Coherent Electron Research Articles

Long-Lived Electronic Coherences in Molecules.

We demonstrate long-lived electronic coherences in molecules using a combination of measurements with shaped octave spanning ultrafast laser pulses and calculations of the light matter interaction. Our pump-probe measurements prepare and interrogate entangled nuclear-electronic wave packets whose electronic phase remains well defined despite vibrational motion along many degrees of freedom. The experiments and calculations illustrate how coherences between excited states can survive, even when coherence with the ground state is lost, and may have important implications for many areas of attosecond science and photochemistry.

Quantum wavefront shaping with a 48-element programmable phase plate for electrons

We present a 48-element programmable phase plate for coherent electron waves produced by a combination of photolithography and focused ion beam. This brings the highly successful concept of wavefront shaping from light optics into the realm of electron optics and provides an important new degree of freedom to prepare electron quantum states. The phase plate chip is mounted on an aperture rod placed in the C2 plane of a transmission electron microscope operating in the 100-300 kV range. The phase plate’s behavior is characterized by a Gerchberg-Saxton algorithm, showing a phase sensitivity of 0.075 rad/mV at 300 kV, with a phase resolution of approximately 3$1010^{-3} $. In addition, we provide a brief overview of possible use cases and support it with both simulated and experimental results.

Universal Conductance Fluctuations in a MnBi2Te4 Thin Film.

Quantum coherence of electrons can produce striking behaviors in mesoscopic conductors. Although magnetic order can also strongly affect transport, the combination of coherence and magnetic order has been largely unexplored. Here, we examine quantum coherence-driven universal conductance fluctuations in the antiferromagnetic, canted antiferromagnetic, and ferromagnetic phases of a thin film of the topological material MnBi2Te4. In each magnetic phase, we extract a charge carrier phase coherence length of about 100 nm. The conductance magnetofingerprint is repeatable when sweeping applied magnetic field within one magnetic phase. Surprisingly, in the antiferromagnetic and canted antiferromagnetic phases, but not in the ferromagnetic phase, the magnetofingerprint depends on the direction of the field sweep. To explain our observations, we suggest that conductance fluctuation measurements are sensitive to the motion and nucleation of magnetic domain walls in MnBi2Te4.

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.

Understanding Current Density in Molecules Using Molecular Orbitals.

While the use of molecular orbitals (MOs) and their isosurfaces to explain physical phenomena in chemical systems is a time-honored tool, we show that the nodes are an equally important component for understanding the current density through single-molecule junctions. We investigate three different model systems consisting of an alkane, alkene, and even [n]cumulene and show that we can explain the form of the current density using the MOs of the molecule. Essentially, the MOs define the region in which current can flow and their gradients define the direction in which current flows within that region. We also show that it is possible to simplify the current density for improved understanding by either partitioning the current density into more chemically intuitive parts, such as σ- and π-systems, or by filtering out MOs with negligible contributions to the overall current density. Our work highlights that it is possible to infer a non-equilibrium property (current density) given only equilibrium properties (MOs and their gradients), and this, in turn, grants deeper insight into coherent electron transport.

High-resolution nanoscale NMR for arbitrary magnetic fields

Nitrogen vacancy (NV) centers are a major platform for the detection of nuclear magnetic resonance (NMR) signals at the nanoscale. To overcome the intrinsic electron spin lifetime limit in spectral resolution, a heterodyne detection approach is widely used. However, application of this technique at high magnetic fields is yet an unsolved problem. Here, we introduce a heterodyne detection method utilizing a series of phase coherent electron nuclear double resonance sensing blocks, thus eliminating the numerous Rabi microwave pulses required in the detection. Our detection protocol can be extended to high magnetic fields, allowing chemical shift resolution in NMR experiments. We demonstrate this principle on a weakly coupled 13C nuclear spin in the bath surrounding single NV centers, and compare the results to existing heterodyne protocols. Additionally, we identify the combination of NV-spin-initialization infidelity and strong sensor-target-coupling as linewidth-limiting decoherence source, paving the way towards high-field heterodyne NMR protocols with chemical resolution.

