A perspective on the relative merits/demerits of time-propagators based on Floquet theorem

The present report examines the nuances of analytic methods employed in the derivation of evolution operators in periodically driven quantum systems based on Floquet theorem. Specifically, time-propagators of the form, U(t) = P(t)e-iHt defined in the Hilbert space (of finite dimension), are derived through generalized multimodal expansion of the operators involved. While Floquet methods defined in the extended Hilbert space (of infinite dimension) have remained the method of choice for the description of time-evolution at non-stroboscopic time-intervals, the expansion schemes discussed do present an attractive option for similar studies in the standard Hilbert space. Nevertheless, the convergence criteria and suitability of such methods deserve formal validation in problems of experimental relevance. Employing examples comprising periodic Hamiltonians from magnetic resonance spectroscopy, the exactness of Floquet based time-propagators in the Schrodinger and interaction representation is discussed. Through rigorous comparisons between simulations emerging from analytic and exact numerical methods, the relative merits and demerits of different formulations of Floquet based methods are also discussed. The present report examines the nuances of analytic methods employed in the derivation of evolution operators in periodically driven quantum systems based on Floquet theorem.

Automated summary

This report examines the nuances of analytical methods used in the derivation of evolution operators in periodically driven quantum systems based on the Floquet theorem. By employing generalized multimodal expansion, time-propagators are derived in the finite-dimensional Hilbert space. While Floquet methods in the infinite-dimensional extended Hilbert space remain the method of choice for non-stroboscopic time-evolution, the discussed expansion schemes present an attractive option for similar studies in the standard Hilbert space. Nevertheless, the convergence criteria and suitability of such methods require formal validation in experimentally relevant problems.