Semiclassical Simulations Research Articles

Cascade and yoked superfluorescence detected by sum frequency generation spectroscopy.

We investigated the superfluorescent decay process of dense rubidium atomic vapor in a cell. Using a femtosecond laser pulse, the atoms were excited from the 5S ground state to the 6P state. The 2.73μm and 1.37μm fields were generated on the cascaded decay, 6P → 6S → 5P, which further stimulated the 780 nm forward emission on the 5P → 5S transition. Using sum frequency generation (SFG) spectroscopy, we observed all emission fields and the time delay between them, with sufficient temporal resolution. The experimental results were successfully reproduced using semiclassical simulations.

Heat transport in an optical lattice via Markovian feedback control

Ultracold atoms offer a unique opportunity to study many-body physics in a clean and well-controlled environment. However, the isolated nature of quantum gases makes it difficult to study transport properties of the system, which are among the key observables in condensed matter physics. In this work, we employ Markovian feedback control to synthesize two effective thermal baths that couple to the boundaries of a one-dimensional Bose–Hubbard chain. This allows for the realization of a heat-current-carrying state. We investigate the steady-state heat current, including its scaling with system size and its response to disorder. In order to study large systems, we use semi-classical Monte-Carlo simulation and kinetic theory. The numerical results from both approaches show, as expected, that for non- and weakly interacting systems with and without disorder one finds the same scaling of the heat current with respect to the system size as it is found for systems coupled to thermal baths. Finally, we propose and test a scheme for measuring the energy flow. Thus, we provide a route for the quantum simulation of heat-current-carrying steady states of matter in atomic quantum gases.

The vertical excitation energies and a lifetime of the two lowest singlet excited states of the conjugated polyenes from C2 to C22: Ab initio, DFT, and semiclassical MNDO-MD simulations.

Electronic excited states in the series of polyene molecules were explored. Optimal ground-state geometry was used for the evaluation of vertical excitation energies. Results of a chosen set of functionals were compared to post-HF methods (EOM-CCSD, NEVPT2, CASPT2, and MRCI). In addition, the semiempirical OM2/MNDO method using MRCISD computational level was confronted with the above-mentioned techniques. Despite the fact that the first excited state has a significant double-excitation character some functionals were able to qualitatively determine the correct state order (where the lowest excited state has a character). The most successful functionals in transition energies predictions were PBE, TPSS and BLYP in Tamm-Dancoff approach (TDA), which had the smallest root-mean-square deviation (RMSD) scoring towards the experimental values. Regarding RMSD scoring, the OM2/MNDO method performed fairly well, too. Besides absorption spectra, lifetimes of the first two excited states were estimated based on a stochastic approach exploring a swarm of OM2/MNDO hopping dynamics using the Tully fewest switch algorithm for each molecule. The longest lifetime of the first excited state (S1 ) was found for decapentaene (about 5ps). Further elongation of the conjugated chain caused a mild decrease of this value to ca 1.5ps for docosaundecaene.

Dynamical Scaling as a Signature of Multiple Phase Competition in Yb_{2}Ti_{2}O_{7}.

Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.

Microscopic Origin of the Effective Spin-Spin Interaction in a Semiconductor Quantum Dot Ensemble

We present a microscopic model for a singly charged quantum dot (QD) ensemble to reveal the origin of the long-range effective interaction between the electron spins in the QDs. Wilson's numerical renormalization group (NRG) is used to calculate the magnitude and the spatial dependency of the effective spin-spin interaction mediated by the growth-induced wetting layer. Surprisingly, we found an antiferromagnetic Heisenberg coupling for very short inter-QD distances that is caused by the significant particle-hole asymmetry of the wetting layer band at very low filling. Using the NRG results obtained from realistic parameters as input for a semiclassical simulation for a large QD ensemble, we demonstrate that the experimentally reported phase shifts in the coherent spin dynamics between single- and two-color laser pumping can be reproduced by our model, solving a long-standing open problem of the microscopic origin of the inter-QD electron spin-spin interaction.

