Nonadiabatic Tunneling Research Articles

Coulomb focusing in attosecond angular streaking

Angular streaking technique employs a close-to-circularly polarized laser pulse to build a mapping between the instant of maximum ionization and the most probable emission angle in the photoelectron momentum distribution, thereby enabling the probe of laser-induced electron dynamics in atoms and molecules with attosecond temporal resolution. Here, through the jointed experimental observations and improved Coulomb-corrected strong-field approximation statistical simulations, we identify that electrons emitted at different initial ionization times converge to the most probable emission angle due to the previously-unexpected Coulomb focusing triggered by the nonadiabatic laser-induced electron tunneling. We reveal that the Coulomb focusing induces the observed nonintuitive energy-dependent trend in the angular streaking measurements on the nonadiabatic tunneling, and that tunneling dynamics under the classically forbidden barrier can leave fingerprints on the resulting signals. Our findings have significant implications for the decoding of the intricate tunneling dynamics with attosecond angular streaking.

Nonadiabatic Tunneling in Chemical Reactions.

Quantum tunneling can have a dramatic effect on chemical reaction rates. In nonadiabatic reactions such as electron transfers or spin crossovers, nuclear tunneling effects can be even stronger than for adiabatic proton transfers. Ring-polymer instanton theory enables molecular simulations of tunneling in full dimensionality and has been shown to be far more reliable than commonly used separable approximations. First-principles instanton calculations predict significant nonadiabatic tunneling of heavy atoms even at room temperature and give excellent agreement with experimental measurements for the intersystem crossing of two nitrenes in cryogenic matrix isolation, the spin-forbidden relaxation of photoexcited thiophosgene in the gas phase, and singlet oxygen deactivation in water at ambient conditions. Finally, an outlook of further theoretical developments is discussed.

Sub-cycle strong-field tunneling dynamics in solids

Tunneling ionization is a crucial process in the interaction between strong laser fields and matter which initiates numerous nonlinear phenomena including high-order harmonic generation, photoelectron holography, etc. Both adiabatic and nonadiabatic tunneling ionization are well understood in atomic systems. However, the tunneling dynamics in solids, especially nonadiabatic tunneling, has not yet been fully understood. Here, we study the sub-cycle resolved strong-field tunneling dynamics in solids via a complex saddle-point method. We compare the instantaneous momentum at the moment of tunneling and the tunneling distances over a range of Keldysh parameters. Our results demonstrate that for nonadiabatic tunneling, tunneling ionization away from Γ point is possible. When this happens the electron has a nonzero initial velocity when it emerges in the conduction band. Moreover, consistent with atomic tunneling, a reduced tunneling distance as compared to the quasi-static case is found. Our results provide remarkable insight into the basic physics governing the sub-cycle electron tunneling dynamics with significant implications for understanding subsequent strong-field nonlinear phenomena in solids.

Classically forbidden nonadiabatic transitions in multidimensional chemical dynamics.

An accurate method is proposed to deal with such nonadiabatic transitions as those energetically inaccessible, namely, classically forbidden transitions. This is formulated by using the corresponding Zhu-Nakamura formulas and finding the optimal paths in the classically forbidden tunneling regions that maximize the overall transition probabilities. This can be done for both the nonadiabatic tunneling type (so-called normal case in electron transfer) in which two diabatic potentials have opposite signs of slopes and the Landau-Zener type (inverted case) in which two diabatic potentials have the same sign of slopes. The method is numerically demonstrated to be useful for clarifying chemical and biological dynamics.

