompanying electronic transitions between different states in the simulations of all thiophene-related compounds studied in this work, which is of interest due to their relevance in organic photovoltaics.

Density matrix and purity evolution in dissipative two-level systems: I. Theory and path integral results for tunneling dynamics

The time evolution of the purity (the trace of the square of the reduced density matrix) and von Neumann entropy in a symmetric two-level system coupled to a dissipative harmonic bath is investigated through analytical arguments and accurate path integral calculations on simple models and the singly excited bacteriochlorophyll dimer. A simple theoretical analysis establishes bounds and limiting behaviors. The contributions to purity from a purely incoherent term obtained from the diagonal elements of the reduced density matrix, a term associated with the difference of the two eigenstate populations, and a third term related to the square of the time derivative of a site population, are discussed in various regimes. In the case of tunneling dynamics from a localized initial condition, the complex interplay among these contributions leads to the recovery of purity under low-temperature, weakly dissipative conditions. Memory effects from the bath are found to play a critical role to the dynamics of purity. It is shown that the strictly quantum mechanical decoherence process associated with spontaneous phonon emission is responsible for the long-time recovery of purity. These analytical and numerical results show clearly that the loss of quantum coherence during the evolution toward equilibrium does not necessarily imply the decay of purity, and that the time scales relevant to these two processes may be entirely different.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates. We point out that the symmetry of the initial condition confines the motion of the RDM elements to a one-dimensional subspace and show that the purity always goes through its maximally mixed value at some time during relaxation, but subsequently recovers and (under low-temperature, weakly dissipative conditions) can rise to values that approach unity. These behaviors are quantified through accurate path integral calculations. Under low-temperature, weakly dissipative conditions, we observe unusual, nonmonotonic population dynamics when the two-level system is initially placed in its ground state. We also analyze the origin of the system-bath interactions responsible for the nonmonotonic behavior of purity during relaxation. Our results show that classical dephasing processes arising from site level fluctuations lead to a monotonic decay of purity, and that the quantum mechanical decoherence events associated with spontaneous phonon emission are responsible for the subsequent recovery of purity. Last, we show that coupling with a low-temperature bath can purify a mixed two-level system. In the case of the maximally mixed initial RDM, the purity increases monotonically even during short time.

Recovery of Purity in Dissipative Tunneling Dynamics

The time evolution of purity for an initially localized state of a symmetric two-level system coupled to a dissipative bath is investigated using numerically exact real-time path integral methods. With strong system-bath coupling and high temperature, the purity decays monotonically to its fully mixed value, with a short-time Gaussian behavior, which is subsequently followed by exponential evolution. However, under low-temperature and weak coupling conditions, a substantial recovery of purity is observed. A simple theoretical analysis reveals three contributions that correspond to a completely incoherent, eigenstate population difference and rate terms. The last two of these terms can counter the early drop of purity and are responsible for its rebound. These findings caution against using purity as a measure of decoherence in the dynamics of quantum dissipative systems.

Toward a First-Principles Evaluation of Transport Mechanisms in Molecular Wires

Understanding charge transport through molecular wires is important for nanoscale electronics and biochemistry. Our goal is to establish a simple first-principles protocol for predicting the charge transport mechanism in such wires, in particular the crossover from coherent tunneling for short wires to incoherent hopping for longer wires. This protocol is based on a combination of density functional theory with a polarizable continuum model introduced by Kaupp et al. for mixed-valence molecules, which we had previously found to work well for length-dependent charge delocalization in such systems. We combine this protocol with a new charge delocalization measure tailored for molecular wires, and we show that it can predict the tunneling-to-hopping transition length with a maximum error of one subunit in five sets of molecular wires studied experimentally in molecular junctions at room temperature. This suggests that the protocol is also well suited for estimating the extent of hopping sites as relevant, for example, for the intermediate tunneling-hopping regime in DNA.

Manipulating Two-Photon-Absorption of Cavity Polaritons by Entangled Light

We demonstrate that two-photon excitations to bipolariton states created by placing several molecules in an optical cavity can be manipulated by quantum light. Entangled photons can access classically dark bipolariton states by modifying the quantum interferences of two-photon transition pathways involving different single-polariton intermediate states and time-ordering of the two photon beams.

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.

Spin-phonon coupling and dynamic zero-field splitting contributions to spin conversion processes in iron(II) complexes

Magnetization dynamics of transition metal complexes manifest in properties and phenomena of fundamental and applied interest [e.g., slow magnetic relaxation in single molecule magnets, quantum coherence in quantum bits (qubits), and intersystem crossing (ISC) rates in photophysics]. While spin-phonon coupling is recognized as an important determinant of these dynamics, additional fundamental studies are required to unravel the nature of the coupling and, thus, leverage it in molecular engineering approaches. To this end, we describe here a combined ligand field theory and multireference ab initio model to define spin-phonon coupling terms in S = 2 transition metal complexes and demonstrate how couplings originate from both the static and dynamic properties of ground and excited states. By extending concepts to spin conversion processes, ligand field dynamics manifest in the evolution of the excited state origins of zero-field splitting (ZFS) along specific normal mode potential energy surfaces. Dynamic ZFSs provide a powerful means to independently evaluate contributions from spin-allowed and/or spin-forbidden excited states to spin-phonon coupling terms. Furthermore, ratios between various intramolecular coupling terms for a given mode drive spin conversion processes in transition metal complexes and can be used to analyze the mechanisms of ISC. Variations in geometric structure strongly influence the relative intramolecular linear spin-phonon coupling terms and will define the overall spin state dynamics. While the findings of this study are of general importance for understanding magnetization dynamics, they also link the phenomenon of spin-phonon coupling across fields of single molecule magnetism, quantum materials/qubits, and transition metal photophysics.

