Recurrence Spectra Research Articles

Signatures of Exciton Orbits in Quantum Mechanical Recurrence Spectra of Cu_{2}O.

The seminal work by Kazimierczuk etal. [Nature 514, 343 (2014)10.1038/nature13832] has shown the existence of highly excited exciton states in a regime, where the correspondence principle is applicable and quantum mechanics turns into classical mechanics; however, any interpretation of exciton spectra based on a classical approach to excitons is still missing. Here, we close this gap by computing and comparing quantum mechanical and semiclassical recurrence spectra of cuprous oxide. We show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. The application of semiclassical theories to exciton physics requires the detailed analysis of the classical exciton dynamics, including three-dimensional orbits, which strongly deviate from hydrogenlike Keplerian orbits. Our findings illuminate important aspects of excitons in semiconductors by directly relating the quantum mechanical band structure splittings of excitons to the corresponding classical exciton dynamics.

Recurrence Spectra of European Temperature in Historical Climate Simulations

We analyse and quantify the recurrences of European temperature extremes using 32 historical simulations (1900–1999) of the fifth Coupled Model Intercomparison Project (CMIP5) and 8 historical simulations (1971–2005) from the EUROCORDEX experiment. We compare the former simulations to the 20th Century Reanalysis (20CRv2c) dataset to compute recurrence spectra of temperature in Europe. We find that, (1) the spectra obtained by the model ensemble mean are generally consistent with those of 20CR; (2) spectra biases have a strong regional dependence; (3) the resolution does not change the order of magnitude of spectral biases between models and reanalysis, (4) the spread in recurrence biases is larger for cold extremes. Our analysis of biases provides a new way of selecting a subset of the CMIP5 ensemble to obtain an optimal estimate of temperature recurrences for a range of time-scales.

Determining periodic orbits via nonlinear filtering and recurrence spectra in the presence of noise

In nonlinear dynamical systems the determination of stable and unstable periodic orbits as part of phase space prediction is problematic in particular if perturbed by noise. Fourier spectra of the time series or its autocorrelation function have shown to be of little use if the dynamic process is not strictly wide-sense stationary or if it is nonlinear. To locate unstable periodic orbits of a chaotic attractor in phase space the least stable eigenvalue can be determined by approximating locally the trajectory via linearisation. This approximation can be achieved by employing a Gaussian kernel estimator and minimising the summed up distances of the measured time series i.e. its estimated trajectory (e.g. via Levenberg-Marquardt). Noise poses a significant problem here. The application of the Wiener-Khinchin theorem to the time series in combination with recurrence plots, i.e. the Fourier transform of the recurrence times or rates, has been shown capable of detecting higher order dynamics (period-2 or period-3 orbits), which can fail using classical FouRiER-based methods. However little is known about its parameter sensitivity, e.g. with respect to the time delay, the embedding dimension or perturbations.Here we provide preliminary results on the application of the recurrence time spectrum by analysing the Hénon and the Rössler attractor. Results indicate that the combination of recurrence time spectra with a nonlinearly filtered plot of return times is able to estimate the unstable periodic orbits. Owing to the use of recurrence plot based measures the analysis is more robust against noise than the conventional Fourier transform.

SENSING STOCHASTICITY OF ATOMIC SYSTEMS BY ANALYSIS OF RECURRENCE SPECTRA IN AN CROSSED DC MAGNETIC AND AC ELECTRIC FIELDS

A new method for sensing stochasticity and chaotic features of atomic and nano-optical systems in the crossed external electric and magnetic fields is developed and a dynamics of atomic systems in fields studied. As a basis for developing a new method for sensing stochasticity we use new quantum approach to calculation of the recurrence energy spectra and their statistical characteristics for atomic systems in crossed electric and magnetic fields in chaotic regime and some experimental data for checking obtained results. Some illustrations regarding the recurrence spectra and stochasticity in a number of atomic systems are presented.

