2

I learned that fancyhdr package seems to do the job, so I tried

\documentclass[aps,pra,twocolumn,superscriptaddress,notitlepage]{revtex4-1}
......
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\fancyfoot[LE,RO]{\thepage}
......

But it turns out all the page numbers appear in the right footer.

2

The mechanism which distinguishes between even/odd pages can work only if the document is set in twoside mode, which is supported by the class revtex4-1. However, while the result is the one you want, you'll get a warning that it's not working, even if it is. The reason is that fancyhdr works best for the standard classes, and revtex4-1 has a slightly different way of implementing the twoside option. As a workaround to suppress the warning you can manually set \@twosidetrue.

\documentclass[aps,pra,twocolumn,superscriptaddress,notitlepage,twoside]{revtex4-1}

\makeatletter
\@twosidetrue % workaround to suppress misleading warning
\makeatother
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\fancyfoot[LE,RO]{\thepage}

\usepackage{lipsum}

\begin{document}
\lipsum[1-40]
\end{document}

enter image description here

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