Geometric Phase Effect Research Articles

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.

Conical Intersection versus Avoided Crossing: Geometric Phase Effect in Molecular High-Order Harmonics

Nonadiabatic dynamics around an avoided crossing or a conical intersection play a crucial role in the photoinduced processes of most polyatomic molecules. The present work shows that the topological phase in conical intersection makes the behavior of pump-probe high-order harmonic signals different from the case of avoided crossing. The coherence built up when the system crosses the avoided crossing will lead to the oscillatory behavior of the spectrum, while the geometric phase erodes these oscillations in the case of conical intersection. Additionally, the dynamical blueshift and the splitting of the time-resolved spectrum allow capturing the snapshot dynamics with the sub-femtosecond resolution.

Directly revealing the geometric phase effect of dissociative D2+ by two-color strong field photodissociation.

We study the geometric phase (GP) effect of D2+ produced by the encirclement of the dissociated nuclear wavefunction around the light-induced conical intersection (LICI) using a linearly polarized two-color (800 nm and its third harmonic at 266 nm) synthesized laser field. We calculate the photofragment momentum distribution of D2+ with the random orientation by solving the time-dependent Schrödinger equation. We reveal the GP effect that manifests as the Aharonov-Bohm-like interference in the photofragment angular distribution along the direction perpendicular to the linear polarization axis. Our work deepens the understanding of the physical mechanisms of the molecular dynamics when driven by the synthesized strong laser field.

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.

Elastic Spin and Orbital Angular Momenta.

Motivated by recent theoretical and experimental interest in the spin and orbital angular momenta of elastic waves, we revisit canonical wave momentum, spin, and orbital angular momentum in isotropic elastic media. We show that these quantities are described by simple universal expressions, which differ from the results of Chaplain etal. [Phys. Rev. Lett. 128, 064301 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.064301] and do not require separation of the longitudinal and transverse parts of the wave field. For cylindrical elastic modes, the normalized z component of the total (spin+orbital) angular momentum is quantized and equals the azimuthal quantum number of the mode, while the orbital and spin parts are not quantized due to the spin-orbit geometric-phase effects. In contrast to the claims of the above article, longitudinal, transverse, and "hybrid" contributions to the angular momenta are equally important in general and cannot be neglected. As another example, we calculate the transverse spin angular momentum of a surface Rayleigh wave.

Geometric phase effect study in electric dipole moment rings

Several proposals to measure a possible small electric dipole moment (EDM) of charged particles aligned with the spin and the well-known magnetic dipole moment (MDM) are based on the concept to circulate bunches with an initial polarization in the horizontal plane and to observe the buildup of a vertical spin component caused by the EDM. Most proposals aim at operating the ring with ``frozen spin,'' such that, with an MDM only, the spin remains aligned with the trajectory. The signature of a finite EDM is the buildup of a vertical spin component. Machine imperfections may lead as well to a vertical spin buildup, which can be misinterpreted as an EDM and thus limit the sensitivity of the experiment. For that reason, a good understanding of spin dynamics is mandatory to estimate and limit such systematic errors in the measurement. In this paper, a coordinate system attached to the trajectory is introduced to expand the spin. This is of particular interest for fully electric EDM rings operated at the ``magic energy'' to satisfy the frozen spin condition. The procedure is used for a straightforward analysis of geometric phase and other second order effects, which limit the possible sensitivity, i.e., the smallest EDM which can be detected in presence of systematic effects.

Coherent atomic orbital polarization probes the geometric phase in photodissociation of polyatomic molecules

