2014/04/30 by А. М. Ishkhanyan, A. M. Ishkhanyan, T. A. Shahverdyan +2 · 1 citation
Mathematics · Physics and Astronomy · #Amplitude #Constant (computer programming) #Field (mathematics) #Function (biology) #Laser-Matter Interactions and Applications #Limiting #Mathematical analysis #Mathematics #Modulation (music) #Parametric statistics #Physics #Pulse (music) #Pulse-amplitude modulation #Pulse-width modulation #Pure mathematics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Transformation (genetics) #quant-ph
paper · pdf · doi:10.1140/epjd/e2014-50386-9
published as Eur. Phys. J. D 69, 10 (2015)
openalex publication_date 2015/01/01 · arxiv created 2015/01/08 · arxiv updated 2015/01/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We derive 35 five-parametric classes of the quantum time-dependent two-state models solvable in terms of the general Heun functions. Each of the classes is defined by a pair of generating functions the first of which is referred to as the amplitude- and the second one as the detuning-modulation function. The classes suggest numerous families of specific field configurations with different physical properties generated by appropriate choices of the transformation of the independent variable, real or complex. There are many families of models with constant detuning or constant amplitude, numerous classes of chirped pulses of controllable amplitude and/or detuning, families of models with double or multiple (periodic) crossings, periodic amplitude modulation field configurations, etc. We present several families of constant-detuning field configurations the members of which are symmetric or asymmetric two-peak finite-area pulses with controllable distance between the peaks and controllable amplitude of each of the peaks. We show that the edge shapes, the distance between the peaks as well as the amplitude of the peaks are controlled almost independently, by different parameters. We identify the parameters controlling each of the mentioned features and discuss other basic properties of pulse shapes. We show that the pulse edges may become step-wise functions and determine the positions of the limiting vertical-wall edges. We show that the pulse width is controlled by only two of the involved parameters. For some values of these parameters the pulse width diverges and for some other values the pulses become infinitely narrow. We show that the effect of the two mentioned parameters is almost similar, that is, both parameters are able to independently produce pulses of almost the same shape and width.