A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy.

Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.

Nonlinear Optical Spectroscopy of Molecular Assemblies: What Is Gained and Lost in Action Detection?

This study elucidates the information content that is extracted from action-2D electronic spectroscopy (A-2DES) when the output intensity is not proportional to the number of excitations generated. Such a scenario can be realized in both fluorescence and photocurrent detection because of direct interaction like exciton-exciton annihilation or indirect effects in the signal generation or detection. By means of an intuitive probabilistic model supported by nonlinear response theory, the study concludes that in molecular assemblies the ground-state bleaching contribution can dominate the nonlinear signal and partially or completely hide the stimulated emission. In this case, the spectral effect resembles incoherent mixing, even in the absence of exciton-exciton annihilation, implying reduced information about the excited-state dynamics with an increasing number of chromophores. This finding has important implications for the selection of samples for A-2DES as well as for its interpretation.

Identification of Design Principles for the Preparation of Colloidal Plexcitonic Materials.

Colloidal plexcitonic materials (CPMs) are a class of nanosystems where molecular dyes are strongly coupled with colloidal plasmonic nanoparticles, acting as nanocavities that enhance the light field. As a result of this strong coupling, new hybrid states are formed, called plexcitons, belonging to the broader family of polaritons. With respect to other families of polaritonic materials, CPMs are cheap and easy to prepare through wet chemistry methodologies. Still, clear structure-to-properties relationships are not available, and precise rules to drive the materials' design to obtain the desired optical properties are still missing. To fill this gap, in this article, we prepared a dataset with all CPMs reported in the literature, rationalizing their design by focusing on their three main relevant components (the plasmonic nanoparticles, the molecular dyes, and the capping layers) and identifying the most used and efficient combinations. With the help of statistical analysis, we also found valuable correlations between structure, coupling regime, and optical properties. The results of this analysis are expected to be relevant for the rational design of new CPMs with controllable and predictable photophysical properties to be exploited in a vast range of technological fields.

Unifying Nonlinear Response and Incoherent Mixing in Action-2D Electronic Spectroscopy.

Action-detection has expanded the scope and applicability of 2D electronic spectroscopy, while posing new challenges for the unambiguous interpretation of spectral features. In this context, identifying the origin of cross-peaks at early waiting times is not trivial, and incoherent mixing is often invoked as an unwanted contribution masking the nonlinear signal. In this work, we elaborate on the relation between the nonlinear response and the incoherent mixing contribution by analyzing the action signal in terms of one- and two-particle observables. Considering a weakly interacting molecular dimer, we show how cross-peaks at early waiting times, reflecting exciton-exciton annihilation dynamics, can be equivalently interpreted as arising from incoherent mixing. This equivalence, on the one hand, highlights the information content of spectral features related to incoherent mixing and, on the other hand, provides an efficient numerical scheme to simulate the action response of weakly interacting systems.

Large barrier behavior of the rate constant from the diffusion equation.

Many processes in chemistry, physics, and biology depend on thermally activated events in which the system changes its state by surmounting an activation barrier. Examples range from chemical reactions to protein folding and nucleation events. Parameterized forms of the mean field potential are often employed in the stochastic modeling of activated processes. In this contribution, we explore the alternative of employing parameterized forms of the equilibrium distribution by means of symmetric linear combination of two Gaussian functions. Such a procedure leads to flexible and convenient models for the landscape and the energy barrier whose features are controlled by the second moments of these Gaussian functions. The rate constants are examined through the solution of the corresponding diffusion problem, that is, the Fokker-Planck-Smoluchowski equation specified according to the parameterized equilibrium distribution. Numerical calculations clearly show that the asymptotic limit of large barriers does not agree with the results of the Kramers theory. The underlying reason is that the linear scaling of the potential, the procedure justifying the Kramers theory, cannot be applied when dealing with parameterized forms of the equilibrium distribution. A different kind of asymptotic analysis is then required and we introduce the appropriate theory when the equilibrium distribution is represented as a symmetric linear combination of two Gaussian functions: first in the one-dimensional case and afterward in the multidimensional diffusion model.

Simulating action-2D electronic spectroscopy of quantum dots: insights on the exciton and biexciton interplay from detection-mode and time-gating.