Experimental isotope shifts in Stark recurrence spectra of Rydberg D2and H2molecules

D${}_{2}$ and H${}_{2}$ Stark recurrence spectra have been measured at scaled energies of $\ensuremath{\epsilon}=\ensuremath{-}2.3$ and $\ensuremath{\epsilon}=\ensuremath{-}3.2$. An isotope shift in the scaled-action locations of recurrence peaks is found and explained by the increased density of states associated with perturbing rotational series. This reinforces the insight gained in previous work on the correspondence between the structures of a quantum spectrum and its classical periodic orbits.

Rydberg-electron decoherence in experimentally obtained recurrence spectra

Using scaled-energy spectroscopy techniques (recurrence spectroscopy) we investigate the influence of collisionally induced decoherence on semiclassical orbits in the Stark-Rydberg system. This experimental investigation represents the first application of recurrence spectroscopy to an atomic system perturbed by collisions with external gas partners. We present high-resolution recurrence spectra of potassium, revealing core-scattered combination orbits, and with minor modifications to the data acquisition process, recurrence spectra were also obtained with the system perturbed by 10 torr of krypton gas. A simple decoherence model is applied to semiclassical theory to explain the loss of recurrence strength at high actions. In several cases we also observe the loss of coherent interference between orbits. The loss of coherent destructive interference causes an increase in the recurrence strength of several core-scattered combination orbits.

Chaotic Dynamics and the Recurrence Spectra of the Rydberg Hydrogen Atom Near a Dielectric Surface

The classical electronic motion of the Rydberg hydrogen atom near a dielectric surface has been studied by using the Poincaré surfaces of section method and the closed orbit theory. The structure and evolution of the phase space as a function of the scaled energy is explored extensively by means of the Poincaré surfaces of section. The results suggest that when the scaled energy is less than the critical energy epsilon(s), the whole phase space structure is regular. However, when the energy is larger than epsilon(s), chaotic motions appear. The recurrence spectra of this system have also been calculated. The results show that, for a given scaled energy larger than the critical energy epsilon(s), when the dielectric constant alpha is small, the influence of the dielectric surface can be neglected and the number of closed orbits is very small. With the increase of the dielectric constant alpha, the effect of the dielectric surface becomes significant, the number of closed orbits increases, and there are more peaks in the recurrence spectra. When alpha = 1.0, the recurrence spectra approach the case of the Rydberg hydrogen atom near a metallic surface. This study provides a new method to explore the dynamic behavior of the Rydberg atom interacting with a dielectric surface.

Recurrence spectra of Rydberg NO molecules in a strong magnetic field

Considering the influence of core rotation, we calculate the recurrence spectra of Rydberg NO molecules in the strong external magnetic field by using the molecular closed orbit theory and the multichannel quantum defect theory. The results indicate that the complicated recurrence spectra can be explained by the molecular closed orbit theory including the molecular core-scattering. Not only the elastic core-scattering effect arising from the intrachannel scattering, but also the inelastic core-scattering effect arising from the interchannel scattering is vital to the dynamical properties of the Rydberg molecule. Especially on the larger scaled action, the contribution of core-scattering is more crucial than that of the primary closed orbits and their repetition, and affects the dynamical properties of system to a large extent.

Multielectron structure and dynamics in scaled-energy Stark photoabsorption and recurrence spectra

We use the $4s{[3/2]}_{2}^{o}$ metastable state of atomic argon created by charge-transfer collisions between a 5 keV ${\text{Ar}}^{+}$ beam and K vapor to perform laser scaled-energy Stark photoabsorption and recurrence spectroscopy of even-parity Rydberg states, detected by field ionization and forced autoionization, in a region of the spectrum that contains two distinct perturbations. We apply a uniform electric field that changes with the frequency of the laser to maintain a constant scaled energy relative to the first ionization limit of the atom, associated with the ion core in a ${^{2}P}_{3/2}$ configuration. Local perturbations to the Rydberg series $(15\ensuremath{\le}n\ensuremath{\le}28)$ occur due to ${n}^{\ensuremath{'}}=8$ and 10 Stark states that belong to the series converging to the second ionization threshold with the ion core in a ${^{2}P}_{1/2}$ configuration. The resulting absorption spectra show multielectron effects due to configuration interaction and angular momentum coupling. These effects have dynamical implications in the recurrence spectrum. In particular, the variations in the Stark structure of the absorption spectrum result in a recurrence spectrum that shows two prominent multielectron features. One is the presence of recurrence peaks with scaled actions less than that of the hydrogenic primitive orbit. We attribute this to excitation in which both the ion core and the Rydberg electron absorb energy during photoexcitation. The second multielectron effect observed is recurrence peaks that occur at the sum of scaled actions of the primitive orbit (and its repetitions) associated with the pair of perturbations and a hydrogenic closed classical orbit. We attribute these peaks to core-changing inelastic scattering of the Rydberg electron with the ionic core due to angular momentum coupling. For comparison, we measured the regular autoionizing Rydberg series of argon between the first and second ionization thresholds, where no perturbing resonances exist.

