Bloch Oscillations & Wannier-Stark Ladders
AC-driven tight-binding lattice — Floquet theory
Parameters
Lattice hopping J:
1.0
DC field F (tilt):
0.5
AC field amplitude A:
0.0
AC frequency ω:
1.0
Initial momentum k₀:
0.00
H = -J Σ(c†ₙ₊₁cₙ + h.c.)
+ F·n + A·cos(ωt)·n
ε(k) = -2J cos(ka)
T_B = 2π/(Fa)
Wannier-Stark ladder:
Eₘ = E₀ + m·Fa
Floquet: J_eff = J·J₀(A/ω)
Reset
Pause
In a DC field, an electron oscillates in momentum space (Bloch period T_B). AC driving renormalizes hopping via Bessel function J₀(A/ω) — dynamic localization when J₀=0 (A/ω ≈ 2.405).