= Optical quadrature
{title2=$X_\vartheta=(ae^{-i\vartheta}+a^\dagger e^{i\vartheta})/2$}
A phase-selected Hermitian field observable. With <annihilation operator> $a$ and $[a,a^\dagger]=1$, define $X_1=(a+a^\dagger)/2$ and $X_2=(a-a^\dagger)/(2i)$. Then $[X_1,X_2]=i/2$ and the <Fock vacuum> has variance $1/4$ in either quadrature. This dimensionless convention gives $X_\vartheta=X_1\cos\vartheta+X_2\sin\vartheta$. <Balanced homodyne detection> selects $\vartheta$ through the reference <wave phase>.
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