English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We discuss the level-crossing field configurations for which the quantumtime-dependent two-state problem is solvable in terms of the confluent Heunfunctions. We show that these configurations belong to fifteen four-parametricfamilies of models that generalize all the known 3- and 2-parametric familiesfor which the problem is solvable in terms of the Gauss hypergeometric and theKummer confluent hypergeometric functions. Analyzing the general case ofvariable Rabi frequency and frequency detuning we mention that the most notablefeatures of the models provided by the derived classes are due to the extraconstant term in the detuning modulation function. Due to this term the classessuggest numerous symmetric or asymmetric chirped pulses and a variety of modelswith two crossings of the frequency resonance. The latter models are generatedby both real and complex transformations of the independent variable. Ingeneral, the resulting detuning functions are asymmetric, the asymmetry beingcontrolled by the parameters of the detuning modulation function. In somecases, however, the asymmetry may be additionally caused by the amplitudemodulation function. We present an example of the latter possibility andadditionally mention a constant amplitude model with periodically repeatedresonance-crossings. Finally, we discuss the excitation of a two-level atom bya pulse of Lorentzian shape with a detuning providing one or two crossings ofthe resonance. Using a series expansion of the solution of the confluent Heunequation in terms of the Kummer hypergeometric functions we derive particularclosed form solutions of the two-state problem for this field configuration.The particular sets of the involved parameters for which these solutions areobtained define curves in the 3D space of the involved parameters belonging tothe complete return spectrum of the considered two-state quantum system.

Time-dependent level crossing models solvable in terms of the confluent Heun functions