Time-resolved subcycle and intercycle interference influenced momentum shift in nonadiabatic tunnelling ionization

Momentum shift is an important sign of nonadiabatic tunnelling ionization process. To investigate the mechanism of momentum shift, we use the strong-field approximation theory to track the formation of ionization momentum spectra of hydrogen atom under the action of different laser pulses in the time domain. By observing the ionization momentum spectra of different structures over time, we find that the momentum shift is formed by the continuous interference and evolution of ionization signals. Meanwhile, we further analyze how subcycle and intercycle interference influence the formation of momentum shift. Before the duration is long enough for intercycle interference to emerge, momentum shift grows smoothly. Our findings reveal different intrinsic mechanisms for the formation of momentum shift in many-cycle and few-cycle laser pulses, showing that subcycle interference plays a dominant role in the former while intercycle interference is critical in the latter. This work lays the foundation for a deeper understanding of the nonadiabatic tunnelling process and makes the regulation of momentum shift possible.

Ultrafast preparation and detection of entangled atoms.

Atoms can form a molecule by sharing their electrons in binding orbitals. These electrons are entangled. Is there a way to break a molecular bond and obtain atoms in their ground state that are spatially separated and still entangled? Here, we show that it is possible to prepare these spatially separated, entangled atoms on femtosecond time scales from single oxygen molecules. The two neutral atoms are entangled in the magnetic quantum number of their valence electrons. In a time-delayed probe step, we use nonadiabatic tunneling, which is a magnetic quantum number-sensitive ionization mechanism. We find a fingerprint of entanglement in the measured ionization probability as a function of the angle between the light's quantization axis and the molecular axis. This establishes a platform for further experiments that harness the time resolution of strong-field experiments to investigate spatially separated, entangled atoms on femtosecond time scales.

Wavelength scaling of photoionization circular dichroism of atomic electron ring currents and its effect on photoelectron spin polarization

Circularly polarized orbitals in atoms are referred to as electron ring currents with a helical angular phase and thus manifest circular dichroism in photoionization by circularly polarized light fields. Opposite circular dichroism has been revealed in single-photon and nonadiabatic tunneling ionization regimes. The transition of the circular dichroism and its underlying mechanism are still not clear. Here, we systematically study the wavelength scaling of photoionization circular dichroism of electron ring currents. We present a universal description of the dichroic photoelectron energy spectra and the spin polarization from the infrared to the extreme ultraviolet regions. We reveal that the channel interference and competition via the intermediate states with different angular quantum numbers in a few-photon ionization regime give rise to the transition of the circular dichroism and the spin polarization of photoelectrons.

Revealing the nonadiabatic tunneling dynamics in solid-state high harmonic generation

Revealing the nonadiabatic tunneling dynamics in solid-state high harmonic generation

Nonadiabatic tunneling ionization of atoms in few-cycle elliptically polarized laser pulses

We theoretically investigate nonadiabatic effects in tunneling ionization of a hydrogen atom induced by a few-cycle elliptically polarized laser pulse. We find a deflection angle between the maximum of the photoelectron momentum distribution and the direction of the negative vector potential corresponding to the electric-field peak. This deflection angle mainly originates from the fact that the instant of the maximal ionization rate does not exactly correspond to the instant of the electric-field peak in the few-cycle elliptically polarized laser pulse, revealing an ionization time shift between those two instants. The ionization time shift is a result of the nonadiabatic effect induced by the envelope of the few-cycle elliptically polarized laser pulse, which disappears in a long-pulsed laser. Our study is useful for understanding attoclock experiments using few-cycle elliptically polarized laser pulses.

Nonadiabatic heavy atom tunneling in 1nσ*-mediated photodissociation of thioanisole.

The 1nσ*-mediated photodissociation dynamics of thioanisole is investigated quantum mechanically using a three-dimensional model based on a newly constructed diabatic potential energy matrix. The lifetimes of the low-lying S1(1ππ*) resonances are determined and found to accord well with available experimental data. Specifically, our theoretical results demonstrate that the photodissociation of thioanisole at the low-lying S1(1ππ*) levels takes place via the heavy atom tunneling due to the higher S1/S2 conical intersection and two equivalent out-of-plane saddle points appearing on the dissociation path. The isotopic effect on the lifetimes is found to be pronounced, manifesting the nature of the tunneling process. Moreover, the geometric phase effect around the S1/S2 conical intersection is found to slightly impact the lifetimes due to the weak destructive or constructive interferences in this heavy atom tunneling, which differs significantly from the scenario in the nonadiabatic hydrogen atom tunneling. Importantly, the quantum mechanical treatment is essentially required to accurately describe the 1nσ*-mediated photodissociation dynamics of thioanisole owing to involving quantum tunneling and geometric phase effects near the conical intersection.

