(H.c. is shorthand for the Hermitian conjugate.) We can apply a displacement transformation, U = D ( − − ξ ξ 1 e − − i ω ω 1 t − − ξ ξ 2 e − − i ω ω 2 t ) , to mode c . For carefully chosen amplitudes, this transformation will cancel H drive while also displacing the ladder operator, c → → c + ξ ξ 1 e − − i ω ω 1 t + ξ ξ 2 e − − i ω ω 2 t . This leaves us with