Dense Spectrum Research Articles

Coupling a Superconducting Qubit to a Left-Handed Metamaterial Resonator

Metamaterial resonant structures made from arrays of superconducting lumped circuit elements can exhibit microwave mode spectra with left-handed dispersion, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this novel regime for multi-mode circuit quantum electrodynamics, we have performed a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we have observed the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we have probed the qubit dispersively and characterized the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we have investigated the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation and quantum memories.

Energy-Efficient PRBS Impedance Spectroscopy on a Digital Versatile Platform

This article presents the digital design of a versatile and low-power broadband impedance spectroscopy (IS) system based on the pseudorandom binary sequence (PRBS) excitation. The PRBS technique allows fast and low-power estimation of the impedance spectrum over a wide bandwidth with adequate accuracy, proving to be a good candidate for portable medical devices, especially. This article covers the low-power design of the firmware algorithms and implements them on a versatile and reconfigurable digital platform that can be easily adjusted to the specific application. It will analyze the digital platform with the aim of reducing power consumption while maintaining adequate accuracy of the estimated spectrum. This article studies two main algorithms (time-domain and frequency-domain) used for PRBS-based IS and implements both of them on the ultralow- power GAP-8 digital platform. They are compared in terms of accuracy, measurement time, and power budget, while the general design tradeoffs are drawn out. The time-domain algorithm demonstrated the best accuracy, while the frequency-domain one contributes more to save power and energy. However, the analysis of the energy-per-error FOM revealed that the time-domain algorithm outperforms the frequency-domain algorithm, offering better accuracy for the same energy consumption. Numerical methods and microprocessor resources are exploited to optimize the implementation of both algorithms, achieving a 27-ms processing time, the power consumption of as low as 1.4 mW, and a minimum energy consumption per measurement of 0.5 mJ, for a dense impedance spectrum estimation of 214 points.

Investigation of mode interaction for a gyrotron with dense mode spectrum

ABSTRACT Influence of the density of mode spectrum in the gyrotron cavity on the possibility of stable single-mode operation has been investigated for high-order modes. Interaction of the operating mode with its two neighboring satellites, symmetrically spaced in frequency, is analyzed. Some threshold value of mode spectrum density dependent on the beam current is found.

Highly Sensitive Complicated Spectrum Analysis in Micro-Bubble Resonators Using the Orthogonal Demodulation Pound–Drever–Hall Technique

Whispering gallery mode micro-bubble optical cavities are asymmetrical ellipsoids in experimental settings, which makes their modes nondegenerate. A complicated dense spectrum is thus generated. Overlapping and coupled resonances exist in this dense spectrum. In this study, we determined that the orthogonal demodulation Pound-Drever-Hall technique can be used to analyze complicated resonances. Using this method, overlapping weak and strong coupling resonances can be analyzed. Compared to spectrum simplification and the ab initio theory of Fano resonances, this method is repeatable, simple, sensitive, and accurate. The method can increase the measurement range of differential resonance sensing, thus allowing the differential sensing of overlapped resonances.

Undecidability of the Spectral Gap in One Dimension

The spectral gap problem - determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations - pervades quantum many-body physics. Recently, this important problem was shown to be undecidable for quantum spin systems in two (or more) spatial dimensions: there exists no algorithm that determines in general whether a system is gapped or gapless, a result which has many unexpected consequences for the physics of such systems. However, there are many indications that one dimensional spin systems are simpler than their higher-dimensional counterparts: for example, they cannot have thermal phase transitions or topological order, and there exist highly-effective numerical algorithms such as DMRG - and even provably polynomial-time ones - for gapped 1D systems, exploiting the fact that such systems obey an entropy area-law. Furthermore, the spectral gap undecidability construction crucially relied on aperiodic tilings, which are not possible in 1D. So does the spectral gap problem become decidable in 1D? In this paper we prove this is not the case, by constructing a family of 1D spin chains with translationally-invariant nearest neighbour interactions for which no algorithm can determine the presence of a spectral gap. This not only proves that the spectral gap of 1D systems is just as intractable as in higher dimensions, but also predicts the existence of qualitatively new types of complex physics in 1D spin chains. In particular, it implies there are 1D systems with constant spectral gap and non-degenerate classical ground state for all systems sizes up to an uncomputably large size, whereupon they switch to a gapless behaviour with dense spectrum.