Semiclassical Calculation of Recurrence Spectra of Rydberg Hydrogen Atom Near a Metal Surface

Using closed orbit theory, we give a clear physical picture description of the Rydberg hydrogen atom near a metal surface and calculate the Fourier transformed recurrence spectra of this system at different scaled energies below ionization threshold. The results show that with the increase of the scaled energy, the number of the closed orbit increases greatly. Some of the orbits are created by the bifurcation of the perpendicular orbit. This case is quite similar to the Rydberg atom in an electric field. When the scaled energy increases furthermore, chaotic orbits appear. This study provides a different perspective on the dynamical behavior of the Rydberg atom near a metal surface.

The dynamics of Rydberg atom in an electric field near the saddle point

The system composed of Rydberg Li atom in an electric field is chaotic because of the core scattering. The period orbits and the closed orbits both exist near the saddle point. The dynamics of this system is studied with the closed-orbit-theory and Poincaré SOS method. The relations of the two methods are discussed for the first time and new information is obtained which can't be retrieved from the recurrence spectra.

The recurrence spectra of Rydberg HeH+ molecule ion in a magnetic field

Making use of the molecular closed-orbit theory and a new model potential for the Rydberg molecule, we calculated the recurrence spectra of HeH(+) molecule ion in a magnetic field for different quantum defects. The Fourier transformed spectra of HeH(+) molecule ion have allowed direct comparison between peaks in the spectra and the scaled action values of closed orbits of the excited electron in the external fields. We find that the spectral modulations can be analyzed in terms of the scattering of the excited electron on the molecular core. Unlike the case of the Rydberg atom where the elastic scattering is predominant, modulations produced by inelastic scattering are also vital to the photoabsorption spectrum of Rydberg molecule. Our results are in good agreement with the quantum results, which suggest that our method is correct.

Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincaré surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy εc, for ε < εc, the system is near-integrable, and as the decrease of ε the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if ε > εc, with the increase of ε, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.

Recurrence spectra and dynamical simulation of Rydberg hydrogen atom near a metal surface

By using the closed-orbit theory including the effect of Coulomb scattering together with an electrical image potential approach, the recurrence spectra and the dynamical behaviours of the Rydberg hydrogen atom near a metal surface are presented. Theoretical analysis and numerical simulation reveal that the impacts of the image potential contributing to the recurrence spectrum are qualitatively analogous to that of the parallel electrical and magnetic fields on the Rydberg atom. The recurrence spectra are computed for a few selected scaled energies and the results demonstrate that the scaled energy dominates the dynamical properties of system. With the increase of the scaled energy e from small to large, the whole trend of spectral structure is from simple to complex,and then simple.

The recurrence spectra of the Rydberg hydrogen atom interacting with a metallic surface and an electric field

The classical electronic motion of the Rydberg hydrogen atom near a metallic surface in the presence of a uniform electric field has been studied by using the closed orbit theory. The recurrence spectra of this system have also been calculated. The results show: for a given scaled energy larger than the critical energy ɛ s, as the scaled electric field is very small ( f = 0.01), the influence of the electric field can be neglected and the recurrence spectra are nearly the same as those of the Rydberg hydrogen atom near a metallic surface. With the increase of the scaled electric field, the electric field force acting on the electron counteracts the metallic attraction, and then the probability that the electron might be captured by the metal surface is small. Therefore, the number of the closed orbits increases and there are more peaks in the recurrence spectra accordingly. As f = 1.0, the influence of the metallic surface becomes small and the recurrence spectra are similar to the case as only electric field exists.

