\documentclass[a4paper]{report}
\usepackage{mleftright}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{braket}
\begin{document}
\begin{align}
\langle \hat{\widetilde{S_{\hat{a}}}}^{\, \, \, \mleft( 1 \mright) } \hat{\widetilde{S_{\hat{b}}}}^{\, \, \, \mleft( 2 \mright) } \rangle_{\ket{ss}} & = \langle \mleft( \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \hat{\mathbb{I}}^{ \mleft( 2 \mright) } \mright) \mleft( \hat{\mathbb{I}}^{ \mleft( 1 \mright) } \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \mright) \rangle_{\ket{ss}} \nonumber \\
& = \langle \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \rangle_{\ket{ss}} \, .
\end{align}
\end{document}
produces the following output:
In fact, it creates a bunch of errors which seem to be due to using nested expressions of \widetilde, \hat, and such via the amsmath package. Curiously, those errors do not show up in my overall document.
Anyway, the same output is produces and as you can see, sigmas somehow show up at the S symbol although they are only used later in the line ...
Also, the equation reference parenthesis are right of the page limit in my overall document, which may not be so obvious here.
I tried the same thing without \mleft( and such, but I like it better this way.
EDIT: After properly reading the question that egreg linked to, this is what comes closest to the desired result for me:
\documentclass[a4paper]{report}
\usepackage{mleftright}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{braket}
\newsavebox{\accentbox}
\newcommand{\compositeaccents}[2]{%
\sbox\accentbox{$#2$}#1{\usebox\accentbox}}
\begin{document}
\begin{align}
\langle \compositeaccents{\hat}{\widetilde{S_{\hat{a}}^{\mleft( 1 \mright) }}} \compositeaccents{\hat}{\widetilde{S_{\hat{b}}^{\mleft( 2 \mright) }}} \rangle_{\ket{ss}} & = \langle \mleft( \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \hat{\mathbb{I}}^{ \mleft( 2 \mright) } \mright) \mleft( \hat{\mathbb{I}}^{ \mleft( 1 \mright) } \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \mright) \rangle_{\ket{ss}} \nonumber \\
& = \langle \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \rangle_{\ket{ss}} \, .
\end{align}
\end{document}
The sigmas have disappeared but through use of the saveboxes, the S operators look somewhat different than in other instances in the document, but it's good enough for me.
