The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.

Plasmons in metal nanoparticles (MNPs) promise to enhance solar energy conversion in semiconductors. Two essential mechanisms of enhancement in the near-field regime are hot electron injection (HEI) and plasmon-induced resonance energy transfer (PIRET). Individual studies of both mechanisms indicate that the PIRET efficiency is limited by the short lifetime of the plasmon, whereas the hot electrons result from the plasmon decay. The development of a unified theory of the coupled HEI and PIRET processes is fundamentally interesting and necessary for making reliable predictions but is complicated by the multiple interactions between various components that participate in the enhancement process. In this paper, we use the model-Hamiltonian approach to develop a combined theoretical framework including both PIRET and HEI. The coupled dynamics as well as the time evolution of hot electron energy distribution are studied. The theory further predicts an interference-induced asymmetry in the spectral dependence of PIRET, which can be used to distinguish it from HEI. As the relative contributions of PIRET and HEI strongly depend on the size of the MNPs, this presents itself as a simple route to control the strength of their contributions. The results presented here can further guide future applications of plasmonic solar energy harvesting.

Plasmon-generated hot carriers are currently being studied intensively for their role in enhancing the efficiency of photovoltaic and photocatalytic processes. Theoretical studies of the hot electrons subsystem have generated insight, but we show that a unified quantum-mechanical treatment of the plasmon and hot electrons reveals new physical phenomena. Instead of a unidirectional energy transfer process in Landau damping, back energy transfer is predicted in small metal nanoparticles (MNPs) within a model-Hamiltonian approach. As a result, the single Lorentzian plasmonic line shape is modulated by a multipeak structure, whose individual line width provides a direct way to probe the electronic dephasing. More importantly, the hot electron generation can be enhanced greatly by matching the incident energy to the peaks of the modulated line shape.

Plasmon resonances in metal nanoparticles (MNPs) can be used to enhance the efficiency of photoinduced electron transfer from a sensitizer (a molecule or a quantum dot (QD)) to a semiconductor electrode. Here we use a model Hamiltonian approach to study the optical response and the steady state electron injection rate (SSIR) of a hybrid system, consisting of a sensitizer that is coupled to a metal nanoparticle via dipole coupling and to a semiconductor electrode via electronic coupling. Counterintuitively, the total absorption cross section for the coupled system and the SSIR are correlated only for small coupling; in the relevant domain of large enhancement we observe anticorrelation. A maximum SSIR as a function of the dipole coupling strength is predicted analytically, and shown to result from the competition between the plasmonic field enhancement and the Purcell effect. In the case of pulsed excitation, the appearance of a Fano resonance and its reversal is illustrated as the dipole coupling strength grows, and for strong couplings Rabi splitting is observed. Interestingly, in the case of continuous wave (CW) excitation, we find plasmon-induced resonance energy transfer, leading to strong SSIR at incident light frequencies that are far detuned from the sensitizer transition frequency and are fully controllable.

A data-analytical approach that can extract the history and dynamics of complex systems from noisy snapshots on timescales much shorter than the uncertainty with which the data were recorded is described; the approach is demonstrated by extracting the dynamics on the few-femtosecond timescale from experimental data recorded with 300-femtosecond timing uncertainty. When reconstructing climate histories from ice cores or ultrafast dynamics from X-ray free-electron laser (XFEL) experiments, the uncertain time stamps can muddle the sequence of events, making it difficult to recover accurate dynamical information. These authors introduce a data analysis technique, based on nonlinear Laplacian spectral analysis, that circumvents this problem and is capable of extracting dynamical information from noisy data despite the timing uncertainties. They demonstrate reconstruction of few-femtosecond dynamics using XFEL data with 300-femtosecond timing uncertainty. In principle, this approach could be useful in all measurements plagued by time uncertainty, so might find applications from geoscience to gravitational physics. Imperfect knowledge of the times at which ‘snapshots’ of a system are recorded degrades our ability to recover dynamical information, and can scramble the sequence of events. In X-ray free-electron lasers, for example, the uncertainty—the so-called timing jitter—between the arrival of an optical trigger (‘pump’) pulse and a probing X-ray pulse can exceed the length of the X-ray pulse by up to two orders of magnitude1, marring the otherwise precise time-resolution capabilities of this class of instruments. The widespread notion that little dynamical information is available on timescales shorter than the timing uncertainty has led to various hardware schemes to reduce timing uncertainty2,3,4. These schemes are expensive, tend to be specific to one experimental approach and cannot be used when the record was created under ill-defined or uncontrolled conditions such as during geological events. Here we present a data-analytical approach, based on singular-value decomposition and nonlinear Laplacian spectral analysis5,6,7, that can recover the history and dynamics of a system from a dense collection of noisy snapshots spanning a sufficiently large multiple of the timing uncertainty. The power of the algorithm is demonstrated by extracting the underlying dynamics on the few-femtosecond timescale from noisy experimental X-ray free-electron laser data recorded with 300-femtosecond timing uncertainty1. Using a noisy dataset from a pump-probe experiment on the Coulomb explosion of nitrogen molecules, our analysis reveals vibrational wave-packets consisting of components with periods as short as 15 femtoseconds, as well as more rapid changes, which have yet to be fully explored. Our approach can potentially be applied whenever dynamical or historical information is tainted by timing uncertainty.