Self-consistent method to extract non-linearities from pulsating star light curves – I. Combination frequencies

ABSTRACT Stellar pulsation is a common phenomenon and is sustained because of coherent driving mechanisms. When pulsations are driven by heat or convective mechanisms, it is usual to observe combination frequencies in the power spectra of the stellar light-curves. These combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light-curve of a given multiperiodic pulsating star, they can compromise the mode identification in asteroseismic analyses, and hence they must be treated as spurious frequencies and removed. In this paper, a method based on fitting the set of frequencies that best describes a general non-linear model, like the Volterra series, is presented. The method allows these frequencies to be extracted from the power spectrum, thereby improving the frequency analysis and enabling hidden frequencies to emerge from what was initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, which is sometimes used as if it were an error when identifying combination frequencies. Furthermore, it is compatible with the classical counting cycles method, the so-called O-C method, which is valid only for mono-periodic stars. The method creates the possibility of characterizing the non-linear behaviour of a given pulsating star by studying in detail the complex generalized transfer functions on which the model is based.

Remarks on Scattering Matrices for Schrödinger Operators with Critically Long-Range Perturbations

We consider scattering matrix for Schrödinger-type operators on \(\mathbb {R}^d\) with perturbation \(V(x)=O(\langle x \rangle ^{-1})\) as \(|x|\rightarrow \infty \). We show that the scattering matrix (with time-independent modifiers) is a pseudodifferential operator and analyze its spectrum. We present examples of which the spectrum of the scattering matrices has dense point spectrum, and absolutely continuous spectrum, respectively. These give a partial answer to an open question posed by Yafaev (Scattering theory: some old and new problems. Springer Lecture Notes in Mathematical, vol 1735, 2000).

Conformational Panorama and Chirality Controlled Structure-Energy Relationship in a Chiral Carboxylic Acid Dimer.

Chirality recognition in dimers of tetrahydro-2-furoic acid (THFA) was studied in a conformer-specific manner using rotational spectroscopy and theoretical approaches. THFA shows a strong preference for the trans- over the cis-COOH configuration. Two drastically different scenarios are possible for the detectable (THFA)2 : a kinetically preferred dimer bound by feeble interactions between two trans THFAs or a thermodynamically favored dimer with a double hydrogen-bonded ring structure between two cis subunits. To identify the conformers responsible for the extremely dense rotational spectra observed, it was essential not only to locate several hundred homo/heterochiral (THFA)2 minima in ab initio calculations but also to evaluate the energetic connectivities among the minima. The study further reveals an interesting chirality dependent structure-energy ordering relationship. A method for enantiomeric excess (ee) determination of THFA is presented using a recently proposed chiral self-tag approach.

Conformational Panorama and Chirality Controlled Structure–Energy Relationship in a Chiral Carboxylic Acid Dimer

AbstractChirality recognition in dimers of tetrahydro‐2‐furoic acid (THFA) was studied in a conformer‐specific manner using rotational spectroscopy and theoretical approaches. THFA shows a strong preference for the trans‐ over the cis‐COOH configuration. Two drastically different scenarios are possible for the detectable (THFA)2: a kinetically preferred dimer bound by feeble interactions between two trans THFAs or a thermodynamically favored dimer with a double hydrogen‐bonded ring structure between two cis subunits. To identify the conformers responsible for the extremely dense rotational spectra observed, it was essential not only to locate several hundred homo/heterochiral (THFA)2 minima in ab initio calculations but also to evaluate the energetic connectivities among the minima. The study further reveals an interesting chirality dependent structure–energy ordering relationship. A method for enantiomeric excess (ee) determination of THFA is presented using a recently proposed chiral self‐tag approach.

A structural health monitoring Python code to detect small changes in frequencies

Observing the occurrence of cracks in the early stage remains a challenge, as changes in the modal parameters produced by these cracks are small. This remark is also valid for deeper cracks because in most experiments it is possible to acquire short signals, which ensure a coarse frequency resolution. Therefore, the accurate estimation of frequency by standard methods is impossible. To improve frequency readability, we designed an algorithm that we implemented in the PyFEST application, written in Python programming language. It allows a fast and accurate calculation of harmonic components of a signal. PyFEST is based on an original signal post-processing algorithm, which consists of overlapping spectra for the signal iteratively cropped. The different signal lengths ensure different positions of the spectral lines in the overlapped spectrum. Therefore, adding numerous spectral lines of different positions in the overlapped spectrum we obtain a dense spectrum with significantly increased frequency resolution. From this spectrum, we select the three magnitudes of the individual spectra found in the frequency range of interest. By interpolation, we attain the maximum that has usually an inter-line position representing the estimated frequency. To this frequency, we apply a correction term that is known a priori and so we improve the frequency estimation. To test the reliability of PyFEST, we provide examples for signals generated with known frequencies that have one or more harmonic components. For signals containing one harmonic component the exact frequency was found, while for signals with multiple components the error are less than 0.1%. The frequency change is exactly estimated for both types of signals. Because PyFEST allows observing minor frequency changes, so we succeed to localize the crack position and severity in real beams with high precision.