Competing quantum effects in heavy-atom tunnelling through conical intersections.

Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.

πσ*-Mediated Nonadiabatic Tunneling Dynamics of Thiophenols in S1: The Semiclassical Approaches.

The S-H bond tunneling predissociation dynamics of thiophenol and its ortho-substituted derivatives (2-fluorothiophenol, 2-methoxythiophenol, and 2-chlorothiphenol) in S1 (ππ*) where the H atom tunneling is mediated by the nearby S2 (πσ*) state (which is repulsive along the S-H bond extension coordinate) have been investigated in a state-specific way using the picosecond time-resolved pump-probe spectroscopy for the jet-cooled molecules. The effects of the specific vibrational mode excitations and the SH/SD substitutions on the S-H(D) bond rupture tunneling dynamics have been interrogated, giving deep insights into the multidimensional aspects of the S1/S2 conical intersection, which also shapes the underlying adiabatic tunneling potential energy surfaces (PESs). The semiclassical tunneling rate calculations based on the Wentzel-Kramers-Brillouin (WKB) approximation or Zhu-Nakamura (ZN) theory have been carried out based on the ab initio PESs calculated in the (one, two, or three) reduced dimensions to be compared with the experiment. Though the quantitative experimental results could not be reproduced satisfactorily by the present calculations, the qualitative trends among different molecules in terms of the behavior of the tunneling rate versus the (adiabatic) barrier height or the number of PES dimensions could be rationalized. Most interestingly, the H/D kinetic isotope effect observed in the tunneling rate could be much better explained by the ZN theory compared to the WKB approximation, indicating that the nonadiabatic coupling matrix elements should be invoked for understanding the tunneling dynamics taking place in the proximity of the conical intersection.

Nonadiabatic Nano-optical Tunneling of Photoelectrons in Plasmonic Near-Fields.

Nonadiabatic nano-optical electron tunneling in the transition region between multiphoton-induced emission and adiabatic tunnel emission is explored in the near-field of plasmonic nanostructures. For Keldysh γ values between ∼1.3 and ∼2.2, measured photoemission spectra show strong-field recollision driven by the nanoscale near-field. At the same time, the photoemission yield shows an intensity scaling with a constant nonlinearity, which is characteristic for multiphoton-induced emission. Our observations in this transition region were well reproduced with the numerical solution of Schrödinger’s equation, mimicking the nanoscale geometry of the field. This way, we determined the boundaries and nature of nonadiabatic tunneling photoemission, building on a key advantage of a nanoplasmonic system, namely, that high-field-driven recollision events and their signature in the photoemission spectrum can be observed more efficiently due to significant nanoplasmonic field enhancement factors.

Nonadiabatic effect on temporal double-slit interference structures in an orthogonal two-color laser field

We theoretically investigate the temporal double-slit interference (DSI) structures in photoelectron momentum distribution driven by an orthogonally polarized two-color (OTC) laser field and focus on the nonadiabatic effect on the subcycle electron dynamics. Distinct discrepancies in the interference structures simulated with a time-dependent Schr\"odinger equation (TDSE) and an adiabatic semiclassical Monte Carlo approach are observed. By adopting the initial conditions derived from the nonadiabatic tunneling picture into the Monte Carlo algorithm, the improved nonadiabatic model well reproduces the TDSE result. Further analysis shows that the improvement is mainly attributed to the nonzero electron initial longitudinal velocity from the nonadiabatic tunneling and moreover, its influence on the subsequent electron dynamics is revealed. Our work demonstrates the sensitivity of the temporal DSI structures in an OTC field to the exit momentum, providing a way for comprehension of the nonadiabatic tunneling electron dynamics.