Coherent ultrafast photoemission from a single quantized state of a one-dimensional emitter.

Femtosecond laser-driven photoemission source provides an unprecedented femtosecond-resolved electron probe not only for atomic-scale ultrafast characterization but also for free-electron radiation sources. However, for conventional metallic electron source, intense lasers may induce a considerable broadening of emitting energy level, which results in large energy spread (>600 milli-electron volts) and thus limits the spatiotemporal resolution of electron probe. Here, we demonstrate the coherent ultrafast photoemission from a single quantized energy level of a carbon nanotube. Its one-dimensional body can provide a sharp quantized electronic excited state, while its zero-dimensional tip can provide a quantized energy level act as a narrow photoemission channel. Coherent resonant tunneling electron emission is evidenced by a negative differential resistance effect and a field-driven Stark splitting effect. The estimated energy spread is ~57 milli-electron volts, which suggests that the proposed carbon nanotube electron source may promote electron probe simultaneously with subangstrom spatial resolution and femtosecond temporal resolution.

Short-Range Charge Transfer in DNA Base Triplets: Real-Time Tracking of Coherent Fluctuation Electron Transfer.

The short-range charge transfer of DNA base triplets has wide application prospects in bioelectronic devices for identifying DNA bases and clinical diagnostics, and the key to its development is to understand the mechanisms of short-range electron dynamics. However, tracing how electrons are transferred during the short-range charge transfer of DNA base triplets remains a great challenge. Here, by means of ab initio molecular dynamics and Ehrenfest dynamics, the nuclear-electron interaction in the thymine-adenine-thymine (TAT) charge transfer process is successfully simulated. The results show that the electron transfer of TAT has an oscillating phenomenon with a period of 10 fs. The charge density difference proves that the charge transfer proportion is as high as 59.817% at 50 fs. The peak position of the hydrogen bond fluctuates regularly between -0.040 and -0.056. The time-dependent Marcus-Levich-Jortner theory proves that the vibrational coupling between nucleus and electron induces coherent electron transfer in TAT. This work provides a real-time demonstration of the short-range coherent electron transfer of DNA base triplets and establishes a theoretical basis for the design and development of novel biological probe molecules.

A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics.

Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet dynamics.

A multi-state mapping approach to surface hopping.

We describe a multiple electronic state adaptation of the mapping approach to surface hopping introduced recently by Mannouch and Richardson [J. Chem. Phys. 158, 104111 (2023)]. Our modification treats populations and coherences on an equal footing and is guaranteed to give populations in any electronic basis that tend to the correct quantum-classical equilibrium values in the long-time limit (assuming ergodicity). We demonstrate its accuracy by comparison with exact benchmark results for three- and seven-state models of the Fenna-Matthews-Olson complex, obtaining electronic populations and coherences that are significantly more accurate than those of fewest switches surface hopping and at least as good as those of any other semiclassical method we are aware of. Since these results were obtained by adapting the scheme of Mannouch and Richardson, we go on to compare our results with theirs for a variety of problems with two electronic states. We find that their method is sometimes more accurate, especially in the Marcus inverted regime. However, in other situations, the accuracies are comparable, and since our scheme can be used with multiple electronic states it can be applied to a wider variety of electronically nonadiabatic systems.

Quantum dynamics simulations of the 2D spectroscopy for exciton polaritons.

We develop an accurate and numerically efficient non-adiabatic path-integral approach to simulate the non-linear spectroscopy of exciton-polariton systems. This approach is based on the partial linearized density matrix approach to model the exciton dynamics with explicit propagation of the phonon bath environment, combined with a stochastic Lindblad dynamics approach to model the cavity loss dynamics. Through simulating both linear and polariton two-dimensional electronic spectra, we systematically investigate how light-matter coupling strength and cavity loss rate influence the optical response signal. Our results confirm the polaron decoupling effect, which is the reduced exciton-phonon coupling among polariton states due to the strong light-matter interactions. We further demonstrate that the polariton coherence time can be significantly prolonged compared to the electronic coherence outside the cavity.