Controlling electron recollision with combined linear and circular polarization

We theoretically investigate the non-sequential double ionization of Ar atoms in the combined fields of linearly polarized laser and circularly polarized laser through 3D semiclassical simulations. By partially overlapping the two time-delayed multicycle laser pulses, we construct an optical waveform whose polarization ellipticity increase slowly for consecutive optical cycles. This composite laser pulses with the time-dependent ellipticity can tunnel-ionize atoms and steer the first tunneling electron to recollision with the second bound electron through different trajectories, in which the recollision occurs with different return times of the first ionized electron. Through tuning delay time between the two laser pulses, the double ionization yields and recollision trajectories with different return times can be controlled. The time-dependent ellipticity with different delay time can enhance or suppress the probability of different return times. This work provides a scheme exploring electron dynamics in few optical cycle or even subcycle time scale in a multicycle laser field without having to be limited to near-single-cycle laser pulses.

Disentangling the Ultrafast Nonlinear Optical Behavior of Plasmonic Resonances Near the Interband Transition

The photoexcitation of plasmonic nanostructures with ultrashort laser pulses allows for elucidating the mechanisms underlying the ultrafast nonlinear optical response of such systems, gaining insight into the fundamental processes triggered by light absorption at the nanoscale. To date, the complex temporal and spectral features of the photoinduced response are not fully understood, especially when the photon energies are close to the interband transitions of the metallic medium. Herein, the effects of photoexcitation of plasmonic nanostructures are studied by resorting to a combinaion of broadband transient absorption spectroscopy and semiclassical nonlinear simulations of the energy relaxation processes following illumination. The proposed approach enables an in‐depth disentanglement of all the contributions to the ultrafast transient optical response of supported gold nanocrystals. From these methods, the apparent transient blue shift of the localized plasmon resonance observed in the pump–probe signals is rationalized as an interplay between different and spectrally dispersed permittivity modulations, instead of a simple negative permittivity change, as it could be concluded based on the Fröhlich condition. The results provide a comprehensive understanding of the thermo‐modulational nonlinearities of plasmonic nanostructures exhibiting resonances close to the interband transition threshold.

Incorporating Lindblad decay dynamics into mixed quantum-classical simulations.

We derive the L-mean-field Ehrenfest (MFE) method to incorporate Lindblad jump operator dynamics into the MFE approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the L-MFE method that satisfies this exact mapping. This establishes a method that uses independent trajectories that exactly reproduce Lindblad decay dynamics using a wavefunction description, with deterministic changes of the magnitudes of the quantum expansion coefficients, while only adding on a stochastic phase. We further demonstrate that when including nuclei in the Ehrenfest dynamics, the L-MFE method gives semi-quantitatively accurate results, with the accuracy limited by the accuracy of the approximations present in the semiclassical MFE approach. This work provides a general framework to incorporate Lindblad dynamics into semiclassical or mixed quantum-classical simulations.

Semi-classical simulation of spin-1 magnets

Theoretical studies of magnets have traditionally concentrated on either classical spins, or the extreme quantum limit of spin-1/2. However, magnets built of spin-1 moments are also intrinsically interesting, not least because they can support quadrupole, as well as dipole moments, on a single site. For this reason, spin-1 models have been extensively studied as prototypes for quadrupolar (spin-nematic) order in magnetic insulators, and Fe-based superconductors. At the same time, because of the presence of quadrupoles, the classical limit of a spin-1 moment is not an $O(3)$ vector, a fact which must be taken into account in describing their properties. In this Article we develop a method to simulate spin-1 magnets based on a $u(3)$ algebra which treats both dipole and quadrupole moments on equal footing. This approach is amenable to both classical and quantum calculations, and we develop the techniques needed to calculate thermodynamic properties through Monte Carlo simulations and classical low-temperature expansion, and dynamical properties, through "molecular dynamics" simulations and a multiple-boson expansion. As a case study, we present detailed analytic and numerical results for the thermodynamic properties of ferroquadrupolar order on the triangular lattice, and its associated dynamics. At low temperatures, we show that it is possible to "correct" for the effects of classical statistics in simulations, and extrapolate to the zero-temperature quantum results found in flavour-wave theory.

Modeling of second sound in carbon nanostructures

The study of thermal transport in low-dimensional materials has attracted a lot of attention recently after discovery of high thermal conductivity of graphene. Here we study numerically phonon transport in low-dimensional carbon structures being interested in the hydrodynamic regime revealed through the observation of second sound. We demonstrate that correct numerical modeling of such two-dimensional systems requires semi-classical molecular dynamics simulations of temperature waves that take into account quantum statistics of thermalized phonons. We reveal that second sound can be attributed to the maximum group velocity of bending optical oscillations of carbon structures, and the hydrodynamic effects disappear for $T>200$K, being replaced by diffusive dynamics of thermal waves. Our numerical results suggest that the velocity of second sound in such low-dimensional structures is about 6 km/s, and the hydrodynamic effects are manifested stronger in carbon nanotubes rather than in carbon nanoribbons.

