Floquet Theory — Quasi-Energy Bands

Floquet theorem: for a time-periodic Hamiltonian H(t+T)=H(t), solutions are ψ(t)=e^{−iεt/ℏ}φ(t) where φ(t) is T-periodic and ε is the quasi-energy. This lab shows quasi-energy bands for a driven two-level system and a tight-binding chain under periodic driving.

System

ω/Δ ratio:
Resonance:
Band gap:
Floquet zones: ±ω/2
H(t) = Δ·σz/2
+ A·cos(ωt)·σx/2
ε ∈ [−ω/2, ω/2]