Action-2D electronic spectroscopy is emerging as a powerful technique to investigate exciton dynamics in molecular aggregates and nanostructures. While maintaining the power of highlighting coherent evolution between the laser pulses, action detection is based on measuring the incoherent signal proportional to the excited-state populations generated by an additional laser pulse. Numerical simulations of the action signal play a crucial role in aiding the interpretation of the spectral features, which may differ from those of the analog coherent technique in a non-trivial way. We present a numerical investigation of the action response of a model of quantum dot as a case study to unravel the exciton and biexciton contributions in the 2D-spectra of nanostructures. The simulation protocol is based on a non-perturbative treatment of the light-matter interaction by solving the Lindblad quantum master equation and the different contributions to the non-linear response are disentangled using a phase-modulation scheme. We analyze how the relative weights of the exciton and biexciton signals determine the lineshape of the spectrum, how they depend upon the physical nature of the detected signal, i.e., fluorescence or photocurrent, and on the relaxation dynamics during the detection-time. Compatibly with the experimental conditions, the choice of the detection-mode and the use of time-gating may eventually facilitate the evaluation of relevant parameters, such as the biexciton binding energy and the timescale of the biexciton relaxation.

Spectral shift, electronic coupling and exciton delocalization in nanocrystal dimers: insights from all-atom electronic structure computations.

Delocalization of excitons promoted by electronic coupling between clusters or quantum dots (QD) changes the dynamical processes in nanostructured aggregates enhancing energy transport. A spectroscopic shift of the absorption spectrum upon QD aggregation is commonly observed and ascribed to quantum mechanical coupling between neighbouring dots but also to exciton delocalization over the sulphur-based ligand shell or to other mechanisms as a change in the dielectric constant of the surrounding medium. We address the question of electronic coupling and exciton delocalization in nanocrystal aggregates by performing all-atom electronic structure calculations in models of colloidal QD dimers. The relation between spectral shift, interdot coupling and exciton delocalization is investigated in atomistic detail in models of dimers formed by CdSe clusters kept together by bridging organic ligands. Our results support the possibility of obtaining exciton delocalization over the dimer and point out the crucial role of the bridging ligand in enhancing interdot electronic coupling.

Stability of antibacterial Te(IV) compounds: A combined experimental and computational study.

Inorganic Te(IV) compounds are important cysteine protease inhibitors and antimicrobial agents; AS-101 [ammonium trichloro (dioxoethylene-O,O')tellurate] is the first compound of a family with formula NH4[C2H4Cl3O2Te], where a Te(IV) centre is bound to a chelate ethylene glycol, and showed several protective therapeutic applications. This compound is lacking in stability performance and is subjected to hydrolysis reaction with displacement of the diol ligand. In this paper, we report the stability trend of a series of analogues complexes of AS-101 with generic formula NH4[(RC2H3O2)Cl3Te], where R is an alkyl group with different chain length and different electronic properties, in order to find a correlation between structure and stability in aqueous-physiological conditions. The stability was studied in solution via multinuclear NMR spectroscopy (1H, 13C, 125Te) and computationally at the Density Functional Theory level with an explicit micro solvation model. The combined experimental and theoretical work highlights the essential role of the solvating environment and provides mechanistic insights into the complex decomposition reaction. Antimicrobial activity of the compounds was assessed against different bacterial strains.

Thermal Pure States for Finite and Isolated Quantum Systems.

We study an ensemble of quantum pure states, the thermalization resilient ensemble (TRE), providing the statistical characterization of the thermal equilibrium of isolated quantum systems. Following a previous work where the ensemble was defined based on the invariance of the average populations upon thermal contact of identical systems, here we introduce a general methodology to generate quantum states according to the TRE statistic. The sampling is employed to characterize the ensemble distribution of thermodynamic functions like the entropy, internal energy, and temperature. The possibility of defining the temperature also for isolated quantum systems with a limited number of degrees of freedom is a distinctive feature of the TRE statistic which has no counterpart in other quantum statistical ensembles. The results are illustrated by explicit calculations for spin model systems.

Implementation of Multivariable Logic Functions in Parallel by Electrically Addressing a Molecule of Three Dopants in Silicon.

To realize low-power, compact logic circuits, one can explore parallel operation on single nanoscale devices. An added incentive is to use multivalued (as distinct from Boolean) logic. Here, we theoretically demonstrate that the computation of all the possible outputs of a multivariate, multivalued logic function can be implemented in parallel by electrical addressing of a molecule made up of three interacting dopant atoms embedded in Si. The electronic states of the dopant molecule are addressed by pulsing a gate voltage. By simulating the time evolution of the non stationary electronic density built by the gate voltage, we show that one can implement a molecular decision tree that provides in parallel all the outputs for all the inputs of the multivariate, multivalued logic function. The outputs are encoded in the populations and in the bond orders of the dopant molecule, which can be measured using an STM tip. We show that the implementation of the molecular logic tree is equivalent to a spectral function decomposition. The function that is evaluated can be field-programmed by changing the time profile of the pulsed gate voltage.