Quasiclassical theory of non-adiabatic tunneling in nanocontacts induced by phase-controlled ultrashort light pulses

We theoretically investigate tunneling through free-space or dielectric nanogaps between metallic nanocontacts driven by ultrashort ultrabroadband light pulses. For this purpose we develop a time-dependent quasiclassical theory being especially suitable to describe the tunneling process in the non-adiabatic regime, when tunneling can be significantly influenced by photon absorption as the electron moves in the classically forbidden region. Firstly, the case of driving by an ideal half-cycle pulse is studied. For different distances between the contacts, we analyze the main solutions having the form of a quasiclassical wave packet of the tunneling electron and an evanescent wave of the electron density. For each of these solutions the resulting tunneling probability is determined with the exponential accuracy inherent to the method. We identify a crossover between two tunneling regimes corresponding to both solutions in dependence on the field strength and intercontact distance that can be observed in the corresponding behaviour of the tunneling probability. Secondly, considering realistic temporal profiles of few-femtosecond pulses, we demonstrate that the preferred direction of the electron transport through the nanogap can be controlled by changing the carrier-envelope phase of the pulse, in agreement with recent experimental findings and numerical simulations. We find analytical expressions for the tunneling probability, determining the resulting charge transfer in dependence on the pulse parameters. Further, we determine temporal shifts of the outgoing electron trajectories with respect to the peaks of the laser field as a function of the pulse phase and illustrate when the non-adiabatical character of the tunneling process is particularly important.

Femtosecond Field‐Driven On‐Chip Unidirectional Electronic Currents in Nonadiabatic Tunneling Regime

AbstractRecently, asymmetric plasmonic nanojunctions have shown promise as on‐chip electronic devices to convert femtosecond optical pulses to current bursts, with a bandwidth of multi‐terahertz scale, although yet at low temperatures and pressures. Such nanoscale devices are of great interest for novel ultrafast electronics and opto‐electronic applications. Here, the device is operated in air and at room temperature, revealing the mechanisms of photoemission from plasmonic nanojunctions, and the fundamental limitations on the speed of optical‐to‐electronic conversion. Inter‐cycle interference of coherent electronic wavepackets results in a complex energy electron distribution and birth of multiphoton effects. This energy structure, as well as reshaping of the wavepackets during their propagation from one tip to the other, determine the ultrafast dynamics of the current. It is shown that, up to some level of approximation, the electron flight time is well‐determined by the mean ponderomotive velocity in the driving field.

InSitu Generation of High-Energy Spin-Polarized Electrons in a Beam-Driven Plasma Wakefield Accelerator.

Insitu generation of a high-energy, high-current, spin-polarized electron beam is an outstanding scientific challenge to the development of plasma-based accelerators for high-energy colliders. In this Letter, we show how such a spin-polarized relativistic beam can be produced by ionization injection of electrons of certain atoms with a circularly polarized laser field into a beam-driven plasma wakefield accelerator, providing a much desired one-step solution to this challenge. Using time-dependent Schrödinger equation (TDSE) simulations, we show the propensity rule of spin-dependent ionization of xenon atoms can be reversed in the strong-field multiphoton regime compared with the non-adiabatic tunneling regime, leading to high total spin polarization. Furthermore, three-dimensional particle-in-cell simulations are incorporated with TDSE simulations, providing start-to-end simulations of spin-dependent strong-field ionization of xenon atoms and subsequent trapping, acceleration, and preservation of electron spin polarization in lithium plasma. We show the generation of a high-current (0.8kA), ultralow-normalized-emittance (∼37 nm), and high-energy (2.7GeV) electron beam within just 11cm distance, with up to ∼31% net spin polarization. Higher current, energy, and net spin-polarization beams are possible by optimizing this concept, thus solving a long-standing problem facing the development of plasma accelerators.