Recent experiments have shown that the efficiency of photoinduced electron transfer from sensitizers (molecules or quantum dots) to semiconductors can be enhanced by coupling the sensitizers to plasmon resonances in metal nanoparticles. Here, we use a model-Hamiltonian approach to show theoretically that there is an optimal coupling between the sensitizer and plasmons that maximizes the electron-transfer efficiency. This optimum results from the competition between electron transfer, plasmon relaxation, and plasmon decoherence. For coupling values that exceed the optimal value, the dynamics of electron transfer from the sensitizer to the semiconductor can be significantly modified due to the sensitizer–plasmon coupling.

We introduce analytical models of torsional alignment by moderately intense laser pulses that are applicable to the limiting cases of the torsional barrier heights. Using these models, we explore in detail the role that the laser intensity and pulse duration play in coherent torsional dynamics, addressing both experimental and theoretical concerns. Our results suggest strategies for minimizing the risk of off-resonant ionization, noting the qualitative differences between the case of torsional alignment subject to a field-free torsional barrier and that of torsional alignment of a barrier-less system (equivalent to a 2D rigid rotor). We also investigate several interesting torsional phenomena, including the onset of impulsive alignment of torsions, field-driven oscillations in quantum number space, and the disappearance of an alignment upper bound observed for a rigid rotor in the impulsive torsional alignment limit.

This paper describes analytical and numerical results from a model Hamiltonian method applied to electron transfer (ET) from a quasicontinuum (QC) of states to a set of discrete states, with and without a mediating bridge. Analysis of the factors that determine ET dynamics yields guidelines for achieving high-yield electron transfer in these systems, desired for instance for applications in heterogeneous catalysis. These include the choice of parameters of the laser pulse that excites the initial state into a continuum electronic wavepacket and the design of the coupling between the bridge molecule and the donor and acceptor. The vibrational mode on a bridging molecule between donor and acceptor has an influence on the yield of electron transfer via Franck-Condon factors, even in cases where excited vibrational states are only transiently populated. Laser-induced coherence of the initial state as well as energetic overlap is crucial in determining the ET yield from a QC to a discrete state, whereas the ET time is influenced by competing factors from the coupling strength and the coherence properties of the electronic wavepacket.

We present a model for strong field coherent control of torsional modes of molecules with a focus on exploring the controllability of molecular torsions subject to dissipative media and understanding how phase information is exchanged between torsional modes and a dissipative environment. Our theory is based on a density matrix formalism, wherein dissipation is accounted for within a multilevel Bloch equation model. Our results point to new and interesting phenomena in wavepacket dissipation dynamics that are unique to torsions and also enrich our general understanding of wavepacket phenomena. In addition, we suggest guidelines for designing torsional control experiments for molecules interacting with a dissipative bath.

We propose and illustrate numerically the possibility of imaging rotational wave packets in angular space and time by using different pump-probe spectroscopic techniques. A general theoretical framework to perform such rotational mapping is derived and three specific spectroscopies, namely, birefringence, high harmonic generation, and angle-resolved photoelectron spectroscopy, are numerically explored. All three approaches are shown to provide direct mapping of the rotational coherences of molecules but they are not equivalent; comparison of their results yields interesting insights into their relative merits. Finally, we illustrate the role played by the symmetry of the molecular orbitals in determining the quality of the images generated by high harmonic and photoelectron signals. The potential of rotational imaging as a route to both intramolecular coupling mechanisms and the interaction of molecules with different environments is discussed. DOI: 10.1103/PhysRevA.87.023411

We discuss several interesting phenomena in the dynamics of strong field-triggered torsional wavepackets, which carry implications for the problem of torsional alignment in nonrigid molecules. Our results point to the origin and consequences of the fundamental differences between rotational and torsional coherences. In addition, we provide design guidelines for torsional control experiments by illustrating the role played by the laser intensity, pulse width, temperature, and molecular parameters. Specifically, as an example of several classes of molecules expected to make suitable candidates for laboratory experiments, we explore the torsional control of 9-[2-(anthracen-9-yl)ethynyl]anthracene and contrast it with that of biphenyl. Finally, we propose several potential applications for coherent torsional control in chemistry, physics, and material science.