Sub-8-fs pulses in the visible to near-infrared by a degenerate optical parametric amplifier.

This work presents a single-stage optical parametric amplifier (OPA) operating at degeneracy (DOPA) and pumped by the third harmonic of a Yb:KGW laser system. This DOPA exploits the broad amplification bandwidth that occurs with type-I phase-matching in β-barium borate (BBO) when signal and idler overlap in the spectrum. The output pulses span from 590 to 780 nm (1.59-2.10 eV) with 7.75-fs duration after compression. Ultrashort pulses with similar bandwidths in this spectral window complement the existing array of optical parametric amplifiers that cover either the visible or the near-IR spectral regions with sub-10-fs pulses. This source of ultrashort optical pulses will enable the application of sophisticated spectroscopy techniques to the study of electronic coherences and energy migration pathways in biological, chemical, and condensed matter systems.

Effects of electronic-vibrational resonance on the absorption and two-dimensional rephasing spectra of the Fenna–Matthews–Olson complex

The absorption and two-dimensional rephasing spectra of the Fenna–Matthews–Olson (FMO) complex at 77 K have been simulated using the hierarchical equations of motion method. Three cases of vibrational coupling have been studied in the FMO complex model. In the first case, no specific vibrational mode is coupled. In the second and third cases, low-energy and high-energy electronic-vibrational resonance dimers are considered in the model, respectively. It has been observed that the vibrational mode significantly weakens the intensity of the absorption peak of resonant high-energy electronic transitions. We have also confirmed that long-lived quantum beatings originate from vibration, while short-lived electronic coherence still persists. Furthermore, although the electronic resonance mode speeds up the rephasing dynamics, it is not directly proportional to the coupling strength. The low-energy electronic-vibrational resonance dimer exhibits a greater speed-up of rephasing dynamics.

Time-Frequency Signatures of Electronic Coherence of Colloidal CdSe Quantum Dot Dimer Assemblies Probed at Room Temperature by Two-Dimensional Electronic Spectroscopy.

Electronic coherence signatures can be directly identified in the time-frequency maps measured in two-dimensional electronic spectroscopy (2DES). Here, we demonstrate the theory and discuss the advantages of this approach via the detailed application to the fast-femtosecond beatings of a wide variety of electronic coherences in ensemble dimers of quantum dots (QDs), assembled from QDs of 3 nm in diameter, with 8% size dispersion in diameter. The observed and computed results can be consistently characterized directly in the time-frequency domain by probing the polarization in the 2DES setup. The experimental and computed time-frequency maps are found in very good agreement, and several electronic coherences are characterized at room temperature in solution, before the extensive dephasing due to the size dispersion begins. As compared to the frequency-frequency maps that are commonly used in 2DES, the time-frequency maps allow exploiting electronic coherences without additional post-processing and with fewer 2DES measurements. Towards quantum technology applications, we also report on the modeling of the time-frequency photocurrent response of these electronic coherences, which paves the way to integrating QD devices with classical architectures, thereby enhancing the quantum advantage of such technologies for parallel information processing at room temperature.

Disentangling the complexity of coupled vibrations by two-dimensional electronic-vibrational spectroscopy

We employ two-dimensional electronic-vibrational (2DEV) spectroscopy to study the coherent dynamics of coupled vibrational modes in an excitonically-coupled dimer model. The advantage of separating excitation and detection in different frequency regimes allows us to directly probe the electronic and vibrational coherences in the time-evolved 2DEV spectra. The complexity of vibrational coherence of two coupled modes is directly revealed by cross peaks in the 2DEV spectra. With the help of the ensuing time traces, we can follow how the vibrational coherence changes over time in the monomer model and, subsequently, in the dimer model. We show that the complexity of two coupled vibrational modes and the interaction between electronic and vibrational coherences in molecular systems can be effectively disentangled using the 2DEV spectroscopy technique.

Ultracoherent Single-Electron Emission of Carbon Nanotubes.

