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\centerline{\textbf{Spin-$\frac{1}{2}$ Interferometer}}
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\begin{enumerate}
\item Make an interferometer as shown:

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\centerline{\includegraphics[width=4 in]{spanalyzespinhalfinthandfig1.png}}

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Use \underline{Random} as the initial state.  Measure the relative probabilities of spin up and spin down after the final SG device.  Do this for the three cases where (1) the spin up beam from the middle SG device is used, (2) the spin down beam from the middle SG device is used, and (3) both beams from the middle SG device are used (as the figure shows).  Put your experimental results in the table of the worksheet.  Repeat for the case where the spin down state is used from the first SG device.

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\centerline{Spin-$\frac{1}{2}$ Interferometer} 

\begin{tabular}{|c|c|c|c|c|c|} \hline

\multicolumn{2}{|c|}{Beams Used} & \multicolumn{2}{c|}{Experiment} &          \multicolumn{2}{c|}{Theory} \\

SG1 & SG2 & P$\uparrow$ & P$\downarrow$ & P$\uparrow$ & P$\downarrow$  \\ \hline

& $\vert + \rangle_{x}$ & & & &  \\ \cline{2-6} 

$\vert + \rangle$ & $\vert - \rangle_{x}$ & & & & \\ \cline{2-6}

& $\vert + \rangle_{x}$ , $\vert - \rangle_{x}$ & & & & \\ \hline 

& $\vert + \rangle_{x}$ & & & & \\ \cline{2-6}

$\vert - \rangle$ & $\vert - \rangle_{x}$ & & & & \\ \cline{2-6}

& $\vert + \rangle_{x} $ , $\vert - \rangle_{x}$ & & & & \\ \hline


\end{tabular}

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\item Using the interferometer shown above, select \underline{Watch} under the \underline{Control} menu.  This feature causes a light to flash at the port where an atom exits.  The program now only allows the \underline{Go} mode.  Run the experiment and notice how your results compare to the results obtained above.

\end{enumerate}

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