The periodic table and the physics that drives it.

Mendeleev's introduction of the periodic table of elements is one of the most important milestones in the history of chemistry, as it brought order into the known chemical and physical behaviour of the elements. The periodic table can be seen as parallel to the Standard Model in particle physics, in which the elementary particles known today can be ordered according to their intrinsic properties. The underlying fundamental theory to describe the interactions between particles comes from quantum theory or, more specifically, from quantum field theory and its inherent symmetries. In the periodic table, the elements are placed into a certain period and group based on electronic configurations that originate from the Pauli and Aufbau principles for the electrons surrounding a positively charged nucleus. This order enables us to approximately predict the chemical and physical properties of elements. Apparent anomalies can arise from relativistic effects, partial-screening phenomena (of type lanthanide contraction) and the compact size of the first shell of every l-value. Further, ambiguities in electron configurations and the breakdown of assigning a dominant configuration, owing to configuration mixing and dense spectra for the heaviest elements in the periodic table. For the short-lived transactinides, the nuclear stability becomes an important factor in chemical studies. Nuclear stability, decay rates, spectra and reaction cross sections are also important for predicting the astrophysical origin of the elements, including the production of the heavy elements beyond iron in supernova explosions or neutron-star mergers. In this Perspective, we critically analyse the periodic table of elements and the current status of theoretical predictions and origins for the heaviest elements, which combine both quantum chemistry and physics.

Koopman spectra in reproducing kernel Hilbert spaces

Every invertible, measure-preserving dynamical system induces a Koopman operator, which is a linear, unitary evolution operator acting on the $L^2$ space of observables associated with the invariant measure. Koopman eigenfunctions represent the quasiperiodic, or non-mixing, component of the dynamics. The extraction of these eigenfunctions and their associated eigenfrequencies from a given time series is a non-trivial problem when the underlying system has a dense point spectrum, or a continuous spectrum behaving similarly to noise. This paper describes methods for identifying Koopman eigenfrequencies and eigenfunctions from a discretely sampled time series generated by such a system with unknown dynamics. Our main result gives necessary and sufficient conditions for a Fourier function, defined on $N$ states sampled along an orbit of the dynamics, to be extensible to a Koopman eigenfunction on the whole state space, lying in a reproducing kernel Hilbert space (RKHS). In particular, we show that such an extension exists if and only if the RKHS norm of the Fourier function does not diverge as $ N \to \infty $, in which case the corresponding Fourier frequency is also a Koopman eigenfrequency. If such an RKHS extension does not exist, we can still construct an $L^2$ approximation of the eigenfunction. Numerical experiments on mixed-spectrum systems with weak periodic components demonstrate that this approach has significantly higher skill in identifying Koopman eigenfrequencies compared to conventional spectral estimation techniques based on the discrete Fourier transform.

The Emergence of Chaos in Quantum Mechanics

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere.

Analysis of the Coriolis perturbed rovibrational spectrum of the C[sbnd]O asymmetric stretch and C[sbnd]C symmetric stretch of trimethylene oxide

Rotationally-resolved vibrational spectra of trimethylene oxide (c-C3H6O) were recorded using synchrotron radiation from the Canadian Light Source between 400 and 1200 cm−1 with a resolution of 0.000959 cm−1. The dense spectra are composed of transitions arising from excitation of several fundamental vibrations as well as hotbands and combination bands involving the very low frequency ring puckering (ν18) vibration at ~53 cm−1. To date, 3452 transitions have been assigned corresponding to the CO asymmetric stretch (ν23) at ~1008 cm−1 and the CC symmetric stretch (ν6) at ~1033 cm−1 which are coupled via second order c-type Coriolis interaction. An additional perturbation from a lower energy state was observed and attributed to a first order b-type interaction with a state that is likely the combination of the CC asymmetric stretching (ν24) at ~937 cm−1 and ring puckering motions. An additional 916 transitions involving the CO stretching mode were assigned to two hotbands that originate in the first and second excited ring puckering states of trimethylene oxide. Accurate band centers for the ν6, ν23, ν23 + ν18, ν23 + 2ν18 and ν24 + ν18 vibrational states were determined and are compared with harmonic and anharmonic frequency estimates at the MP2 and DFT B3LYP levels using the 6-311++G(d,p) basis set. The analysis of additional features at lower frequency is in progress and will be reported in a subsequent article.