AbstractQuantum interference between multiple pathways in molecular photodissociation often results in angular momentum polarization of atomic products and this can give deep insight into fundamental physical processes. For dissociation of diatomic molecules, the resulting orbital polarization is fully understood and consistent with quantum mechanical theory. For polyatomic molecules, however, coherent photofragment orbital polarization is frequently observed but so far has eluded theoretical explanation, and physical insight is lacking. Here, we present a model of these effects for ozone photodissociation that reveals the importance of a novel manifestation of the geometric phase. We show this geometric phase effect permits the existence of coherent polarization in cases where it would otherwise vanish, and cancels it in some cases where it might otherwise exist. The model accounts for measurements in ozone that have hitherto defied explanation, and represents a step toward a deeper understanding of coherent electronic excitation in polyatomic molecules and a new role of the geometric phase.Key Points Coherent photofragment atomic orbital polarization reveals matter wave interference in dissociation along multiple paths. In diatomic molecules, this is well‐understood, but in polyatomic molecules, large effects are seen but these have defied a rigorous explanation. A model is developed describing these phenomena in the UV dissociation of ozone that accounts for a number of conflicting observations and reveals a new manifestation of the geometric phase in molecular physics.

The moving crude adiabatic alternative to the adiabatic representation in excited state dynamics.

The choice of the electronic representation in on-the-fly quantum dynamics is crucial. The adiabatic representation is appealing since adiabatic states are readily available from quantum chemistry packages. The nuclear wavepackets are then expanded in a basis of Gaussian functions, which follow trajectories to explore the potential energy surfaces and approximate the potential using a local expansion of the adiabatic quantities. Nevertheless, the adiabatic representation is plagued with severe limitations when conical intersections are involved: the diagonal Born-Oppenheimer corrections (DBOCs) are non-integrable, and the geometric phase effect on the nuclear wavepackets cannot be accounted for unless a model is available. To circumvent these difficulties, the moving crude adiabatic (MCA) representation was proposed and successfully tested in low energy dynamics where the wavepacket skirts the conical intersection. We assess the MCA representation in the case of non-adiabatic transitions through conical intersections. First, we show that using a Gaussian basis in the adiabatic representation indeed exhibits the aforementioned difficulties with a special emphasis on the possibility to regularize the DBOC terms. Then, we show that MCA is indeed able to properly model non-adiabatic transitions. Tests are done on linear vibronic coupling models for the bis(methylene) adamantyl cation and the butatriene cation. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Chemistry without the Born-Oppenheimer approximation.

Chemistry without the Born-Oppenheimer approximation.

Tracking Conical Intersections with Nonlinear X-ray Raman Spectroscopy

Conical intersections are formed when 2 or more electronic states become degenerate and give rise to ultrafast nonadiabatic processes such as radiation-less decay channels and geometric phase effects. The branching of nuclear wave packets near a conical intersection creates a coherent superposition of electronic states, which carries information about the energy difference of the involved states. X-ray Raman techniques have been proposed to observe the coherent superposition of the electronic states and to monitor the evolving electronic state separation. However, these techniques rely on the coherence generated as the wave packet passes through the conical intersection, and the electronic energy gap before the wave packet passes through the conical intersection is not tracked. In this paper, we theoretically demonstrate how a nonlinear Raman detection scheme can be used to gain further insight into the nonadiabatic dynamics in the vicinity of the conical intersection. We employ a combination of a resonant visible/infrared pulse and an off-resonant x-ray Raman probe to map the electronic state separation around the conical intersection. We demonstrate that this technique can achieve high contrast and is able to selectively probe the narrow electronic state separation around the conical intersection.

Nanostructured silica spin–orbit optics for modal vortex beam shaping

Abstract Modality is a generic concept of wave-optics at the basis of optical information and communications. One of the challenges of photonics technologies based on optical orbital angular momentum consists in the production of a modal content for both the azimuthal and radial degrees of freedom. This basically requires shaping the complex amplitude of an incident light beam, which is usually made up from adaptive spatial light modulators or bespoke devices. Here, we report on the experimental attempt of a recent theoretical proposal [Opt. Lett. 42, 1966 (2017)] toward the production of various optical vortex modes of the Laguerre–Gaussian type relying on the spin–orbit interaction of light. This is done in the visible domain from optical elements made out of silica glass. The idea consists in exploiting the combined effects of azimuthally-varying geometric phase with that of radially-varying propagation features. The proposed approach can be readily extended to any wavelength as well as to other families of optical modes, although some dynamic phase problems remain to be solved to make it a turnkey technology.

Conical intersection seams in spin-orbit coupled systems with an even number of electrons: A numerical study based on neural network fit surfaces.

