Lindblad Master Equation
dρ/dt = −i[H,ρ] + Σ_k(L_k ρ L_k† − ½{L_k†L_k, ρ}) — driven-dissipative steady state
Bloch Vector Dynamics
Density Matrix ρ (real part)
Parameters
Drive Ω (Rabi):
1.00
Decay γ (spont.):
0.50
Dephasing γ_φ:
0.20
Detuning Δ:
0.00
System:
—
Qubit (2-level)
3-Level (Λ)
Harmonic Osc (N=5)
⟨σz⟩_ss:
—
Purity Tr(ρ²):
—
Entropy S:
—
T1 = 1/γ:
—
T2 = 1/(γ/2+γφ):
—
Lindblad jump operators: L₁=√γ σ₋ (decay), L₂=√γ_φ σz (dephasing).
Steady state: driven 2-level atom. At resonance: ⟨σz⟩_ss = −γ²/(γ²+2Ω²). Bloch vector traces helix to SS.
Eigenvalue Spectrum of Liouvillian