Implementation of Probabilistic Algorithms by Multi-chromophoric Molecular Networks with Application to Multiple Travelling Pathways.

The implementation of probabilistic algorithms by deterministic hardware is demanding and requires hundreds of instructions to generate a pseudo-random sequence of numbers. On the contrary, the dynamics at the molecular scale is physically governed by probabilistic laws because of the stochastic nature of thermally activated and quantum processes. By simulating the exciton transfer dynamics in a multi-chromophoric system, we demonstrate the implementation of a random walk that samples the possible pathways of a traveler through a network and can be probed by time-resolved fluorescence spectroscopy. The ability of controlling the spatial arrangement of the chromophores allows us to design the "landscape" in which the traveler is moving and therefore to program the molecular device.

A Probabilistic Finite State Logic Machine Realized Experimentally on a Single Dopant Atom.

Exploiting the potential of nanoscale devices for logic processing requires the implementation of computing functionalities departing from the conventional switching paradigm. We report on the design and the experimental realization of a probabilistic finite state machine in a single phosphorus donor atom placed in a silicon matrix electrically addressed and probed by scanning tunneling spectroscopy (STS). The single atom logic unit simulates the flow of visitors in a maze whose topology is determined by the dynamics of the electronic transport through the states of the dopant. By considering the simplest case of a unique charge state for which three electronic states can be resolved, we demonstrate an efficient solution of the following problem: in a maze of four connected rooms, what is the optimal combination of door opening rates in order to maximize the time that visitors spend in one specific chamber? The implementation takes advantage of the stochastic nature of electron tunneling, while the output remains the macroscopic current whose reading can be realized with standard techniques and does not require single electron sensitivity.

Quantum Statistical Ensemble Resilient to Thermalization.

The sampling of the wave function within a suitable ensemble is an important tool in the statistical analysis of a molecule interacting with its environment. The uniform statistical distribution of quantum pure states in an active space is often the privileged choice. However, such a distribution with constant average populations of eigenstates is not preserved upon the interaction between quantum systems. This appears as a severe methodological shortcoming, as long as a quantum system can be always considered as the result of interactions among previously isolated subsystems. In the present work we formulate an alternative statistical ensemble of pure states that is robust with respect to interaction, and it is thus preserved when subsystems are merged. It is derived from the condition of invariance of the average populations upon interaction between quantum systems in the same thermal state. These average populations allow a simple identification of the thermodynamic properties of the system. We find that such a statistical distribution is robust with respect to interaction of systems at different temperatures reproducing the thermalization of macroscopic bodies, and for this reason we identify it as the Thermalization Resilient Ensemble.

Force measurements reveal how small binders perturb the dissociation mechanisms of DNA duplex sequences.

The force-driven separation of double-stranded DNA is crucial to the accomplishment of cellular processes like genome transactions. Ligands binding to short DNA sequences can have a local stabilizing or destabilizing effect and thus severely affect these processes. Although the design of ligands that bind to specific sequences is a field of intense research with promising biomedical applications, so far, their effect on the force-induced strand separation has remained elusive. Here, by means of AFM-based single molecule force spectroscopy, we show the co-existence of two different mechanisms for the separation of a short DNA duplex and demonstrate how they are perturbed by small binders. With the support of Molecular Dynamics simulations, we evidence that above a critical pulling rate one of the dissociation pathways becomes dominant, with a dramatic effect on the rupture forces. Around the critical threshold, we observe a drop of the most probable rupture forces for ligand-stabilized duplexes. Our results offer a deep understanding of how a stable DNA-ligand complex behaves under force-driven strand separation.

Information processing in parallel through directionally resolved molecular polarization components in coherent multidimensional spectroscopy.

We propose that information processing can be implemented by measuring the directional components of the macroscopic polarization of an ensemble of molecules subject to a sequence of laser pulses. We describe the logic operation theoretically and demonstrate it by simulations. The measurement of integrated stimulated emission in different phase matching spatial directions provides a logic decomposition of a function that is the discrete analog of an integral transform. The logic operation is reversible and all the possible outputs are computed in parallel for all sets of possible multivalued inputs. The number of logic variables of the function is the number of laser pulses used in sequence. The logic function that is computed depends on the chosen chromophoric molecular complex and on its interactions with the solvent and on the two time intervals between the three pulses and the pulse strengths and polarizations. The outputs are the homodyne detected values of the polarization components that are measured in the allowed phase matching macroscopic directions, kl, kl=∑iliki where ki is the propagation direction of the ith pulse and {li} is a set of integers that encodes the multivalued inputs. Parallelism is inherently implemented because all the partial polarizations that define the outputs are processed simultaneously. The outputs, which are read directly on the macroscopic level, can be multivalued because the high dynamical range of partial polarization measurements by nonlinear coherent spectroscopy allows for fine binning of the signals. The outputs are uniquely related to the inputs so that the logic is reversible.