Influence of initial geometric imperfections on the 1:1:1:1 internal resonances and nonlinear vibrations of thin-walled cylindrical shells

The analysis of internal resonances in continuous structural systems is one of the main research areas in the field of nonlinear dynamics. Internal resonances enable the transfer of energy between the related vibration modes, usually leading to new phenomena that have a profound influence on nonlinear oscillations, bifurcations and dynamic instabilities. Shells of revolution usually exhibit internal resonances due to their inherent circumferential symmetry and dense frequency spectrum in the lower frequency range, which may lead not only to m:n internal resonances but also to multiple internal resonances. In this work, the nonlinear response of an imperfect circular cylindrical shell, simply supported at the edges, to harmonic excitation is studied. Geometries that have two modes with n and n+1 circumferential waves, corresponding to the lowest natural frequency, are identified. These two modes are driven to resonance, with each being in one-to-one internal resonance with its companion mode, thus leading to a possible 1:1:1:1 internal resonance, a topic rarely investigated in the technical literature. The investigation of internal resonances in continuous systems is usually conducted using low-dimensional discrete models. Here, using a perturbation procedure, a consistent modal expansion is derived for an arbitrary number of interacting modes, leading to reliable low-dimensional models. Using the discrete models derived in this way, the shell nonlinear dynamics is explored by using bifurcation diagrams of the Poincaré map, continuation techniques and the Floquet stability criterion. The importance of internal resonances to the nonlinear vibrations and instabilities of the shell is clarified. It is well known that small geometric imperfections in the order of the shell thickness have a strong influence on the buckling and post buckling behavior of a thin-walled shell. However, their influence on internal resonances, dynamic instability and energy transfer is largely unknown. Thus, a detailed parametric analysis that considers different types of modal imperfection is conducted in the present work, and the influence of such imperfections on the activation of energy exchanges between the modes involved is analyzed. The results confirm that the form and magnitude of initial geometric imperfections have a profound influence on the results, enabling or preventing the transfer of energy among the resonant modes being considered. • Derivation of a consistent modal expansion by a perturbation procedure considering arbitrary number of interacting modes. • The influence of geometric imperfections on internal resonances, dynamic instability and energy transfer between modes. • Analysis of 1:1:1:1 internal resonance considering four vibration modes with the same natural frequency. • The dynamic bifurcations are sensitive to the form and magnitude of initial geometric imperfections.

A new program for the assignment and fitting of dense rotational spectra based on spectral progressions: Application to the microwave spectrum of pivalic anhydride

A new computerized package for the rapid processing and analysis of dense rotational spectra is described. The package is based on the automated identification of user-specified spectral progressions and interacts with the operator through a simple graphical user interface. In addition to containing an algorithm for obtaining spectral assignments, the package includes a peak-finder with adjustable baseline drift compensation, seamless interfacing with Pickett’s SPFIT and SPCAT programs, and a number of visualization features. The utility of the program is illustrated through its application to the analysis of new spectra of pivalic anhydride, (CH3)3CCOOCOC(CH3)3. Spectra of the parent, as well as all isotopologues with single heavy-atom substitution, are reported, as are calculations for the parent species at the M06-2X/6-311++G(3df,3pd) level of theory. The central oxygen atom is poorly located due to its proximity to the center of mass of the molecule, but a Kraitchman analysis of the fitted rotational constants otherwise provides a detailed structural characterization of the heavy-atom frame. The two carbonyl groups are not coplanar, but rather form a dihedral angle of 53.9(39) deg.

Synchrotron-Based High Resolution Far-Infrared Spectroscopy of trans-Butadiene.

