Lindblad Master Equation

The most general Markovian open quantum system dynamics. Lindblad operators L_k describe irreversible processes: spontaneous emission, cavity decay, pure dephasing. The density matrix ρ(t) evolves toward a unique steady state.

Cavity Decay

Spontaneous Emission

Pure Dephasing

Thermal Bath

Decay rate κ (or Γ): 0.30

Hamiltonian ω (oscillation): 1.00

Density Matrix Evolution ρ(t)

Bloch Vector Trajectory

ρ₀₀ (population |0⟩)

0.500

ρ₁₁ (population |1⟩)

0.500

|ρ₀₁| (coherence)

0.500

Tr(ρ²) (purity)

1.000

—

T₁ (energy)

—

T₂ (coherence)

0.00

Time t

—

Steady state ρ₀₀

Lindblad Master Equation

dρ/dt = -i[H,ρ] + Σₖ γₖ(LₖρLₖ† - ½{Lₖ†Lₖ,ρ})

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