Two-lattice-vibration theory for proton transfer in cubic perovskites: Barium zirconate versus potassium tantalate

Proton transfer (PT) in proton-conducting oxides is an intrinsically quantum phenomenon, due to the very strong quantization of the OH stretching vibration (ℏω~ 0.4 eV). Up to high temperatures, the proton is frozen in the ground state associated with the OH stretching motion, and thus does not undergo the thermal agitation for this vibration. Therefore, these are the thermal fluctuations of the (heavier) lattice atoms which make PT possible, at least above ~ half the Debye temperature of the lattice. These fluctuations may occasionally and randomly produce specific lattice configurations in which the quantum protonic ground levels in the two wells are equalized (coincidence), making PT possible, however with a certain probability. An analytical expression of this transfer probability may be obtained as the solution of a curve-crossing quantum-mechanical problem, and thus described by the Landau-Zener (LZ) formula. Two lattice vibrations play a fundamental role in intra-octahedral PT: (i) a reorganization of the lattice, that sends the protonated system from its initial self-trapped configuration up to the coincidence manifold, and (ii) a reduction of the (donor) oxygen - (acceptor) oxygen distance Q, which facilitates PT by leading the system to coincidence configurations with smaller proton barrier, and thus larger LZ probability. In cubic perovskites, the set of the coincidence configurations plays the role of the transition state for PT. The implementation of this theory of proton transfer [G. Geneste, Solid State Ionics 323, 172 (2018)] is here strongly improved on several points: description of the coincidence configurations, proton zero-point energies and proton potential at coincidence. It is then re-applied to barium zirconate (BZO), and also to potassium tantalate (KTO), with parameters derived from density-functional theory (DFT) calculations. The theory confirms the adiabatic PT regime in BZO, common to most proton conductors, with a negligible contribution of non-adiabatic tunneling transfers to the transfer rate. In KTO, by contrast, the relative contribution of non-adiabatic tunneling transfers is larger than in BZO, especially below ~ 250–300 K. The present work helps to characterize intrinsic features common to most proton conductors, at least from the point of view of proton mobility within the lattice. The activations energies for proton transfer at high temperature are predicted at 0.11 eV (BZO) and 0.25 eV (KTO).

Sub-barrier pathways to Freeman resonances

The problem of Freeman resonances [R. R. Freeman \textit{et al.}, Phys. Rev. Lett. \textbf{59}, 1092 (1987)] when strong field ionization is enhanced due to the transient population of excited states during the ionization, is revisited. An intuitive model is put forward which explains the mechanism of the intermediate population of excited states during nonadiabatic tunneling ionization via the under-the-barrier recollision and recombination. The theoretical model is based on perturbative strong-field approximation (SFA), where the sub-barrier bound-continuum-bound pathway is described in the second-order SFA, while the further ionization from the excited state by an additional perturbative step. The enhancement of ionization is shown to arise due to the constructive interference of contributions into the excitation amplitudes originating from different laser cycles. The applied model provides an intuitive understanding of the electron dynamics during a Freeman resonance in strong-field ionization, as well as means of enhancing the process and possible applications to related processes.

Theory of Subcycle Linear Momentum Transfer in Strong-Field Tunneling Ionization.

Interaction of a strong laser pulse with matter transfers not only energy but also linear momentum of the photons. Recent experimental advances have made it possible to detect the small amount of linear momentum delivered to the photoelectrons in strong-field ionization of atoms. We present numerical simulations as well as an analytical description of the subcycle phase (or time) resolved momentum transfer to an atom accessible by an attoclock protocol. We show that the light-field-induced momentum transfer is remarkably sensitive to properties of the ultrashort laser pulse such as its carrier-envelope phase and ellipticity. Moreover, we show that the subcycle-resolved linear momentum transfer can provide novel insights into the interplay between nonadiabatic and nondipole effects in strong-field ionization. This work paves the way towards the investigation of the so-far unexplored time-resolved nondipole nonadiabatic tunneling dynamics.