## Floquet analysis of a quantum system with modulated periodic driving

**Speaker:**Viktor Novicenko , Institute of Theoretical Physics and Astronomy Vilnius University

**When:**October 25, 2019 (Fri), 12:00PM to 01:00PM (add to my calendar)

**Location:**SCI 352

*This event is part of the Condensed Matter Theory Seminar Series. *

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 will be 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. As an illustration of the importance of slowly varying parameters, 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.

[1] Phys. Rev. A 95, 023615 (2017) [2] Phys. Rev. A 100, 012127 (2019) [3] arXiv:1908.11275