Parallel and Multivalued Logic by the Two-Dimensional Photon-Echo Response of a Rhodamine−DNA Complex.

Implementing parallel and multivalued logic operations at the molecular scale has the potential to improve the miniaturization and efficiency of a new generation of nanoscale computing devices. Two-dimensional photon-echo spectroscopy is capable of resolving dynamical pathways on electronic and vibrational molecular states. We experimentally demonstrate the implementation of molecular decision trees, logic operations where all possible values of inputs are processed in parallel and the outputs are read simultaneously, by probing the laser-induced dynamics of populations and coherences in a rhodamine dye mounted on a short DNA duplex. The inputs are provided by the bilinear interactions between the molecule and the laser pulses, and the output values are read from the two-dimensional molecular response at specific frequencies. Our results highlights how ultrafast dynamics between multiple molecular states induced by light−matter interactions can be used as an advantage for performing complex logic operations in parallel, operations that are faster than electrical switching.

Atomistic account of structural and dynamical changes induced by small binders in the double helix of a short DNA.

Nucleic acids are flexible molecules and their dynamical properties play a key role in molecular recognition events. Small binders interacting with DNA fragments induce both structural and dynamical changes in the double helix. We study the dynamics of a DNA dodecamer and of its complexes with Hoechst 33258, which is a minor groove binder, and with the ethidium cation, which is an intercalator, by molecular dynamics simulation. The thermodynamics of DNA-drug interaction is evaluated in connection with the structure and the dynamics of the resulting complexes. We identify and characterize the relevant changes in the configurational distribution of the DNA helix and relate them to the corresponding entropic contributions to the binding free energy. The binder Hoechst locks the breathing motion of the minor groove inducing a reduction of the configurational entropy of the helix, which amounts to 20 kcal mol(-1). In contrast, intercalations with the ethidium cation enhance the flexibility of the double helix. We show that the balance between the energy required to deform the helix for the intercalation and the gain in configurational entropy is the origin of cooperativity in the binding of a second ethidium and of anti-cooperativity in the binding of a third one. The results of our study provide an understanding of the relation between structure, dynamics and energetics in the interaction between DNA fragments and small binders, highlighting the role of dynamical changes and consequent variation of the configurational entropy of the DNA double helix for both types of binders.

Molecular decision trees realized by ultrafast electronic spectroscopy.

The outcome of a light-matter interaction depends on both the state of matter and the state of light. It is thus a natural setting for implementing bilinear classical logic. A description of the state of a time-varying system requires measuring an (ideally complete) set of time-dependent observables. Typically, this is prohibitive, but in weak-field spectroscopy we can move toward this goal because only a finite number of levels are accessible. Recent progress in nonlinear spectroscopies means that nontrivial measurements can be implemented and thereby give rise to interesting logic schemes where the outputs are functions of the observables. Lie algebra offers a natural tool for generating the outcome of the bilinear light-matter interaction. We show how to synthesize these ideas by explicitly discussing three-photon spectroscopy of a bichromophoric molecule for which there are four accessible states. Switching logic would use the on-off occupancies of these four states as outcomes. Here, we explore the use of all 16 observables that define the time-evolving state of the bichromophoric system. The bilinear laser-system interaction with the three pulses of the setup of a 2D photon echo spectroscopy experiment can be used to generate a rich parallel logic that corresponds to the implementation of a molecular decision tree. Our simulations allow relaxation by weak coupling to the environment, which adds to the complexity of the logic operations.

Beyond quantum microcanonical statistics.

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e., the wavefunction, of an isolated system is determined to calculate molecular properties and their time evolution according to the unitary Schrödinger equation. On the other hand a mixed state, i.e., a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem.

Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory.

Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework is introduced to clarify the connections between a purely mechanical description and the thermodynamic characterization of the equilibrium state of an isolated quantum system. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects in the description of isolated quantum systems. Like in the classical statistical mechanics, the equilibrium distribution of any property is identified on the basis of the time evolution of the considered system. As a consequence equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schrodinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.