General framework for quantifying dissipation pathways in open quantum systems. II. Numerical validation and the role of non-Markovianity.

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1-214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics.

General framework for quantifying dissipation pathways in open quantum systems. I. Theoretical formulation.

We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima-Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems.

Bexcitonics: Quasiparticle approach to open quantum dynamics.

We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths of arbitrary complexity based on the Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM dynamics and mapping it into that of the system in interaction with a few bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from a decomposition of the bath correlation function into discrete features. Specifically, bexciton creation and annihilation couple the auxiliary density matrices in the HEOM. The approach provides a systematic strategy to construct exact quantum master equations that include the system-bath coupling to all orders even for non-Markovian environments. Specifically, by introducing different metrics and representations for the bexcitons it is possible to straightforwardly generate different variants of the HEOM, demonstrating that all these variants share a common underlying quasiparticle picture. Bexcitonic properties, while unphysical, offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence. For instance, we use it to analyze the instability of the HEOM when the bath is composed of underdamped oscillators and show that it leads to the creation of highly excited bexcitons. The bexcitonic picture can also be used to develop more efficient approaches to propagate the HEOM. As an example, we use the particle-like nature of the bexcitons to introduce mode-combination of bexcitons in both number and coordinate representation that uses the multi-configuration time-dependent Hartree to efficiently propagate the HEOM dynamics.

Microscopic theory, analysis, and interpretation of conductance histograms in molecular junctions.

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here we develop a microscopic theory for the conductance histogram by merging the theory of force-spectroscopy with molecular conductance. The procedure yields analytical equations that accurately fit the conductance histogram of a wide range of molecular junctions and augments the information content that can be extracted from them. Our formulation captures contributions to the conductance dispersion due to conductance changes during the mechanical elongation inherent to the experiments. In turn, the histogram shape is determined by the non-equilibrium stochastic features of junction rupture and formation. The microscopic parameters in the theory capture the junction's electromechanical properties and can be isolated from separate conductance and rupture force (or junction-lifetime) measurements. The predicted behavior can be used to test the range of validity of the theory, understand the conductance histograms, design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

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.

Learning Conductance: Gaussian Process Regression for Molecular Electronics.

Experimental studies of charge transport through single molecules often rely on break junction setups, where molecular junctions are repeatedly formed and broken while measuring the conductance, leading to a statistical distribution of conductance values. Modeling this experimental situation and the resulting conductance histograms is challenging for theoretical methods, as computations need to capture structural changes in experiments, including the statistics of junction formation and rupture. This type of extensive structural sampling implies that even when evaluating conductance from computationally efficient electronic structure methods, which typically are of reduced accuracy, the evaluation of conductance histograms is too expensive to be a routine task. Highly accurate quantum transport computations are only computationally feasible for a few selected conformations and thus necessarily ignore the rich conformational space probed in experiments. To overcome these limitations, we investigate the potential of machine learning for modeling conductance histograms, in particular by Gaussian process regression. We show that by selecting specific structural parameters as features, Gaussian process regression can be used to efficiently predict the zero-bias conductance from molecular structures, reducing the computational cost of simulating conductance histograms by an order of magnitude. This enables the efficient calculation of conductance histograms even on the basis of computationally expensive first-principles approaches by effectively reducing the number of necessary charge transport calculations, paving the way toward their routine evaluation.

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.

Light-field control of real and virtual charge carriers.

Light-driven electronic excitation is a cornerstone for energy and information transfer. In the interaction of intense and ultrafast light fields with solids, electrons may be excited irreversibly, or transiently during illumination only. As the transient electron population cannot be observed after the light pulse is gone, it is referred to as virtual, whereas the population that remains excited is called real1-4. Virtual charge carriers have recently been associated with high-harmonic generation and transient absorption5-8, but photocurrent generation may stem from real as well as virtual charge carriers9-14. However, a link between the generation of the carrier types and their importance for observables of technological relevance is missing. Here we show that real and virtual charge carriers can be excited and disentangled in the optical generation of currents in a gold-graphene-gold heterostructure using few-cycle laser pulses. Depending on the waveform used for photoexcitation, real carriers receive net momentum and propagate to the gold electrodes, whereas virtual carriers generate a polarization response read out at the gold-graphene interfaces. On the basis of these insights, we further demonstrate a proof of concept of a logic gate for future lightwave electronics. Our results offer a direct means to monitor and excite real and virtual charge carriers. Individual control over each type of carrier will markedly increase the integrated-circuit design space and bring petahertz signal processing closer to reality15,16.

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.

Electronic Coherence and Coherent Dephasing in the Optical Control of Electrons in Graphene.

Electronic coherence is of utmost importance for the access and control of quantum-mechanical solid-state properties. Using a purely electronic observable, the photocurrent, we measure a lower bound of the electronic coherence time of 22 ± 4 fs in graphene. The photocurrent is ideally suited to measure electronic coherence, as it is a direct result of coherent quantum-path interference, controlled by the delay between two ultrashort two-color laser pulses. The maximum delay for which interference between the population amplitude injected by the first pulse interferes with that generated by the second pulse determines the electronic coherence time. In particular, numerical simulations reveal that the experimental data yields a lower bound on the electronic coherence time, masked by coherent dephasing due to the broadband absorption in graphene. We expect that our results will significantly advance the understanding of coherent quantum control in solid-state systems ranging from excitation with weak fields to strongly driven systems.

