Airy wavepackets are Perelomov coherent states

Vyas, Vivek M.

doi:10.1119/1.5051181

Cited by 5 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the realm of QED, which describes the radiationmatter interaction with unprecedented precision, and nonlinear optics, many phenomena can be modeled by a driven time-dependent HO. In fact, it can be shown that a HO, initially in its fundamental state which is acted by an external time-dependent force, is necessarily brought into a coherent state [6][7][8][9][10]. The counterpart of this result in quantum optics is the fact that any classical current coupled to the radiation field gives rise to a coherent state of the (quantized) electromagnetic field [11].…”

Section: Introductionmentioning

confidence: 99%

A Time-Dependent Harmonic Oscillator with Two Frequency Jumps: an Exact Algebraic Solution

et al. 2020

View full text Add to dashboard Cite

We consider a harmonic oscillator (HO) with a time-dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency ω 0 , then, at t = 0, its frequency suddenly increases to ω 1 and, after a finite time interval τ , it comes back to its original value ω 0. Contrary to what one could naively think, this problem is quite a non-trivial one. Using algebraic methods, we obtain its exact analytical solution and show that at any time t > 0 the HO is in a vacuum squeezed state. We compute explicitly the corresponding squeezing parameter (SP) relative to the initial state at an arbitrary instant and show that, surprisingly, it exhibits oscillations after the first frequency jump (from ω 0 to ω 1), remaining constant after the second jump (from ω 1 back to ω 0). We also compute the time evolution of the variance of a quadrature. Last, but not least, we calculate the vacuum (fundamental state) persistence probability amplitude of the HO, as well as its transition probability amplitude for any excited state.

show abstract

Section: Introductionmentioning

confidence: 99%

A Time-Dependent Harmonic Oscillator with Two Frequency Jumps: an Exact Algebraic Solution

et al. 2020

View full text Add to dashboard Cite

show abstract

“…However, almost half of a century ago it was shown [1] that there existed a specific solution of that equation expressed in the Airy function which on the one hand did not change its form (that is why it is called a coherent state), and on the other hand, it demonstrated an accelerating motion. This exotic solutions have recently aroused some interest [2] in possible applications of the description of non-spreading optical beams [3] and the generation and control of plasma in dielectrics [4].…”

Section: Introductionmentioning

confidence: 99%

Classical analog to the Airy wave packet

Matulis¹,

Acus²

2019

physics

View full text Add to dashboard Cite

The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packetswith an infinite and restricted distribution of velocities of particles -and also the motion of their fronts, we demonstrate in the simplest and most definite way why the packet can display a more sophisticated behavior (even acceleration) as compared with a free individual particle that moves at a fixed velocity. A comparison of this classical solution with the quantum one in the Wigner representation of quantum mechanics which provides the closest analogy is also presented.

show abstract

“…These novel wave packets contain boundless energy and a distinct self-focusing property. Researchers were encouraged by Berry and Balazs' discovery to expand theoretical investigations on similar waves [4][5][6]. Three decades after their theoretical prediction, an experimental observation of a shortened Airy wave packet was made in optics, where the paraxial equation of diffraction and the Schrödinger equation are identical [7][8][9][10][11][12].…”

mentioning

confidence: 99%

Density prediction of self-accelerating waves

2023

IJANSER

View full text Add to dashboard Cite

Self-accelerating waves have attracted a lot of attention not merely in terms of principles and practical demonstrations, but also in terms of a diverse variety of applications. Some of these applications are filamentation, biomedical imaging, particle manipulation, material processing and plasmons. In this paper, we study the prediction of maximum points of self-accelerating waves. We predict maximum points of the self-accelerating waves. We apply machine learning algorithm to predict the maximum point. We use two machine learning algorithm Decision Tree Classifying and Logistic Regression. The data is processed in python programming using two main Machine Learning Algorithm namely Decision Tree Algorithm and Logistic Regression which shows the best algorithm among these two in terms of accuracy level of maximum point of a self-accelerating wave.

show abstract

Airy wavepackets are Perelomov coherent states

Cited by 5 publications

References 15 publications

A Time-Dependent Harmonic Oscillator with Two Frequency Jumps: an Exact Algebraic Solution

A Time-Dependent Harmonic Oscillator with Two Frequency Jumps: an Exact Algebraic Solution

Classical analog to the Airy wave packet

Density prediction of self-accelerating waves

Contact Info

Product

Resources

About