where a is the lowering operator for the cavity field, and σ σ = 1 2 ( σ σ x − − i σ σ y ) is the atomic lowering operator written as a combination of Pauli matrices. The time dependence can be removed by transforming the wavefunction according to | ψ ψ ⟩ ⟩ → → e − − i ω ω l t ( a † † a + σ σ † † σ σ ) ⁡ ⁡ | ψ ψ ⟩ ⟩ , leading to a transformed Hamiltonian