In this work, we consider the existence and topography of seams of conical intersections (CIs) for two key singlet-triplet systems, including a uniformly scaled spin-orbit interaction. The basic one triplet and one singlet state system denoted as (S0,T1) and the two singlets and one triplet system denoted as (S0,S1,T1) are treated. Essential to this analysis are realistic electronic structure data taken from a recently reported neural network fit for the 1,21A and 13A states of NH3, including Hsf (spin-free) and Hso (spin-orbit) surfaces derived from high quality ab initio wavefunctions. Three types of seams for the (S0,S1,T1) system are reported, which depend on the choice of the electronic Hamiltonian, He. The nonrelativistic CI seam [He = Hsf, (S0,S1)], the energy minimized nonrelativistic singlet-triplet intersection seam [He = Hsf, (S0,T1)], and the fully relativistic seam in the spin-diabatic representation (He = Htot = Hsf + Hso) are reported as functions of R(N-H). The derivative couplings are computed using He = Htot and Hsf from the fit data. The line integral of the derivative coupling is employed to juxtapose the geometric phase in the relativistic, He = Htot, and nonrelativistic, He = Hsf, cases. It is found for the (S0,T1) system that there is no CI in the spin-adiabatic representation, while for the (S0,S1,T1) system, CI can only be formed for two pairs of spin-adiabatic electronic states. The geometric phase effect thus needs to be handled with care when it comes to spin-nonconserving dynamics simulations.

Dynamics near a conical intersection-A diabolical compromise for the approximations of ab initio multiple spawning.

Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.

Spin-orbit interactions of transverse sound

Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. Here, we theoretically and experimentally demonstrate that airborne sound can possess artificial transversality in an acoustic micropolar metamaterial and thus carry both spin and orbital angular momentum. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. We demonstrate that acoustic activity of the metamaterial can induce coupling between the spin and linear crystal momentum k, which leads to negative refraction of the transverse sound. In addition, we show that the scattering of the transverse sound by a dipole particle can generate spin-dependent acoustic vortices via the geometric phase effect. The acoustic SOIs can provide new perspectives and functionalities for sound manipulations beyond the conventional scalar degree of freedom and may open an avenue to the development of spin-orbit acoustics.

Geometric heat pump: Controlling thermal transport with time-dependent modulations

The second law of thermodynamics dictates that heat simultaneously flows from the hot to cold bath on average. To go beyond this picture, a range of works in the past decade show that, other than the average dynamical heat flux determined by instantaneous thermal bias, a non-trivial flux contribution of intrinsic geometric origin is generally present in temporally driven systems. This additional heat flux provides a free lunch for the pumped heat and could even drive heat against the bias. We review here the emergence and development of this so called “geometric heat pump”, originating from the topological geometric phase effect, and cover various quantum and classical transport systems with different internal dynamics. The generalization from the adiabatic to the non-adiabatic regime and the application of control theory are also discussed. Then, we briefly discuss the symmetry restriction on the heat pump effect, such as duality, supersymmetry and time-reversal symmetry. Finally, we examine open problems concerning the geometric heat pump process and elucidate their prospective significance in devising thermal machines with high performance.

Laser control of polariton using Landau–Zener–Stückelberg interferometry theory

We have investigated the dynamic of cooled and trapped polariton state using Landau–Zener–Stuckelberg interferometry theory (LZSIT). The effects of exciton–cavity coupling and the laser cooling over the qubit dynamics are analyzed in multi-crossing scenarios, supporting some of our basic results (Kenfack et al. in Comput Condens Matter 11:47–54, 2017; Ekengoue et al. in Comput Condens Matter 14:106–113, 2018). We have performed detailed calculations of the energy eigenvalues, non-adiabatic and adiabatic transition probabilities in the framework of weak- and strong-coupling regime under the laser light. As a main result, we pointed out the braking down of the Pauli exclusion principle providing the applicability of LZSIT for the analysis of polariton’s dynamic through a model which satisfies Fermi–Dirac statistics. Moreover, we found the generation of arbitrary waveforms of interferometric signals including sinusoidal, for weak coupling and strong laser amplitude. Thus, the dynamics of the polariton induces the destruction and the construction of interferences patterns in strong coupling between cavity laser and qubit. Extremely accurate interferometric signals generation by means of geometric phase effect has been demonstrated in this work with the goal of realizing robust control of the quantum coherent states of the polaritonic system. This geometric phase enhancement, which is essentially originated from the dynamic behavior of cooled and trapped polariton, is a significant consequence of the fastest population transfer and quantized energy of the system. Therefore, the geometric phase plays a crucial role in the study of the alter crossings behavior through cooled and trapped polariton, especially in the population transfer and energy of the system.

