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Location of crossings in the Floquet spectrum of a driven two-level system

C. E. Creffield
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Abstract

Calculation of the Floquet quasi-energies of a system driven by a time-periodic field is an efficient way to understand its dynamics. In particular, the phenomenon of dynamical localization can be related to the presence of close approaches between quasi-energies (either crossings or avoided crossings). We consider here a driven two-level system, and study how the locations of crossings in the quasi-energy spectrum alter as the field parameters are changed. A perturbational scheme provides a direct connection between the form of the driving field and the quasi-energies which is exact in the limit of high frequencies. We firstly obtain relations for the quasi-energies for some common types of applied field in the high-frequency limit. We then show how the locations of the crossings drift as the frequency is reduced, and find a simple empirical formula which describes this drift extremely well in general, and appears to be exact for the specific case of square-wave driving.

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C. E. Creffield. 2003-02-13. Location of crossings in the Floquet spectrum of a driven two-level system. https://doi.org/10.1103/physrevb.67.165301

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