The high resolution far-infrared spectrum of trans-butadiene has been reinvestigated by Fourier-transform spectroscopy at two synchrotron radiation facilities, SOLEIL and the Canadian Light Source, at temperatures ranging from 50 to 340 K. Beyond the well-studied bands, two new fundamental bands lying below 1100 cm-1, ν10 and ν24, have been assigned using a combination of cross-correlation (ASAP software) and Loomis-Wood type (LWWa software) diagrams. While the ν24 analysis was rather straightforward, ν10 exhibits obvious signs of a strong perturbation, presumably owing to interaction with the dark ν9 + ν12 state. Effective rotational constants have been derived for both the v10 = 1 and v24 = 1 states. Since only one weak, infrared active fundamental band (ν23) of trans-butadiene remains to be observed at high resolution in the far-infrared, searches for the elusive gauche conformer can now be undertaken with considerably greater confidence in the dense ro-vibrational spectrum of the trans form.

Spatial forced oscillations of axisymmetric inhomogeneous systems

The aim of this paper is to develop an adequate mathematical model, methods and algorithms for solving three-dimensional problems for axisymmetric spatial inhomogeneous viscoelastic systems (shells, foundations and bases) and to assess the dynamics of protective shell (containment) of a nuclear power plant (NPP) under resonant modes of vibration. The problem is solved using the semi-analytical finite element method. Firstly, the eigenmodes of vibration of the system are determined in an elastic three-dimensional statement, secondly, the solution to the problem of forced vibrations of viscoelastic systems is constructed using the expansion of these eigenmodes of vibration. Viscoelastic properties of the material are described using the hereditary Boltzmann-Volterra theory. The principle of virtual displacements is used to simulate dynamic processes in inhomogeneous viscoelastic systems. The convergence and accuracy of the solutions obtained are investigated by test problems. The frequency response characteristics (FRC) in various points of the NPP containment are estimated at various viscosity parameters of the material. It was revealed that the highest amplitude of vibrations in resonance modes occurs at close values of the frequency of external effect to the first eigen frequencies of the system; in the presence of dense spectra of eigen frequencies of the system, the highest amplitudes can occur at higher frequencies of external effect.

Local and global bifurcations in magnetic resonance force microscopy

The focus of this paper is on the investigation of local and global bifurcations in a continuum mechanics-based resonator model proposed for measurement of electron spin via magnetic resonance force microscopy (MRFM). The resonator model, derived using the extended Hamilton’s principle incorporating the Bloch equations for magnetization, is investigated analytically and numerically. Analysis of both adiabatic and non-adiabatic equilibrium configurations enables formulation of the dynamical system bifurcation structure and identification of the parameter space required for stable MRFM operation. A multiple-scales analysis of the limiting adiabatic model enables estimation of the local bifurcation thresholds for bistable solutions and prediction of the frequency shift that enables spin detection. Orbital instabilities of the adiabatic model reveal a global bifurcation structure where lengthy chaotic transients occur below a homoclinic jump-to-contact threshold which is determined via a Melnikov–Holmes analysis. Both local and global bifurcations are verified numerically in the non-adiabatic model and reveal a dense power spectra for the magnetic moments. The computation of the parameter space governing the model orbital instabilities enables a consistent estimation of robust MRFM operation conditions.

Investigation of the Effect of Electron Beam Quality on a 0.68-THz Second Harmonic Gyrotron

The lack of high-power terahertz sources is a major impediment to the development of terahertz science and technology. The gyrotron has great potential to generate high-power terahertz radiation, and so attracts extensive attention. In order to alleviate the problems of limited power capacity and wall loading, the high-order modes are often chosen to be the operating modes. Due to the dense spectrum of the modes, it will cause intense mode competition, which is harmful for the stable operation of a gyrotron. Currently, a 0.68-THz second harmonic gyrotron is under development in the Terahertz Research Center of University of Electronic Science and Technology (UESTC). The experiment shows that the measured output power is 2.75 kW with the efficiency of 9.05%. In order to determine whether the operating mode is the desired mode TE−15,2, the calculation of the starting current should be more accurate. In this article, we generalize the existing linear theory for the starting current, considering the effects of beam thickness and velocity spread. The starting currents of the operating mode and its competing modes are calculated using our designed gyrotron. We find out that the velocity spread and the beam thickness have significant influence on the starting current. The calculations also show that the desired mode TE−15,2 can be triggered first at the operating point. Besides, the measured output power from the experiment is much lower than that of the simulation result. Therefore, the effects of the velocity spread and beam thickness on beam–wave interactions are also analyzed; our results show that the efficiency is sensitive to the beam quality.