The equations of motion for the expectation values of the operators can be derived from the master equation by the formulas ⟨ ⟨ O ⟩ ⟩ = tr ⁡ ⁡ ( O ρ ρ ) and ⟨ ⟨ O ˙ ˙ ⟩ ⟩ = tr ⁡ ⁡ ( O ρ ρ ˙ ˙ ) . The equations of motion for ⟨ ⟨ a ⟩ ⟩ , ⟨ ⟨ σ σ ⟩ ⟩ , and ⟨ ⟨ σ σ z ⟩ ⟩ , the cavity field, atomic coherence, and atomic inversion respectively, are