scholarly journals Spontaneous transition rates near the focus of a parabolic mirror with identification of the vectorial modes involved

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
R. Gutiérrez-Jáuregui ◽  
R. Jáuregui
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Control ◽  
Natural Mode ◽  
Electrodynamic System ◽  
Emission Rates ◽  
Parabolic Mirror ◽  
Spontaneous Transition ◽  
Atomic Systems ◽  
Clear Identification ◽  
Trapping Regions

Abstract Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.

scholarly journals The Nyquist Issue in Linear Inverse Modeling

2019 ◽  
Vol 147 (4) ◽  
pp. 1341-1349 ◽  
Author(s):  
Cécile Penland
Keyword(s):  
Time Series ◽  
Markov Process ◽  
Covariance Matrix ◽  
Inverse Modeling ◽  
Degrees Of Freedom ◽  
Multivariate Time Series ◽  
Statistical Technique ◽  
Natural Mode ◽  
Dimensional System ◽  
Best Fit

Abstract Linear inverse modeling (LIM) is a statistical technique based on covariance statistics that estimates the best-fit linear Markov process to a multivariate time series. An integral, often-ignored part of the technique is a test of whether or not the linear assumptions are valid. One test for linearity is the so-called tau test. While this test can be trusted when it passes, it sometimes fails when it ought to pass. In this article, we discuss one of the reasons for spurious failure, the “Nyquist issue,” which occurs when the lagged covariance matrix used in the analysis is numerically performed at a lag greater than or nearly equal to half the period of a natural mode of variability represented in the time series. As an illustration relevant to a system with many degrees of freedom, but simple enough to solve analytically, we consider a four-dimensional system consisting of two modal pairs. Within this framework, we suggest one solution that can be applied if the time series are long enough. It is hoped that awareness of this issue can prevent misinterpretation of LIM results.

KINETICS OF THE SPONTANEOUS DECAY IN COLD ATOMIC SYSTEMS

2020 ◽  
Author(s):  
Oleg Prepelita
Keyword(s):  
Emission Spectrum ◽  
Initial Temperature ◽  
Dipole Interaction ◽  
Time Profile ◽  
Spontaneous Decay ◽  
Spontaneous Transition ◽  
Atomic Systems ◽  
Leading Role ◽  
Kinetics Of ◽  
Strong Dipole

We discuss the spontaneous decay in a system of cold identical two-level atoms when, due to the strong dipole-dipole interaction, the collision-induced spontaneous decay plays the leading role in the process. We show that the time profile of the spontaneous transition is essentially non-exponential. Also, we argue that at a low initial temperature of the atomic system the spontaneous decay is accompanied by a strong heating caused by the inelastic atom-atom collisions. We show that the spontaneous emission spectrum is asymmetric. In addition, the width of the emission spectrum is a function of time. While atoms decay the emission spectrum becomes broader. The spectrum’s asymmetry and the atomic system’s heating have the same physical origin coming from the peculiarities of the atoms distribution function.

Some General Considerations on the Natural Mode Technique

1969 ◽  
Vol 73 (700) ◽  
pp. 361-368 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Degrees Of Freedom ◽  
General Procedure ◽  
Practical Significance ◽  
Natural Mode ◽  
Curved Beams ◽  
Normal Forces ◽  
Natural Modes ◽  
Straight Beam ◽  
Mode Technique ◽  
Made In

We continue our fundamental discourse on the natural modes in an element and extend our considerations to large displacements. First, we present a general procedure for establishing the so-called geometrical stiffness k G , when the natural modes of the complete element are given. The theory is a substantial generalisation and clarification of the method initially given in refs. 2 and 3 and shows that in establishing the modification to the transformation matrix a N it is necessary to ignore the contribution of the natural modes, which cause rotation at the nodal points but no displacement there. The point is subtle and was not made in ref. 2, although the applications given there are correct. As an example, the geometrical stiffness of a straight beam in space with all degrees of freedom is established. There follows the extension of the geometrical stiffness concept to a sub-element. This is of great practical significance for two reasons. First, it allows to derive the geometrical stiffness of elements of complex shape and behaviour, e.g. curved beams in space subjected to normal forces, bending moments and torque.