Theory of dissipation pathways in open quantum systems.

We introduce a simple and effective method to decompose the energy dissipation in the dynamics of open quantum systems into contributions due to individual bath components. The method is based on a vibronic extension of the Förster resonance energy transfer theory that enables quantifying the energy dissipated by specific bath degrees of freedom. Its accuracy is determined by benchmarking against mixed quantum-classical simulations that reveal that the method provides a semi-quantitative frequency-dependent decomposition of the overall dissipation. The utility of the method is illustrated by using a model donor-acceptor pair interacting to a thermal harmonic bath with different coupling strengths. The method can be used to identify the key features of a bath that leads to energy dissipation as required to develop a deep understanding of the dynamics of open quantum systems and to engineer environments with desired dissipative features.

Symmetry breaking in the Stark Control of Electrons at Interfaces (SCELI).

Ultrafast control of electron dynamics is essential for future innovations in nanoelectronics, catalysis, and molecular imaging. Recently, we developed a general scheme (Stark Control of Electrons at Interfaces or SCELI) to control electron dynamics at interfaces [A. J. Garzón-Ramírez and I. Franco, Phys. Rev. B 98, 121305 (2018)] that is based on using few-cycle lasers to open quantum tunneling channels for interfacial electron transfer. SCELI uses the Stark effect induced by non-resonant light to create transient resonances between a donor level in material B and an acceptor level in material A, resulting in B → A electron transfer. Here, we show how SCELI can be employed to generate net charge transport in ABA heterojunctions without applying a bias voltage, a phenomenon known as laser-induced symmetry breaking. The magnitude and sign of such transport can be controlled by simply varying the time asymmetry of the laser pulse through manipulation of laser phases. In particular, we contrast symmetry breaking effects introduced by manipulation of the carrier envelope phase with those introduced by relative phase control in ω + 2ω laser pulses. The ω + 2ω pulse is seen to be far superior as such pulses exhibit a larger difference in field intensity for positive and negative amplitudes. The results exemplify the power of Stark-based strategies for controlling electrons using lasers.

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.

Optical properties of periodically driven open nonequilibrium quantum systems.

Characterization and control of matter by optical means is at the forefront of research both due to fundamental insights and technological promise. Theoretical modeling of periodically driven systems is a prerequisite to understanding and engineering nanoscale quantum devices for quantum technologies. Here, we develop a theory for transport and optical response of molecular junctions, open nonequilibrium quantum systems, under external periodic driving. Periodic driving is described using the Floquet theory combined with nonequilibrium Green's function description of the system. Light-matter interaction is modeled by employing the self-consistent Born approximation. A generic three-level model is utilized to illustrate the effect of the driving on optical and transport properties of junctions.

When can quantum decoherence be mimicked by classical noise?

Quantum decoherence arises due to uncontrollable entanglement between a system and its environment. However, the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here, we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes, we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation function of the environmental operators that enter into the system-bath interaction. In particular, for the exemplifying spin-boson problem with a Lorentz-Drude spectral density, we show that the high-temperature quantum decoherence is quantitatively mimicked by colored Gaussian noise. In turn, for dissipative environments, we show that classical noise models cannot describe decoherence effects due to relaxation through spontaneous emission of photons/phonons. These developments provide a rigorous platform to assess the validity of classical noise models of decoherence.

Force-conductance spectroscopy of a single-molecule reaction.

We demonstrate how simultaneous measurements of conductance and force can be used to monitor the step-by-step progress of a mechanically-activated cis-to-trans isomerization single-molecule reaction, including events that cannot be distinguished using force or conductance alone. To do so, we simulated the force-conductance profile of cyclopropane oligomers connected to graphene nanoribbon electrodes that undergo a cis-to-trans isomerization during mechanical elongation. This was done using a combination of classical molecular dynamics simulation of the pulling using a reactive force field, and Landauer transport computations of the conductance with nonequilibrium Green's function methods. The isomerization events can be distinguished in both force and conductance profiles. However, the conductance profile during the mechanical elongation distinguishes between reaction intermediates that cannot be resolved using force. In turn, the force signals non-reactive deformations in the molecular backbone which are not visible in the conductance profile. These observations are shown to be robust to the choice of electrode and Hamiltonian model. The computations exemplify the potential of the integration of covalent mechanochemistry with molecular conductance to investigate chemical reactivity at the single-entity limit.

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.

How Structural Defects Affect the Mechanical and Electrical Properties of Single Molecular Wires.

We report how individual defects affect single graphene nanoribbons by scanning tunneling and atomic force microscopy pulling experiments simultaneously accessing their electrical and mechanical properties. The on-surface polymerization of the graphene nanoribbons is controlled by cooperative effects as theoretically suggested. Further, we find, with the help of atomistic simulations, that defects substantially vary the molecule-substrate coupling and drastically increase the flexibility of the graphene nanoribbons while keeping their desirable electronic properties intact.