Regularized Born-Oppenheimer molecular dynamics

While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of Mead-Truhlar minimal coupling, this paper presents a new closure of the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics scheme capturing geometric phase effects. Specifically, a semiclassical closure of the nuclear Ehrenfest dynamics is obtained through a convenient prescription for the nuclear Bohmian trajectories. The conical intersections are suitably regularized in the resulting nuclear particle motion and the associated Lorentz force involves a smoothened Berry curvature identifying a loop-dependent geometric phase. In turn, this geometric phase rapidly reaches the usual topological index as the loop expands away from the original singularity. This feature reproduces the phenomenology appearing in recent exact nonadiabatic studies, as shown explicitly in the Jahn-Teller problem for linear vibronic coupling. Likewise, a newly proposed regularization of the diagonal correction term is also shown to reproduce quite faithfully the energy surface presented in recent nonadiabatic studies.

Observation of the geometric phase effect in the H+HD\u2192H2+D reaction below the conical intersection

It has long been known that there is a conical intersection (CI) between the ground and first excited electronic state in the H3 system. Its associated geometric phase (GP) effect has been theoretically predicted to exist below the CI since a long time. However, the experimental evidence has not been established yet and its dynamical origin is waiting to be elucidated. Here we report a combined crossed molecular beam and quantum reactive scattering dynamics study of the H+HD → H2+D reaction at 2.28 eV, which is well below the CI. The GP effect is clearly identified by the observation of distinct oscillations in the differential cross section around the forward direction. Quantum dynamics theory reveals that the GP effect arises from the phase alteration of a small part of the wave function, which corresponds to an unusual roaming-like abstraction pathway, as revealed by quasi-classical trajectory calculations.

Nonadiabatic Ultracold Quantum Reactive Scattering of Hydrogen with Vibrationally Excited HD(v = 5-9).

The results from electronically non-adiabatic and adiabatic quantum reactive scattering calculations are presented for the H + HD(v = 5-9) → H + HD(v', j') reaction at ultracold collision energies from 10 nK to 60 K. Several experimentally verifiable signatures of the geometric phase are reported in the total and vibrationally and rotationally resolved rate coefficients. Most notable is the predicted 2 orders of magnitude enhancement of the rotationally resolved ultracold rates of odd symmetry relative to those of even symmetry. Prominent shape resonances appear at higher collision energies (100 mK to 20 K), which could be measured experimentally. Significant geometric phase effects are also reported on the resonance energies and lifetimes. In particular, an enhancement (suppression) of the l = 1 (l = 2) shape resonances for HD(v = 5, 6) is predicted for even symmetry relative to those of odd symmetry.

Geometrical phase and Hall effect associated with the transverse spin of light

By analyzing the vectorial Helmholtz equation within the thin-layer approach, we find that light acquires another geometrical phase, in addition to the usual one (the optical Berry phase), during the propagation along a curved path. Unlike the optical Berry phase, the additional geometrical phase is induced by the curvature of the curve and associated with the transverse spin of light. Furthermore, we show an additional Hall effect of light induced by the torsion of the curve and associated with the transverse spin of light, which is different from the usual spin Hall effect of light. Finally, we demonstrate that the usual and transverse-spin-dependent geometrical phase phenomena are described by different geometry-induced U(1) gauge fields in different adiabatic approximations. In the general case, these gauge fields are united in an effective SO(3) gauge field, and the optical Berry phase and transverse-spin-dependent geometrical phase are united in a general geometrical phase of light.