A Theory of Substructure Modal Synthesis

1982 ◽  
Vol 49 (4) ◽  
pp. 903-909 ◽  
Author(s):  
K. Kubomura
Keyword(s):  
Degrees Of Freedom ◽  
Order Approximation ◽  
Second Order ◽  
Natural Mode ◽  
Frequency Range ◽  
Hybrid Mode ◽  
Second Order Approximation ◽  
First Order ◽  
Modal Synthesis ◽  
Modal Coordinates

A theory is presented for representing the displacements of a substructure finite-element mathematical model with a reduced number of degrees of freedom. A first or second-order approximation is used for the substructure’s modal coordinates associated with significantly larger or smaller eigenvalues than the system eigenvalues of excitation. The derived representations of the substructure displacements are capable of employing any type of substructure natural mode; free-free, cantilever or hybrid mode, and of retaining the dynamic behavior of any frequency range. It is shown that the present representations compute the system eigenvalues of interest with satisfactory accuracy, and it appears that the second-order approximation methods compute the system eigenvalues with greater accuracy than the first-order methods.

scholarly journals The Current Status of EMG Signals on Kinematics Needed for Precise Online Myoelectric Control and the Development Direction

2021 ◽  
Vol 271 ◽  
pp. 01029
Author(s):  
Tong Kang
Keyword(s):  
Pattern Recognition ◽  
Degrees Of Freedom ◽  
Quantum Control ◽  
Quantum Information Processing ◽  
Current Status ◽  
Prosthetic Control ◽  
Pattern Recognition Problem ◽  
Emg Signal ◽  
Traditional Pattern ◽  
Electric Signals

Widely accepted idea is the prosthetic control problem could be regarded as the pattern recognition problem. The prosthetic control means there are several differences such as distinguishable electric signals between different activation of muscle. However, this conventional method could not provide proper control of the artificial limbs. Kinematics behavior is continuous and needs the coordination of multiple physiological degrees of freedom (DOF) among various joints. Currently, a huge challenge is achieving precise, coherent and elegant coordination protheses which needs many DOFs to rehabilitation of patients with limb deficiency. This article analyzed the principles of control of bionic limbs from the aspect of EMG and traditional pattern recognition. According to the research results, the following conclusions can be given. Since the quantum amplitudes are complex numbers generally, different parameter should be included and analyzed together during the quantum information processing. Besides, the quantum control scheme could be combined with the classic one. What is more, other sensor modes should be applied for robust control instead of the EMG signal only.

Atom Optomechanics

2020 ◽  
pp. 329-368
Author(s):  
Philipp Treutlein
Keyword(s):  
Ultracold Atoms ◽  
Quantum Control ◽  
Cold Atoms ◽  
Internal State ◽  
Trapped Atoms ◽  
Sympathetic Cooling ◽  
Atomic Systems ◽  
Mechanical Oscillators ◽  
Optomechanical Coupling ◽  
Coupling Mechanisms

This chapter gives an introduction to optomechanics with ultracold atoms. The opening half deals with optomechanical atom–light interactions. Section 9.2 introduces atom trapping. Section 9.3 discusses the properties of trapped atoms as mechanical oscillators. Section 9.4 describes optomechanical interactions, treating the atoms as polarizable particles, a model used in section 9.5 to derive optomechanical coupling of atoms and a cavity field and briefly review cavity optomechanics experiments with atoms in the quantum regime. The second half deals with hybrid mechanical-atomic systems. We start with an overview of different coupling mechanisms, then focus on light-mediated interactions and derive the coupling of a membrane to an ensemble of laser-cooled atoms. Section 9.8 reviews experiments on sympathetic cooling of a membrane with cold atoms, with perspectives for mechanical quantum control discussed in section 9.9. Section 9.10 introduces the possibilities that arise if the mechanical oscillator is coupled to the atomic internal state.