Toward the laser control of electronic decoherence

Controlling electronic decoherence in molecules is an outstanding challenge in chemistry. Recent advances in the theory of electronic decoherence [B. Gu and I. Franco, J. Phys. Chem. Lett. 9, 773 (2018)] have demonstrated that it is possible to manipulate the rate of electronic coherence loss via control of the relative phase in the initial electronic superposition state. This control emerges when there are both relaxation and pure-dephasing channels for decoherence and applies to initially separable electron-nuclear states. In this paper, we demonstrate that (1) such an initial superposition state and the subsequent quantum control of electronic decoherence can be created via weak-field one-photon photoexcitation with few-cycle laser pulses of definite carrier envelope phase (CEP), provided the system is initially prepared in a separable electron-nuclear state. However, we also demonstrate that (2) when stationary molecular states (which are generally not separable) are considered, such one-photon laser control disappears. Remarkably, this happens even in situations in which the initially factorizable state is an excellent approximation to the stationary state with fidelity above 98.5%. The laser control that emerges for initially separable states is shown to arise because these states are superpositions of molecular eigenstates that open up CEP-controllable interference routes at the one-photon limit. Using these insights, we demonstrate that (3) the laser control of electronic decoherence from stationary states can be recovered by using a two-pulse control scheme, with the first pulse creating a vibronic superposition state and the second one inducing interference. This contribution advances a viable scheme for the laser control of electronic decoherence and exposes a surprising artifact that is introduced by widely used initially factorizable system-bath states in the field of open quantum systems.

The dynamic ligand field of a molecular qubit: decoherence through spin–phonon coupling

A ligand field model highlights chemical design principles for the development of room temperature coherent materials for quantum information processing.

Manipulating nonadiabatic conical intersection dynamics by optical cavities

Optical cavities hold great promise to manipulate and control the photochemistry of molecules. We demonstrate how molecular photochemical processes can be manipulated by strong light-matter coupling. For a molecule with an inherent conical intersection, optical cavities can induce significant changes in the nonadiabatic dynamics by either splitting the pristine conical intersections into two novel polaritonic conical intersections or by creating light-induced avoided crossings in the polaritonic surfaces. This is demonstrated by exact real-time quantum dynamics simulations of a three-state two-mode model of pyrazine strongly coupled to a single cavity photon mode. We further explore the effects of external environments through dissipative polaritonic dynamics computed using the hierarchical equation of motion method. We find that cavity-controlled photochemistry can be immune to external environments. We also demonstrate that the polariton-induced changes in the dynamics can be monitored by transient absorption spectroscopy.

Competition between charge migration and charge transfer induced by nuclear motion following core ionization: Model systems and application to Li2. J Chem Phys 2019;151:124108. [PMID: 31575213 DOI: 10.1063/1.5117246]

Attosecond and femtosecond spectroscopies present opportunities for the control of chemical reaction dynamics and products, as well as for quantum information processing; we address the somewhat unique situation of core-ionization spectroscopy which, for dimeric chromophores, leads to strong valence charge localization and hence tightly paired potential-energy surfaces of very similar shape. Application is made to the quantum dynamics of core-ionized Li₂ ⁺. This system is chosen as Li₂ is the simplest stable molecule facilitating both core ionization and valence ionization. First, the quantum dynamics of some model surfaces are considered, with the surprising result that subtle differences in shape between core-ionization paired surfaces can lead to dramatic differences in the interplay between electronic charge migration and charge transfer induced by nuclear motion. Then, equation-of-motion coupled-cluster calculations are applied to determine potential-energy surfaces for 8 core-excited state pairs, calculations believed to be the first of their type for other than the lowest-energy core-ionized molecular pair. While known results for the lowest-energy pair suggest that Li₂ ⁺ is unsuitable for studying charge migration, higher-energy pairs are predicted to yield results showing competition between charge migration and charge transfer. Central is a focus on the application of Hush's 1975 theory for core-ionized X-ray photoelectron spectroscopy to understand the shapes of the potential-energy surfaces and hence predict key features of charge migration.

Electronic interactions do not affect electronic decoherence in the pure-dephasing limit

The relationship between electronic interactions and electronic decoherence is a fundamental problem in chemistry. Here we show that varying the electron-electron interactions does not affect the electronic decoherence in the pure-dephasing limit. In this limit, the effect of varying the electronic interactions is to rigidly shift in energy the diabatic potential energy surfaces without changing their shape, thus keeping the nuclear dynamics in these surfaces that leads to the electronic decoherence intact. This analysis offers a simple and intuitive understanding of previous theoretical and computational efforts to characterize the influence of electronic interactions on the decoherence and opens opportunities to study exact electronic decoherence with approximate electronic structure theories.