Scattering matrix theory for Cs Rydberg atoms in magnetic field

Based on the closed orbit theory framework together with the quantum defect theory and time-independent scattering matrices theory, we calculate the recurrence spectra of diamagnetic Cs atoms at several different scaled energies near the second ionization threshold. It is revealed that the new extra peaks in spectra are attributed to the combination recurrences of semiclassical closed orbits arising from core-scattered events. This method considers the dynamic states of the Rydberg electron in the core region and long-range region and can be analytically resumed to include all orders of core-scattering automatically. With this approach a convergent recurrence spectrum can be reasonably achieved. It is found that the spectral complexity depends highly sensitively on the scaled energy. With the increase of the scaled energy, the spectral structure changes from simple to complicate and the dynamic feature from regular to chaotic. The comparison of the recurrence spectra with Dando’s result under the same conditions demonstrates that there exist some similarities and differences between them, and furthermore, the feasibility of the scattering matrix method is explained.

Recurrence spectroscopy of potassium near ionization using laser diodes

In this investigation recurrence spectra of potassium are acquired using 405 and $980\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ laser diodes. Atoms were excited to Rydberg-Stark states $(n\ensuremath{\approx}70)$ resonantly via the $5{p}_{3∕2}$ state and recurrence spectra were obtained near the classical ionization threshold. The data suggest that the outgoing distribution of electrons is more symmetric in potassium than in hydrogen or sodium and that phase shifts incurred by the electron wave function as it passes through the atomic core cause regular destructive interference within the recurrence spectra.

Short-ranged potential effects on the recurrence spectra of lithium M = 1 atoms in parallel electric and magnetic fields

This paper presents recurrence spectra of highly excited lithium atoms with M = 1 state in parallel electric and magnetic fields at a fixed scaled energy ∊ = -0.03. Short-ranged potentials including ionic core potential and centrifugal barrier are taken into account. Their effects on the states and photo-absorption spectrum are analysed in detail. This demonstrates that the geometric features of classical orbits are of special importance for modulations of the spectral pattern. Thus the weak polarization as well as the reduction of correlation of electrons induced by short-ranged potentials give rise to the recurrence spectra of lithium M = 1 atoms more compact than that of the M = 0 one, which is in good agreement with the experimental prediction.

Absorption and Recurrence Spectra of Nonhydrogenic Rydberg Atom Near a Metal Surface

Multielectron atoms near a metal surface are essentially more complicated than hydrogen atom with regard to theoretical treatments. By using the semicalssical closed orbit theory generalized to the multielecton atoms, we study the dynamical properties of the Rydberg lithium atom near a metal surface. The photoabsorption spectra and recurrence spectra of this system have also been calculated. Considering the effect of the ionic core potential of the Rydberg lithium atom, the number of the closed orbits increases, which leads to more peaks in the recurrence spectra than the case of hydrogen atom near a metal surface. This result shows that the core-scattered effects play an important role in nonhydrogenic atoms. This study is a new application of the closed-orbit theory and is of potential experimental interest.

Semiclassical calculation of recurrence spectra of Rydberg He2+ molecular ion in a magnetic field

Making use of the molecular closed-orbit theory and a new model potential for the Rydberg molecule, we have calculated the recurrence spectra of He2+ molecular ion in a magnetic field for different quantum defects. The Fourier transform spectra of He2+ molecular ion may be used to perform a direct comparison between peaks in the spectra and the scaled action values of closed orbits of the excited electron in external fields. We find that the spectral modulations can be analysed in terms of the scattering of the excited electron on the molecular core. Unlike the case of the Rydberg atom where the elastic scattering is predominant, modulations produced by inelastic scattering are also vital to the photoabsorption spectrum of the Rydberg molecule. Our results are in good agreement with the quantum results, which suggests that our method is correct.