Floquet Driven Quantum System

Periodically driven two-level system — Rabi oscillations and Floquet quasienergies

Parameters

Hamiltonian:
H(t) = (Δ/2)σz + Ω₀cos(ωt)σx

In the rotating frame (RWA):
H_RWA = (Δ/2)σz + (Ω₀/2)σx

Rabi frequency: Ω_R = √(Δ² + Ω₀²)/2

Floquet theorem: For periodic H(t+T)=H(t), solutions are ψ(t)=e^{−iεt}φ(t) where φ is T-periodic and ε are quasienergies (defined mod ω).

Top-left: Bloch sphere. Bottom-left: population P↑(t). Right: quasienergy vs parameters.