Lateral flexural vibration reduction in a periodic piping system enhanced with two-degrees-of-freedom resonators

2021 ◽  
pp. 146442072110276
Author(s):  
Mohd Iqbal ◽  
Anil Kumar ◽  
Oreste Salvatore Bursi
Keyword(s):  
Band Gap ◽  
Degrees Of Freedom ◽  
Extreme Values ◽  
Flexural Vibration ◽  
Band Gaps ◽  
Natural Mode ◽  
Piping System ◽  
Practical Case ◽  
Two Degrees Of Freedom ◽  
Special Cases

Pipe systems are commonly used in the process and power industries to transport fluid from one terminal to others. Propagation behaviour of lateral flexural waves in a pipe coupled with periodic rack structure is investigated. The pipe-rack system considered in this study is a practical case and is realized as a pipe on periodic elastic supports, while a pipe on simple and without supports represents special cases when the rack stiffness leads to extreme values. The propagation constant relations in terms of frequency are derived using Bloch–Floquet theorem which are successively verified with finite element models. The results show that a pipe with rack creates a narrow locally resonant band gap in low-frequency range which is caused by the first natural mode of the rack. Conversely, a pipe on simple supports entails only Bragg-type band gaps, while a pipe without supports carries no band gap. For tuning the band gap properties, a two-degrees-of-freedom lateral localized resonator is attached to the centre of each unit cell of the pipe. It is found that certain frequency ranges in the targeted pass bands are effectively controlled by the resonator. Furthermore, the effect of various resonator parameters, i.e. mass ratio, stiffness and damping, on band gaps is examined. It is observed that the band gaps are vanished when damping is introduced in the system. The results show a promising way to flexural vibration control of a periodic piping system with various boundary conditions.

scholarly journals Cyclo-Symmetric Modal Synthesis of Rotating Bladed Disc System

1991 ◽  
Author(s):  
Jin Zhang ◽  
W. L. Wang ◽  
X. J. Chen
Keyword(s):  
Large Deformation ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Computational Method ◽  
Mode Analysis ◽  
Natural Mode ◽  
Computational Accuracy ◽  
Deformation Effect ◽  
Simultaneous Iteration ◽  
Computation Work

The natural mode analysis of bladed disc system at an arbitrary constant rotational speed is investigated in this paper and the large deformation effect caused by the pretorsion of the blades is also considered. The computational method of group theory is employed in substructure technique and equilibrium position and stress distribution of the bladed disc system in centrifugal field are obtained through simultaneous iteration, further more, the initial stress stiffness matrix, the large deformation stiffness matrix and the corresponding rotating natural frequencies and modal shapes are determined. Because the large deformation effect of the blades is considered and all the interface degrees of freedom between the substructures can be eliminated in the present method, the computation work can be cut down remarkably under the precondition that the computational accuracy is ensured. It shows practically that the substructure simultaneous iteration method presented in this paper has a good convergency and greatly reduces the computation work.

scholarly journals Non-Gaussian noise spectroscopy with a superconducting qubit sensor

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Youngkyu Sung ◽  
Félix Beaudoin ◽  
Leigh M. Norris ◽  
Fei Yan ◽  
David K. Kim ◽  
...  
Keyword(s):  
Gaussian Noise ◽  
Degrees Of Freedom ◽  
Quantum Control ◽  
Gaussian Approximation ◽  
Spectral Estimation ◽  
Superconducting Qubit ◽  
Major Step ◽  
Noise Sources ◽  
Noise Spectroscopy ◽  
Non Gaussian

Abstract Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.

scholarly journals Quantum control of atomic systems by homodyne detection and feedback

1998 ◽  
Vol 57 (6) ◽  
pp. 4877-4888 ◽  
Author(s):  
Holger F. Hofmann ◽  
Günter Mahler ◽  
Ortwin Hess
Keyword(s):  
Quantum Control ◽  
Homodyne Detection ◽  
Atomic Systems
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