The complex vibrational spectrum of proline explained through the adiabatically switched semiclassical initial value representation.

Proline, a 17-atom amino acid with a closed-ring side chain, has a complex potential energy surface characterized by several minima. Its IR experimental spectrum, reported in the literature, is of difficult and controversial assignment. In particular, the experimental signal at 3559 cm-1 associated with the OH stretch is interesting because it is inconsistent with the global minimum, trans-proline conformer. This suggests the possibility that multiple conformers may contribute to the IR spectrum. The same conclusion is obtained by investigating the splitting of the CO stretch at 1766 and 1789 cm-1 and other, more complex spectroscopic features involving CH stretches and COH/CNH bendings. In this work, we perform full-dimensional, on-the-fly adiabatically switched semiclassical initial value representation simulations employing the ab initio dft-d3-B3LYP level of theory with aug-cc-pVDZ basis set. We reconstruct the experimental spectrum of proline in its main features by studying the vibrational features of trans-proline and cis1-proline and provide a new assignment for the OH stretch of trans-proline.

Spin-lattice dynamics simulation of the Einstein–de Haas effect

The spin and lattice dynamics of a ferromagnetic nanoparticle are studied via molecular dynamics and with semi-classical spin dynamics simulations where spin and lattice degrees of freedom are coupled via a dynamic uniaxial anisotropy term. We show that this model conserves total angular momentum, whereas spin and lattice angular momentum are not conserved. We carry out simulations of the Einstein–de Haas effect for a Fe nanocluster with more than 500 atoms that is free to rotate, using a modified version of the open-source spin-lattice dynamics code (SPILADY). We show that the rate of angular momentum transfer between spin and lattice is proportional to the strength of the magnetic anisotropy interaction. The addition of the anisotropy allows full spin-lattice relaxation to be achieved on previously reported timescales of ∼100 ps and for tight-binding magnetic anisotropy energies comparable to those of small Fe nanoclusters.

Radiative thermalization in semiclassical simulations of light-matter interaction

Prediction of the equilibrium populations in quantum dynamics simulations of molecules exposed to black-body radiation has proved challenging for semiclassical treatments, with the usual Ehrenfest and Maxwell-Bloch methods exhibiting serious failures. In this context, we explore the behavior of a recently introduced semiclassical model of light-matter interaction derived from a dissipative Lagrangian [C. M. Bustamante, E. D. Gadea, A. Horsfield, T. N. Todorov, M. C. Gonz\'alez Lebrero, and D. A. Scherlis, Phys. Rev. Lett. 126, 087401 (2021)]. It is shown that this model reproduces the Boltzmann populations for two-level systems, predicting the black-body spectra in approximate agreement with Planck's distribution. In multilevel systems, small deviations from the expected occupations are seen beyond the first excited level. By averaging over fast oscillations, a rate equation is derived from the dissipative equation of motion that makes it possible to rationalize these deviations. Importantly, it enables us to conclude that this model will produce the correct equilibrium populations provided the occupations of the lowest levels remain close to unity, a condition satisfied at low temperature or small excitations.

Berry-Phase Switch in Electrostatically Confined Topological Surface States.

Here, we visualize the trapping of topological surface states in the circular n-p junctions on the top surface of the seven-quintuple-layer three dimensional (3D) topological insulator (TI) Sb_{2}Te_{3} epitaxial films. As shown by spatially dependent and field-dependent tunneling spectra, these trapped resonances show field-induced splittings between the degenerate time-reversal-symmetric states at zero magnetic field. These behaviors are attributed unambiguously to Berry-phase switch by comparing the experimental data with both numerical and semiclassical simulations. The successful electrostatic trapping of topological surface states in epitaxial films and the observation of Berry-phase switch provide a rich platform of exploiting new ideas for TI-based quantum devices.

Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

We numerically study out-of-equilibrium dynamics in a family of Heisenberg models with $1/r^6$ power-law interactions and positional disorder. Using the semi-classical discrete truncated Wigner approximation (dTWA) method, we investigate the time evolution of the magnetization and ensemble-averaged single-spin purity for a strongly disordered system after initializing the system in an out-of-equilibrium state. We find that both quantities display robust glassy behavior for almost any value of the anisotropy parameter of the Heisenberg Hamiltonian. Furthermore, a systematic analysis allows us to quantitatively show that, for all the scenarios considered, the stretch power lies close to the one analytically obtained in the Ising limit. This indicates that glassy relaxation behavior occurs widely in disordered quantum spin systems, independent of the particular symmetries and integrability of the Hamiltonian.

Analysis of correlations in strong field ionization

We propose to use correlation function analysis as a tool for the study of strong field ionization. We show, in particular, that study of the correlations of electron’s coordinate and velocity reveals patterns which can be naturally interpreted as manifestations of the electron’s exit point (the spatial point where the electron exits the tunneling barrier). This analysis provides an unambiguous definition of the exit point. The location of the exit point thus determined agrees well with the estimates used in the semiclassical simulations.

Gravitational collapse of quantum fields and Choptuik scaling

Gravitational collapse into a black hole has been extensively studied with classical sources. We develop a new formalism to simulate quantum fields forming a black hole. By choosing a convenient coherent state, this formalism taps into well-established techniques used for classical collapse and adds on the evolution of the mode functions of the quantum field operator. Divergences are regularized with the cosmological constant and Pauli-Villars fields. Using a massless spherically symmetric scalar field as an example, we demonstrate the effectiveness of the formalism by reproducing some classical results in gravitational collapse, and identifying the difference due to the quantum effects. We also find that Choptuik scaling in critical collapse survives in the semiclassical simulation, and furthermore the quantum deviation from the classical Choptuik scaling decreases when the system approaches the critical point.

The free electron model and the electronic energy losses of protons at low velocities interacting with polycrystalline tantalum

In this letter, we report experimental data and theoretical work on the electronic energy loss and energy loss straggling of protons transmitted through self-supported thin films of tantalum in a polycrystalline tetragonal phase . Low-energy protons with energies below 10 keV and Ta films with nominal thickness of 6, 9 and 12 nm are used. The aim of this work is to understand the unexpected values of the Ta stopping power for low-energy proton backscattering reported recently, which are far from the prediction of the standard free electron gas model and semi-empirical approaches. This had led the authors to conclude the failure of the free electron model. Our transmission measurements confirm these experimental results. In this work, a qualitative discussion and quantitative explanation of our experimental results is given, using an approach based on the density functional theory within the framework of the free electron gas (FEG) model. We performed semiclassical deterministic trajectory simulations and employ the local density approximation model, using an inhomogeneous electron density distribution and the polycrystalline character of Ta samples.

Multi-scale modeling of 2D GaSe FETs with strained channels

Electronic devices based on bidimensional materials (2DMs) are the subject of an intense experimental research, that demands a tantamount theoretical activity. The latter must be hold up by a varied set of tools able to rationalize, explain and predict the operation principles of the devices. However, in the broad context of multi-scale computational nanoelectronics, there is currently a lack of simulation tools connecting atomistic descriptions with semi-classical mesoscopic device-level simulations and able to properly explain the performance of many state-of-the-art devices. To contribute to filling this gap we present a multi-scale approach that combines fine-level material calculations with a semi-classical drift-diffusion transport model. Its use is exemplified by assessing 2DM field effect transistors with strained channels, showing excellent capabilities to capture the changes in the crystal structure and their impact into the device performance. Interestingly, we verify the capacity of strain in monolayer GaSe to enhance the conduction of one type of carrier, enabling the possibility to mimic the effect of chemical doping on 2D materials. These results illustrate the great potential of the proposed approach to bridge levels of abstraction rarely connected before and thus contribute to the theoretical modeling of state-of-the-art 2DM-based devices.

Collective dynamics of liquid deuterium: Neutron scattering and approximate quantum simulation methods

Quantum liquids are growing in importance both in research and applications. Some of their properties, however, are not easy to measure or simulate. By means of a comprehensive analysis of neutron Brillouin scattering on the semiquantum deuterium liquid, the authors demonstrate that experiment and current semiclassical simulation methods deliver different results for the principal manifestation of the quantum nature of cold liquids in their dynamical properties, which is the rather long lifetimes of collective excitations.