Floquet analysis of a quantum system with modulated periodic driving

Viktor Novičenko, Egidijus Anisimovas, and Gediminas Juzeliūnas
Phys. Rev. A 95, 023615 – Published 15 February 2017

Abstract

We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown that the dynamics of the system can be described in terms of a slowly varying effective Floquet Hamiltonian that captures the long-term evolution, as well as rapidly oscillating micromotion operators. We obtain a systematic high-frequency expansion of all these operators. Generalizing the previous studies, the expanded effective Hamiltonian is now time dependent and contains extra terms appearing due to changes in the periodic driving. The same applies to the micromotion operators which exhibit a slow temporal dependence in addition to the rapid oscillations. As an illustration, we consider a quantum-mechanical spin in an oscillating magnetic field with a slowly changing direction. The effective evolution of the spin is then associated with non-Abelian geometric phases reflecting the geometry of the extended Floquet space. The developed formalism is general and also applies to other periodically driven systems, such as shaken optical lattices with a time-dependent shaking strength, a situation relevant to the cold-atom experiments.

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  • Received 2 September 2016
  • Revised 30 December 2016

DOI:https://doi.org/10.1103/PhysRevA.95.023615

©2017 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Viktor Novičenko, Egidijus Anisimovas, and Gediminas Juzeliūnas

  • Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio Ave. 3, LT-10222 Vilnius, Lithuania

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Issue

Vol. 95, Iss. 2 — February 2017

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