A single-electron emitter, based on a single quantized energy level, can potentially achieve ultimate temporal and spatial coherence with a large emission current, which is desirable for atomic-resolution electron probes. This is first developed by constructing a nano-object on a metal tip to form a quantized double barrier structure. However, the single-electron-emission current can only achieve a picoampere level due to the low electron tunneling rate of the heterojunction with large barrier width, which limits the practical applications. In this study, carbon nanotubes (CNTs) serve as a single-electron emitter and a current up to 1.5nA is demonstrated. The double barrier structure formed on the CNT tip enables a high tunneling rate (≈1012 s-1 ) due to the smaller barrier width. The emitter also shows high temporal coherence (energy dispersion of ≈10meV) and spatial coherence (effective source radius of ≈0.85nm). This work represents a highly coherent electron source to simplify the electron optics system of atomic-resolution electron microscopy and sub-10nm electron beam lithography.

Cover Feature: Observation of a Long‐lived Electronic Coherence Modulated by Vibrational Dynamics in Molecular Nd3+‐Complexes at Room Temperature (ChemPhysChem 12/2023)

The Cover Feature illustrates the creation and probing of a long-lived electronic coherence in molecular Nd-complexes by IR femtosecond laser pulses. The electronic coherence is observed via the Δτ-dependent modulation of the fluorescence signal and shows the influence of additional vibrational dynamics. The Nd-complexes may serve as prototypes for possible future applications in quantum information technology. More information can be found in the Research Article by Hendrike Braun and co-workers.

Improved calibration of rf cavities for relativistic electron beams: Effects of secondary corrections and experimental verification

In the aspect of longitudinal beam bunching, the bunching strength can be controlled by the rf cavity phase and voltage. However, these machine parameters are different from those that interact with the beam itself. In order to gain control of the beam-cavity interaction, cavity calibration must be performed. Furthermore, it relies on fitting the beam energy gain versus cavity phase to a calibration function. Under the conventional assumption of relativistic beam conditions, the calibration function is a first harmonic sinusoidal function (a sinusoidal function with a period of $2\ensuremath{\pi}$). However, this expression is insufficient for a high-voltage bunching cavity. Due to beam acceleration inside the cavity, an energy bias and a second harmonic function should be included to modify the conventional calibration function, even for a relativistic electron beam. In this paper, we will derive this modification and provide a comparison to both the Coherent Electron Cooling Experiment and the impact-t simulation, respectively.

Theoretical Description of Attosecond X-ray Absorption Spectroscopy of Frenkel Exciton Dynamics.

Frenkel excitons are responsible for the transport of light energy in many molecular systems. Coherent electron dynamics govern the initial stage of Frenkel-exciton transfer. Capability to follow coherent exciton dynamics in real time will help to reveal their actual contribution to the efficiency of light-harvesting. Attosecond X-ray pulses are the tool with the necessary temporal resolution to resolve pure electronic processes with atomic sensitivity. We describe how attosecond X-ray pulses can probe coherent electronic processes during Frenkel-exciton transport in molecular aggregates. We analyze time-resolved absorption cross section taking broad spectral bandwidth of an attosecond pulse into account. We demonstrate that attosecond X-ray absorption spectra can reveal delocalization degree of coherent exciton transfer dynamics.

Thermal entanglement and quantum coherence of a single electron in a double quantum dot with Rashba interaction

In this work, we study the thermal quantum coherence and fidelity in a semiconductor double quantum dot. The device consists of a single electron in a double quantum dot with Rashba spin-orbit coupling in the presence of an external magnetic field. In our scenario, the thermal entanglement of the single electron is driven by the charge and spin qubits, the latter controlled by Rashba coupling. Analytical expressions are obtained for thermal concurrence and correlated coherence using the density matrix formalism. The main goal of this work is to provide a good understanding of the effects of temperature and several parameters in quantum coherence. In addition, our findings show that we can use the Rashba coupling to tune in the thermal entanglement, quantum coherence, as well as, the thermal fidelity behavior of the system. Moreover, we focus on the role played by thermal entanglement and correlated coherence responsible for quantum correlations. We observe that the correlated coherence is more robust than the thermal entanglement in all cases, so quantum algorithms based only on correlated coherence may be stronger than those based on entanglement.