1 DESY, Notkestr. 85, 22607 Hamburg, Germany 2 Department of Chemistry, University of Leicester, University Road, Leicester, LE1 7RH, UK 3 Department of Physics and Astronomy, University of Leicester, University Road, Leicester, LE1 7RH, UK 4 Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA 5 Helmholtz-Institute Jena, Max-Wien-Platz 1, 07743 Jena, Germany

We show that high harmonic generation is the most sensitive probe of rotational wave packet revivals, revealing very high-order rotational revivals for the first time using any probe. By fitting high-quality experimental data to an exact theory of high harmonic generation from aligned molecules, we can extract the underlying electronic dipole elements for high harmonic emission and uncover that the electron gains angular momentum from the photon field.

We introduce a time-domain approach to explore rotational dynamics caused by intramolecular coupling or the interaction with dissipative media. It pushes the time resolution toward the ultimate limit determined by the rotational period. Femtosecond pulses create a coherent superposition of two rotational states of carbon monoxide. The wave-packet motion is observed by subsequent Coulomb explosion, which results in a time-dependent asymmetry of spatial fragmentation patterns. The asymmetry oscillation prevails for at least 1 ns, covering more than 300 periods with no decoherence. Long time scans will allow weak perturbations of the order of Delta E/E = 10(-4) to be discerned. Our conclusions are confirmed by a fully quantum-mechanical model.

A theory of time-resolved photoelectron spectroscopy from coherent rotational wavepackets is developed within a density matrix framework, expressing the signal as a partial wave series of rotational operators that tie the underlying electronic and rotational dynamics. The theory is applied to suggest and explore two potential applications of time- and angle-resolved photoelectron signals. First, we consider the possibility of extracting the bound-free electronic dipole matrix elements that underlie the ionization process from experimental data. Next, we investigate the extent to which photoelectron images could serve to map the time-evolving rotational probability distribution, thus providing insights into rotational coherences.

We explore the information content of the polarization of high-order harmonics emitted from aligned molecules driven by a linearly polarized field. The study builds upon our previous work [Ramakrishna et al., Phys. Rev. A 81, 021802(R) (2010)], which illustrated that the phase of the continuum electronic wave function, and hence the underlying molecular potential, is responsible, at least in part, for the ellipticity observed in harmonic spectra. We use a simple model potential and systematically vary the potential parameters to investigate the sense in which, and the degree to which, the shape of the molecular potential is imprinted onto the polarization of the emitted harmonics. Strong ellipticity is observed over a wide range of potential parameters, suggesting that the emission of elliptically polarized harmonics is a general phenomenon, yet qualitatively determined by the molecular properties. The sensitivity of the ellipticity to the model parameters invites the use of ellipticity measurements as a probe of the continuum wave function and the underlying molecular potential.

We address theoretically and numerically the possibility of observing ellipticity in high-order harmonic generation (HHG) from aligned molecules driven by linearly polarized fields---a subject of controversy in the recent literature with significant implications. To that end we develop a numerical method for solution of the electronic dynamics and extend a recently developed theory of HHG from aligned molecules. Our numerical results are in good agreement with recent experimental data. The theory explains analytically several observations of polarization experiments. We note the conditions under which ellipticity can be observed and the information content of elliptically polarized harmonics regarding the molecular system.

We study the fluorescence emitted from filaments in air using a pump-probe scheme with a femtosecond Ti-sapphire laser. The fluorescence intensities from the first negative band (B-2 Sigma(+)(u) -> X-2 Sigma(+)(g)) and the second positive band (C-3 Pi(u) -> B-3 Pi(g)) show enhancement and change periodically as a function of the pump-probe time delay. We attribute this phenomenon to the universal yet probably forgotten phenomenon of population trapping of nitrogen molecules in highly excited states together with field-induced alignment of nitrogen molecules followed by revivals of the rotational wavepackets. Theoretical calculation of the alignment dynamics of nitrogen molecules is consistent with the experimental data.